{"id":1731,"date":"2015-04-22T18:58:02","date_gmt":"2015-04-22T18:58:02","guid":{"rendered":"https:\/\/courses.candelalearning.com\/oschemtemp\/?post_type=chapter&#038;p=1731"},"modified":"2016-10-27T15:36:45","modified_gmt":"2016-10-27T15:36:45","slug":"enthalpy","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/chapter\/enthalpy\/","title":{"raw":"Enthalpy","rendered":"Enthalpy"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>State the first law of thermodynamics<\/li>\r\n \t<li>Define enthalpy and explain its classification as a state function<\/li>\r\n \t<li>Write and balance thermochemical equations<\/li>\r\n \t<li>Calculate enthalpy changes for various chemical reactions<\/li>\r\n \t<li>Explain Hess\u2019s law and use it to compute reaction enthalpies<\/li>\r\n<\/ul>\r\n<\/div>\r\nThermochemistry is a branch of <strong>chemical thermodynamics<\/strong>, the science that deals with the relationships between heat, work, and other forms of energy in the context of chemical and physical processes. As we concentrate on thermochemistry in this chapter, we need to consider some widely used concepts of thermodynamics.\r\n\r\nSubstances act as reservoirs of energy, meaning that energy can be added to them or removed from them. Energy is stored in a substance when the kinetic energy of its atoms or molecules is raised. The greater kinetic energy may be in the form of increased translations (travel or straight-line motions), vibrations, or rotations of the atoms or molecules. When thermal energy is lost, the intensities of these motions decrease and the kinetic energy falls. The total of all possible kinds of energy present in a substance is called the<strong> internal energy (<em>U<\/em>)<\/strong>, sometimes symbolized as <em>E<\/em>.\r\n\r\nAs a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system. Energy is transferred into a system when it absorbs heat (<em>q<\/em>) from the surroundings or when the surroundings do work (<em>w<\/em>) on the system. For example, energy is transferred into room-temperature metal wire if it is immersed in hot water (the wire absorbs heat from the water), or if you rapidly bend the wire back and forth (the wire becomes warmer because of the work done on it). Both processes increase the internal energy of the wire, which is reflected in an increase in the wire\u2019s temperature. Conversely, energy is transferred out of a system when heat is lost from the system, or when the system does work on the surroundings.\r\n\r\nThe relationship between internal energy, heat, and work can be represented by the equation:\r\n<p style=\"text-align: center;\">[latex]\\Delta U=q+w[\/latex]<\/p>\r\nas shown in Figure 1. This is one version of the <strong>first law of thermodynamics<\/strong>, and it shows that the internal energy of a system changes through heat flow into or out of the system (positive <em>q<\/em> is heat flow in; negative <em>q<\/em> is heat flow out) or work done on or by the system. The work, <em>w<\/em>, is positive if it is done on the system and negative if it is done by the system.\r\n\r\n[caption id=\"attachment_5369\" align=\"aligncenter\" width=\"650\"]<img class=\"wp-image-5369 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09032607\/CNX_Chem_05_03_Systemqw1.jpg\" alt=\"A rectangular diagram is shown. A green oval lies in the center of a tan field inside of a gray box. The tan field is labeled \u201cSurroundings\u201d and the equation \u201c\u0394 U = q + w\u201d is written at the bottom of the diagram. Two arrows face into the green oval and are labeled \u201cq subscript in\u201d and \u201cw subscript on\u201d while two more arrows face away from the oval and are labeled \u201cq subscript out\u201d and \u201cw subscript by.\u201d The center of the oval contains the terms \u201c\u0394 U &lt; 0\u201d, \u201cSystem,\u201d and \u201c\u0394 U &gt; 0.\u201d\" width=\"650\" height=\"437\" \/> Figure 1. The internal energy, U, of a system can be changed by heat flow and work. If heat flows into the system, qin, or work is done on the system, won, its internal energy increases, \u0394U &lt; 0. If heat flows out of the system, qout, or work is done by the system, wby, its internal energy decreases, \u0394U &gt; 0.[\/caption]\r\n\r\nA type of work called<strong> expansion work (or pressure-volume work)<\/strong> occurs when a system pushes back the surroundings against a restraining pressure, or when the surroundings compress the system. An example of this occurs during the operation of an internal combustion engine. The reaction of gasoline and oxygen is exothermic. Some of this energy is given off as heat, and some does work pushing the piston in the cylinder. The substances involved in the reaction are the system, and the engine and the rest of the universe are the surroundings. The system loses energy by both heating and doing work on the surroundings, and its internal energy decreases. (The engine is able to keep the car moving because this process is repeated many times per second while the engine is running.) We will consider how to determine the amount of work involved in a chemical or physical change in the chapter on thermodynamics.\r\n<div class=\"textbox\">This view of <a href=\"http:\/\/auto.howstuffworks.com\/engine1.htm\" target=\"_blank\">an internal combustion engine on How Stuff Works<\/a> illustrates the conversion of energy produced by the exothermic combustion reaction of a fuel such as gasoline into energy of motion.<\/div>\r\nAs discussed, the relationship between internal energy, heat, and work can be represented as \u0394<em>U<\/em> = <em>q<\/em> + <em>w<\/em>. Internal energy is a type of quantity known as a <strong>state function<\/strong> (or state variable), whereas heat and work are not state functions. The value of a state function depends only on the state that a system is in, and not on how that state is reached. If a quantity is not a state function, then its value <em>does<\/em> depend on how the state is reached. An example of a state function is altitude or elevation. If you stand on the summit of Mt. Kilimanjaro, you are at an altitude of 5895 m, and it does not matter whether you hiked there or parachuted there. The distance you traveled to the top of Kilimanjaro, however, is not a state function. You could climb to the summit by a direct route or by a more roundabout, circuitous path (Figure 2). The distances traveled would differ (distance is not a state function) but the elevation reached would be the same (altitude is a state function).\r\n\r\n[caption id=\"attachment_5371\" align=\"aligncenter\" width=\"975\"]<img class=\"wp-image-5371 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09032807\/CNX_Chem_05_03_Summit1.jpg\" alt=\"An aerial photo depicts a view of Mount Kilimanjaro. A straight, green arrow labeled X is drawn from the term \u201cbase,\u201d written at the bottom of the mountain, to the term \u201cSummit,\u201d written at the top of the mountain. Another arrow labeled Y is draw from the base to the summit alongside the green arrow, but this arrow is pink and has three large S-shaped curves along its length.\" width=\"975\" height=\"525\" \/> Figure 2. Paths X and Y represent two different routes to the summit of Mt. Kilimanjaro. Both have the same change in elevation (altitude or elevation on a mountain is a state function; it does not depend on path), but they have very different distances traveled (distance walked is not a state function; it depends on the path). (credit: modification of work by Paul Shaffner)[\/caption]\r\n\r\nChemists ordinarily use a property known as <strong>enthalpy (<em>H<\/em>)<\/strong> to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum of a system\u2019s internal energy (<em>U<\/em>) and the mathematical product of its pressure (<em>P<\/em>) and volume (<em>V<\/em>):\r\n<p style=\"text-align: center;\">[latex]H=U+PV[\/latex]<\/p>\r\nSince it is derived from three state functions (<em>U<\/em>, <em>P<\/em>, and <em>V<\/em>), enthalpy is also a state function. Enthalpy values for specific substances cannot be measured directly; only enthalpy <em>changes<\/em> for chemical or physical processes can be determined. For processes that take place at constant pressure (a common condition for many chemical and physical changes), the <strong>enthalpy change (\u0394<em>H<\/em>)<\/strong> is:\r\n<p style=\"text-align: center;\">[latex]\\Delta H=\\Delta U+P\\Delta V[\/latex]<\/p>\r\nThe mathematical product <em>P<\/em>\u0394<em>V<\/em> represents work (<em>w<\/em>), namely, expansion or pressure-volume work as noted. By their definitions, the arithmetic signs of \u0394<em>V<\/em> and <em>w<\/em> will always be opposite:\r\n<p style=\"text-align: center;\">[latex]P\\Delta V=-w[\/latex]<\/p>\r\nSubstituting this equation and the definition of internal energy into the enthalpy-change equation yields:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rll}\\Delta H&amp;=&amp;\\Delta U+P\\Delta V\\\\&amp;=&amp;{q}_{\\text{p}}+w-w\\\\&amp;=&amp;{q}_{\\text{p}}\\end{array}[\/latex]<\/p>\r\nwhere <em>q<sub>p<\/sub><\/em> is the heat of reaction under conditions of constant pressure.\r\n\r\nAnd so, if a chemical or physical process is carried out at constant pressure with the only work done caused by expansion or contraction, then the heat flow (<em>q<sub>p<\/sub><\/em>) and enthalpy change (\u0394<em>H<\/em>) for the process are equal.\r\n\r\nThe heat given off when you operate a Bunsen burner is equal to the enthalpy change of the methane combustion reaction that takes place, since it occurs at the essentially constant pressure of the atmosphere. On the other hand, the heat produced by a reaction measured in a bomb calorimeter is not equal to \u0394<em>H<\/em>, because the closed, constant-volume metal container prevents expansion work from occurring. Chemists usually perform experiments under normal atmospheric conditions, at constant external pressure with <em>q<\/em> = \u0394<em>H<\/em>, which makes enthalpy the most convenient choice for determining heat.\r\n\r\nThe following conventions apply when we use \u0394<em>H<\/em>:\r\n<ol id=\"fs-idm49861360\" data-number-style=\"arabic\">\r\n \t<li>Chemists use a thermochemical equation to represent the changes in both matter and energy. In a thermochemical equation, the enthalpy change of a reaction is shown as a \u0394<em>H<\/em> value following the equation for the reaction. This \u0394<em>H<\/em> value indicates the amount of heat associated with the reaction involving the number of moles of reactants and products <em>as shown in the chemical equation<\/em>. For example, consider this equation:\r\n<p style=\"text-align: center;\">[latex]{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=-286\\text{kJ}[\/latex]<\/p>\r\nThis equation indicates that when 1 mole of hydrogen gas and [latex]\\frac{1}{2}[\/latex] mole of oxygen gas at some temperature and pressure change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released to the surroundings. If the coefficients of the chemical equation are multiplied by some factor, the enthalpy change must be multiplied by that same factor (\u0394<em>H<\/em> is an extensive property):\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}\\left(\\text{two-fold increase in amounts}\\right)\\\\ 2{\\text{H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=2\\times \\left(-286\\text{kJ}\\right)=-572\\text{kJ}\\\\ \\left(\\text{two-fold decrease in amounts}\\right)\\\\ \\frac{1}{2}{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{4}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\frac{1}{2}{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=\\frac{1}{2}\\times \\left(-286\\text{kJ}\\right)=-143\\text{kJ}\\end{array}[\/latex]<\/p>\r\n<\/li>\r\n \t<li>The enthalpy change of a reaction depends on the physical state of the reactants and products of the reaction (whether we have gases, liquids, solids, or aqueous solutions), so these must be shown. For example, when 1 mole of hydrogen gas and [latex]\\frac{1}{2}[\/latex] mole of oxygen gas change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released. If gaseous water forms, only 242 kJ of heat are released.\r\n<p style=\"text-align: center;\">[latex]{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(g\\right)\\Delta\\text{H}=-242\\text{kJ}[\/latex]<\/p>\r\n<\/li>\r\n \t<li>A negative value of an enthalpy change, \u0394<em>H<\/em>, indicates an exothermic reaction; a positive value of \u0394<em>H<\/em> indicates an endothermic reaction. If the direction of a chemical equation is reversed, the arithmetic sign of its \u0394<em>H<\/em> is changed (a process that is endothermic in one direction is exothermic in the opposite direction).<\/li>\r\n<\/ol>\r\n<div class=\"textbox examples\">\r\n<h3>Example 1:\u00a0<strong>Measurement of an Enthalpy Change<\/strong><\/h3>\r\nWhen 0.0500 mol of HCl(<em>aq<\/em>) reacts with 0.0500 mol of NaOH(<em>aq<\/em>) to form 0.0500 mol of NaCl(<em>aq<\/em>), 2.9 kJ of heat are produced. What is \u0394<em>H<\/em>, the enthalpy change, per mole of acid reacting, for the acid-base reaction run under the conditions described in <a href=\".\/chapter\/calorimetry\/\" target=\"_blank\">Example 3 of Calorimetry<\/a>?\r\n<p style=\"text-align: center;\">[latex]\\text{HCl}\\left(aq\\right)+\\text{NaOH}\\left(aq\\right)\\rightarrow\\text{NaCl}\\left(aq\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/p>\r\n[reveal-answer q=\"755793\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"755793\"]\r\n\r\nFor the reaction of 0.0500 mol acid (HCl), <em>q<\/em> = -2.9 kJ. This ratio [latex]\\frac{-2.9\\text{kJ}}{0.0500\\text{mol}\\text{HCl}}[\/latex] can be used as a conversion factor to find the heat produced when 1 mole of HCl reacts:\r\n<p style=\"text-align: center;\">[latex]\\Delta\\text{H}=1\\cancel{\\text{mol}\\text{HCl}}\\times \\frac{-2.9\\text{kJ}}{0.0500\\cancel{\\text{mol}\\text{HCl}}}=-58\\text{kJ}[\/latex]<\/p>\r\nThe enthalpy change when 1 mole of HCl reacts is \u221258 kJ. Since that is the number of moles in the chemical equation, we write the thermochemical equation as:\r\n<p style=\"text-align: center;\">[latex]\\text{HCl}\\left(aq\\right)+\\text{NaOH}\\left(aq\\right)\\rightarrow\\text{NaCl}\\left(aq\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=-58\\text{kJ}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp6958160\"><strong>Check Your Learning<\/strong><\/h4>\r\nWhen 1.34 g Zn(<em>s<\/em>) reacts with 60.0 mL of 0.750 M HCl(<em>aq<\/em>), 3.14 kJ of heat are produced. Determine the enthalpy change per mole of zinc reacting for the reaction:\r\n<p style=\"text-align: center;\">[latex]\\text{Zn}\\left(s\\right)+2\\text{HCl}\\left(aq\\right)\\rightarrow{\\text{ZnCl}}_{2}\\left(aq\\right)+{\\text{H}}_{2}\\left(g\\right)[\/latex]<\/p>\r\n[reveal-answer q=\"227263\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"227263\"]\u0394H = \u2013153 kJ[\/hidden-answer]\r\n\r\n<\/div>\r\nBe sure to take both stoichiometry and limiting reactants into account when determining the \u0394<em>H<\/em> for a chemical reaction.\r\n<div class=\"textbox examples\">\r\n<h3>Example 2:\u00a0<strong>Another Example of the Measurement of an Enthalpy Change<\/strong><\/h3>\r\nA gummy bear contains 2.67 g sucrose, C<sub>12<\/sub>H<sub>22<\/sub>O<sub>11<\/sub>. When it reacts with 7.19 g potassium chlorate, KClO<sub>3<\/sub>, 43.7 kJ of heat are produced. Determine the enthalpy change for the reaction\r\n<p style=\"text-align: center;\">[latex]{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}\\left(aq\\right)+8{\\text{KClO}}_{3}\\left(aq\\right)\\rightarrow 12{\\text{CO}}_{2}\\left(g\\right)+11{\\text{H}}_{2}\\text{O}\\left(l\\right)+8\\text{KCl}\\left(aq\\right)[\/latex]<\/p>\r\n<p id=\"fs-idm42247408\">[reveal-answer q=\"908763\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"908763\"]<\/p>\r\nWe have [latex]2.67\\cancel{\\text{g}}\\times \\frac{1\\text{ mol}}{342.3\\cancel{\\text{g}}}=0.00780\\text{ mol }{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}[\/latex] available, and [latex]7.19\\cancel{\\text{g}}\\times \\frac{1\\text{ mol}}{122.5\\cancel{\\text{g}}}=0.0587\\text{ mol }{\\text{KClO}}_{3}[\/latex] available. Since [latex]0.0587\\text{ mol }{\\text{KClO}}_{3}\\times \\frac{1\\text{ mol }{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}}{8\\text{ mol }{\\text{KClO}}_{3}}=0.00734\\text{ mol }{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}[\/latex] is needed, C<sub>12<\/sub>H<sub>22<\/sub>O<sub>11<\/sub> is the excess reactant and KClO<sub>3<\/sub> is the limiting reactant.\r\n\r\nThe reaction uses 8 mol KClO<sub>3<\/sub>, and the conversion factor is [latex]\\frac{-43.7\\text{kJ}}{0.0587\\text{ mol }{\\text{KClO}}_{3}},[\/latex] so we have\r\n<p style=\"text-align: center;\">[latex]\\Delta\\text{H}=8\\text{mol}\\times \\frac{-43.7\\text{kJ}}{0.0587\\text{ mol }{\\text{KClO}}_{3}}=-5960\\text{kJ}[\/latex]<\/p>\r\nThe enthalpy change for this reaction is -5960 kJ, and the thermochemical equation is:\r\n<p style=\"text-align: center;\">[latex]{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}+8{\\text{KClO}}_{3}\\rightarrow 12{\\text{CO}}_{2}+11{\\text{H}}_{2}\\text{O}+8\\text{KCl}\\Delta\\text{H}=-5960\\text{ kJ}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp82549456\"><strong>Check Your Learning<\/strong><\/h4>\r\nWhen 1.42 g of iron reacts with 1.80 g of chlorine, 3.22 g of FeCl<sub>2<\/sub>(<em>s<\/em>) and 8.60 kJ of heat is produced. What is the enthalpy change for the reaction when 1 mole of FeCl<sub>2<\/sub>(<em>s<\/em>) is produced?\r\n\r\n[reveal-answer q=\"608658\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"608658\"]\u0394H = \u2013338 kJ[\/hidden-answer]\r\n\r\n<\/div>\r\nEnthalpy changes are typically tabulated for reactions in which both the reactants and products are at the same conditions. A <strong>standard state <\/strong>is a commonly accepted set of conditions used as a reference point for the determination of properties under other different conditions. For chemists, the IUPAC standard state refers to materials under a pressure of 1 bar and solutions at 1 M, and does not specify a temperature. Many thermochemical tables list values with a standard state of 1 atm. Because the \u0394<em>H<\/em> of a reaction changes very little with such small changes in pressure (1 bar = 0.987 atm), \u0394<em>H<\/em> values (except for the most precisely measured values) are essentially the same under both sets of standard conditions. We will include a superscripted \u201co\u201d in the enthalpy change symbol to designate standard state. Since the usual (but not technically standard) temperature is 298.15 K, we will use a subscripted \u201c298\u201d to designate this temperature. Thus, the symbol [latex]\\left(\\Delta{H}_{298}^{\\circ}\\right)[\/latex] is used to indicate an enthalpy change for a process occurring under these conditions. (The symbol \u0394<em>H<\/em> is used to indicate an enthalpy change for a reaction occurring under nonstandard conditions.)\r\n\r\nThe enthalpy changes for many types of chemical and physical processes are available in the reference literature, including those for combustion reactions, phase transitions, and formation reactions. As we discuss these quantities, it is important to pay attention to the <em>extensive<\/em> nature of enthalpy and enthalpy changes. Since the enthalpy change for a given reaction is proportional to the amounts of substances involved, it may be reported on that basis (i.e., as the \u0394<em>H<\/em> for specific amounts of reactants). However, we often find it more useful to divide one extensive property (\u0394<em>H<\/em>) by another (amount of substance), and report a per-amount <em>intensive<\/em> value of \u0394<em>H<\/em>, often \u201cnormalized\u201d to a per-mole basis. (Note that this is similar to determining the intensive property specific heat from the extensive property heat capacity, as seen previously.)\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<ol>\r\n \t<li>Explain how the heat measured in <a href=\".\/chapter\/calorimetry\" target=\"_blank\">Example 3 of Calorimetry<\/a> differs from the enthalpy change for the exothermic reaction described by the following equation: [latex]\\text{HCl}\\left(aq\\right)+\\text{NaOH}\\left(aq\\right)\\rightarrow\\text{NaCl}\\left(aq\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/li>\r\n \t<li>Using the data in the check your learning section of <a href=\".chapter\/calorimetry-6-formula-errors\/\" target=\"_blank\">Example 3 of Calorimetry<\/a>, calculate \u0394H in kJ\/mol of AgNO3(aq) for the reaction: [latex]\\text{NaCl(}aq\\text{)}+{\\text{AgNO}}_{3}\\text{(}aq\\text{)}\\rightarrow\\text{AgCl}\\text{(}s\\text{)}+{\\text{NaNO}}_{3}\\text{(}aq\\text{).}[\/latex]<\/li>\r\n \t<li>Calculate the enthalpy of solution (\u0394<em>H<\/em> for the dissolution) per mole of NH<sub>4<\/sub>NO<sub>3<\/sub> under the conditions described in <a href=\"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-admin\/.chapter\/calorimetry-6-formula-errors\" target=\"_blank\">Figure 6\u00a0in\u00a0Calorimetry<\/a>.<\/li>\r\n \t<li>Calculate \u0394<em>H<\/em> for the reaction described by the equation. [latex]\\text{Ba}{\\left(\\text{OH}\\right)}_{2}\\cdot 8{\\text{H}}_{2}\\text{O}\\left(s\\right)+2{\\text{NH}}_{4}\\text{SCN}\\left(aq\\right)\\rightarrow\\text{Ba}{\\left(\\text{SCN}\\right)}_{2}\\left(aq\\right)+2{\\text{NH}}_{3}\\left(aq\\right)+10{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/li>\r\n \t<li>Calculate the enthalpy of solution (\u0394<em>H<\/em> for the dissolution) per mole of CaCl<sub>2<\/sub>.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"631741\"]Show Selected Answers[\/reveal-answer]\r\n[hidden-answer a=\"631741\"]\r\n\r\n1. The enthalpy change of the indicated reaction is for exactly 1 mol HCL and 1 mol NaOH; the heat in the example is produced by 0.0500 mol HCl and 0.0500 mol NaOH.\r\n\r\n3. The molar mass of NH<sub>4<\/sub>NO<sub>3<\/sub> is 80.0423 g\/mol. From the example, 1000 J is required to dissolve 3.21 g of NH<sub>4<\/sub>NO<sub>3<\/sub>.\r\n\r\nOne mole under the same conditions would require\r\n<p style=\"text-align: center;\">[latex]\\frac{80.0432\\cancel{\\text{g}}{\\text{ mol}}^{-1}}{3.21\\cancel{\\text{g}}}\\times 1000\\text{ J}=25\\text{ kJ}{\\text{ mol}}^{-1}.[\/latex]<\/p>\r\n(The heat of solution is positive because the process is endothermic.)\r\n\r\n5. The molar mass of CaCl<sub>2<\/sub> is 40.078 + 2(35.4572) = 110.992 g\/mol. In the previous section, 3.0 g of CaCl<sub>2<\/sub> dissolved in water releases a heat of 2.2 kJ. Therefore,\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{rcl}\\frac{3.0\\cancel{\\text{g}}}{110.992\\cancel{\\text{ g }}{\\text{mol}}^{-1}}&amp;=&amp;0.027\\text{ mol}\\\\ \\frac{2.2\\text{kJ}}{0.027\\text{ mol}}&amp;=&amp;81\\text{ kJ }{\\text{ mol}}^{-1}\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2 data-type=\"title\">Enthalpy of Combustion<\/h2>\r\n<strong>Standard enthalpy of combustion<\/strong> [latex]\\left(\\Delta{H}_{C}^{\\circ }\\right)[\/latex] is the enthalpy change when 1 mole of a substance burns (combines vigorously with oxygen) under standard state conditions; it is sometimes called \u201cheat of combustion.\u201d For example, the enthalpy of combustion of ethanol, -1366.8 kJ\/mol, is the amount of heat produced when one mole of ethanol undergoes complete combustion at 25 \u00b0C and 1 atmosphere pressure, yielding products also at 25 \u00b0C and 1 atm.\r\n<p style=\"text-align: center;\">[latex]{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)+3{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{CO}}_{2}+3{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta{H}_{298}^{\\circ }=\\text{-1366.8}\\text{kJ}[\/latex]<\/p>\r\nEnthalpies of combustion for many substances have been measured; a few of these are listed in Table 1. Many readily available substances with large enthalpies of combustion are used as fuels, including hydrogen, carbon (as coal or charcoal), and hydrocarbons (compounds containing only hydrogen and carbon), such as methane, propane, and the major components of gasoline.\r\n<table id=\"fs-idp98710048\" summary=\"A data table is shown that has three columns and eleven rows. The header row reads \u201cSubstance,\u201d \u201cCombustion reaction,\u201d and \u201cEnthalpy of Combustion, \u0394 H subscript C superscript degree symbol (k J\/ mol at 25 \u00b0 C).\u201d The first column contains entries reading \u201ccarbon,\u201d \u201chydrogen,\u201d \u201cmagnesium,\u201d \u201csulfur,\u201d \u201ccarbon monoxide,\u201d \u201cmethane,\u201d \u201cacetylene,\u201d \u201cethanol,\u201d \u201cmethanol,\u201d and \u201cisooctane.\u201d The second column contains the equations \u201cC (s) + O (g) right-facing arrow C O subscript 2 (g),\u201d \u201cH subscript 2 (g) + one half O subscript 2 (g) right-facing arrow H subscript 2 O (l),\u201d \u201cM g (s) + one half O subscript 2 (g) right-facing arrow M g O (s),\u201d \u201cS (s) + O subscript 2 (g) right-facing arrow S O subscript 2 (g),\u201d \u201cC O (g) + one half O subscript 2 (g) right-facing arrow C O subscript 2 (g),\u201d \u201cC H subscript 4 (g) + 2 O subscript 2 (g) right-facing arrow C O subscript 2 (g) + 2 H subscript 2 O (g),\u201d \u201cC subscript 2 H subscript 2 (g) + five halves O subscript 2 (g) right-facing arrow 2 C O subscript 2 (g) + H subscript 2 O (l),\u201d \u201cC subscript 2 H subscript 5 O H (l) + 2 O subscript 2 (g) right-facing arrow C O subscript 2 (g) + 3 H subscript 2 O (l),\u201d \u201cC H subscript 3 O H (l) + three halves O subscript 2 (g) right-facing arrow C O subscript 2 (g) + 2 H subscript 2 O (l),\u201d and \u201cC subscript 8 H subscript 18 (l) + twenty five halves O subscript 2 (g) right-facing arrow 8 C O subscript 2 (g) + 9 H subscript 2 O (l).\u201d The final column contains the values \u201c\u2013393.5,\u201d \u201c\u2013285.8,\u201d \u201c\u2013601.6,\u201d \u201c\u2013296.8,\u201d \u201c\u2013283.0,\u201d \u201c\u2013890.8,\u201d \u201c\u20131301.1,\u201d \u201c\u20131366.8,\u201d \u201c\u2013726.1,\u201d and \u201c\u20135461.\u201d\">\r\n<thead>\r\n<tr>\r\n<th colspan=\"3\">Table 1. Standard Molar Enthalpies of Combustion<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<th width=\"20%\">Substance<\/th>\r\n<th width=\"40%\">Combustion Reaction<\/th>\r\n<th width=\"40%\">Enthalpy of Combustion, [latex]\\Delta{H}_{c}^{\\circ }[\/latex] [latex]\\left(\\frac{\\text{kJ}}{\\text{mol}}\\text{ at }25^{\\circ}\\text{ C}\\right)[\/latex]<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>carbon<\/td>\r\n<td>[latex]\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)[\/latex]<\/td>\r\n<td>\u2212393.5<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>hydrogen<\/td>\r\n<td>[latex]{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>\u2212285.8<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>magnesium<\/td>\r\n<td>[latex]\\text{Mg}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{MgO}\\left(s\\right)[\/latex]<\/td>\r\n<td>\u2212601.6<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>sulfur<\/td>\r\n<td>[latex]\\text{S}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{SO}}_{2}\\left(g\\right)[\/latex]<\/td>\r\n<td>\u2212296.8<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>carbon monoxide<\/td>\r\n<td>[latex]\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)[\/latex]<\/td>\r\n<td>\u2212283.0<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>methane<\/td>\r\n<td>[latex]{\\text{CH}}_{4}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>\u2212890.8<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>acetylene<\/td>\r\n<td>[latex]{\\text{C}}_{2}{\\text{H}}_{2}\\left(g\\right)+\\frac{5}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{CO}}_{2}\\left(g\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>\u22121301.1<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>ethanol<\/td>\r\n<td>[latex]{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)+3{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>\u22121366.8<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>methanol<\/td>\r\n<td>[latex]{\\text{CH}}_{3}\\text{OH}\\left(l\\right)+\\frac{3}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>\u2212726.1<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>isooctane<\/td>\r\n<td>[latex]{\\text{C}}_{8}{\\text{H}}_{18}\\left(l\\right)+\\frac{25}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow 8{\\text{CO}}_{2}\\left(g\\right)+9{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\r\n<td>\u22125461<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<div class=\"textbox examples\">\r\n<h3>Example 3:\u00a0<strong>Using Enthalpy of Combustion<\/strong><\/h3>\r\nAs Figure 3 suggests, the combustion of gasoline is a highly exothermic process. Let us determine the approximate amount of heat produced by burning 1.00 L of gasoline, assuming the enthalpy of combustion of gasoline is the same as that of isooctane, a common component of gasoline. The density of isooctane is 0.692 g\/mL.\r\n\r\n[caption id=\"attachment_5374\" align=\"aligncenter\" width=\"1200\"]<img class=\"wp-image-5374 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033040\/CNX_Chem_05_03_GasBurning1.jpg\" alt=\"A picture shows a large ball of fire burning on a road. A fire truck and fireman are shown in the foreground.\" width=\"1200\" height=\"313\" \/> Figure 3. The combustion of gasoline is very exothermic. (credit: modification of work by \u201cAlexEagle\u201d\/Flickr)[\/caption]\r\n\r\n&nbsp;\r\n\r\n[reveal-answer q=\"583919\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"583919\"]\r\n\r\nStarting with a known amount (1.00 L of isooctane), we can perform conversions between units until we arrive at the desired amount of heat or energy. The enthalpy of combustion of isooctane provides one of the necessary conversions. Table 1 gives this value as \u22125460 kJ per 1 mole of isooctane (C<sub>8<\/sub>H<sub>18<\/sub>).\r\n\r\nUsing these data,\r\n<p style=\"text-align: center;\">[latex]1.00\\cancel{\\text{L }{\\text{C}}_{8}{\\text{H}}_{18}}\\times \\frac{1000\\cancel{\\text{mL }{\\text{C}}_{8}{\\text{H}}_{18}}}{1\\cancel{\\text{L }{\\text{C}}_{8}{\\text{H}}_{18}}}\\times \\frac{0.692\\cancel{\\text{g }{\\text{C}}_{8}{\\text{H}}_{18}}}{1\\cancel{\\text{mL }{\\text{C}}_{8}{\\text{H}}_{18}}}\\times \\frac{1\\cancel{\\text{mol}{\\text{C}}_{8}{\\text{H}}_{18}}}{114\\cancel{\\text{g}{\\text{C}}_{8}{\\text{H}}_{18}}}\\times \\frac{-5460\\text{kJ}}{1\\cancel{\\text{mol}{\\text{C}}_{8}{\\text{H}}_{18}}}=-3.31\\times {10}^{4}\\text{kJ}[\/latex]<\/p>\r\nThe combustion of 1.00 L of isooctane produces 33,100 kJ of heat. (This amount of energy is enough to melt 99.2 kg, or about 218 lbs, of ice.)\r\n\r\nNote: If you do this calculation one step at a time, you would find:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}\\\\ 1.00\\text{L }{\\text{C}}_{8}{\\text{H}}_{18}\\rightarrow 1.00\\times {10}^{3}\\text{mL }{\\text{C}}_{8}{\\text{H}}_{18}\\\\ 1.00\\times {10}^{3}\\text{mL }{\\text{C}}_{8}{\\text{H}}_{18}\\rightarrow 692\\text{g}{\\text{C}}_{8}{\\text{H}}_{18}\\\\ 692\\text{g}{\\text{C}}_{8}{\\text{H}}_{18}\\rightarrow 6.07\\text{mol}{\\text{C}}_{8}{\\text{H}}_{18}\\\\ 692\\text{g}{\\text{C}}_{8}{\\text{H}}_{18}\\rightarrow-3.31\\times {10}^{4}\\text{kJ}\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp49733232\"><strong>Check Your Learning<\/strong><\/h4>\r\nHow much heat is produced by the combustion of 125 g of acetylene?\r\n\r\n[reveal-answer q=\"413251\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"413251\"]6.25 \u00d7 10<sup>3<\/sup> kJ[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3 style=\"text-align: left;\">Emerging Algae-Based Energy Technologies (Biofuels)<\/h3>\r\nAs reserves of fossil fuels diminish and become more costly to extract, the search is ongoing for replacement fuel sources for the future. Among the most promising biofuels are those derived from algae (Figure 4). The species of algae used are nontoxic, biodegradable, and among the world\u2019s fastest growing organisms. About 50% of algal weight is oil, which can be readily converted into fuel such as biodiesel. Algae can yield 26,000 gallons of biofuel per hectare\u2014much more energy per acre than other crops. Some strains of algae can flourish in brackish water that is not usable for growing other crops. Algae can produce biodiesel, biogasoline, ethanol, butanol, methane, and even jet fuel.\r\n\r\n[caption id=\"attachment_5376\" align=\"aligncenter\" width=\"1200\"]<img class=\"size-full wp-image-5376\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033150\/CNX_Chem_05_03_AlgalFuel11.jpg\" alt=\"Three pictures are shown and labeled a, b, and c. Picture a shows a microscopic view of algal organisms. They are brown, multipart strands and net-like structures on a background of light violet. Picture b shows five large tubs full of a brown liquid containing these algal organisms. Picture c depicts a cylinder full of green liquid in the foreground and a poster in the background that has the title \u201cFrom Field to Fleet.\u201d\" width=\"1200\" height=\"425\" \/> Figure 4. (a) Tiny algal organisms can be (b) grown in large quantities and eventually (c) turned into a useful fuel such as biodiesel. (credit a: modification of work by Micah Sittig; credit b: modification of work by Robert Kerton; credit c: modification of work by John F. Williams)[\/caption]\r\n\r\n&nbsp;\r\n\r\nAccording to the US Department of Energy, only 39,000 square kilometers (about 0.4% of the land mass of the US or less than [latex]\\frac{1}{7}[\/latex] of the area used to grow corn) can produce enough algal fuel to replace all the petroleum-based fuel used in the US. The cost of algal fuels is becoming more competitive\u2014for instance, the US Air Force is producing jet fuel from algae at a total cost of under $5 per gallon. The process used to produce algal fuel is as follows: grow the algae (which use sunlight as their energy source and CO<sub>2<\/sub> as a raw material); harvest the algae; extract the fuel compounds (or precursor compounds); process as necessary (e.g., perform a transesterification reaction to make biodiesel); purify; and distribute (Figure 5).\r\n\r\n[caption id=\"attachment_5377\" align=\"aligncenter\" width=\"1008\"]<img class=\"size-full wp-image-5377\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033252\/CNX_Chem_05_03_AlgalFuel21.jpg\" alt=\"A flowchart is shown that contains pictures and words. Reading from left to right, the terms \u201cGrow,\u201d \u201cHarvest,\u201d \u201cExtract,\u201d \u201cProcess and purify,\u201d and \u201cJet fuel gasoline diesel\u201d are shown with right-facing arrows in between each. Above each term, respectively, are diagrams of three containers, three cylinders lying side-by-side, a pyramid-like container with liquid inside, a factory, and a fuel pump. In the space above all of the diagrams and to the left of the images is a diagram of the sun.\" width=\"1008\" height=\"365\" \/> Figure 5. Algae convert sunlight and carbon dioxide into oil that is harvested, extracted, purified, and transformed into a variety of renewable fuels.[\/caption]\r\n\r\n<\/div>\r\n<div class=\"textbox\">\r\n\r\nWatch this video to learn more about the process of creating algae biofuel.\r\n\r\nhttps:\/\/youtu.be\/q9X7UNLRbds\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<ol>\r\n \t<li>Although the gas used in an oxyacetylene torch (Figure 6) is essentially pure acetylene, the heat produced by combustion of one mole of acetylene in such a torch is likely not equal to the enthalpy of combustion of acetylene listed in Table 1. Considering the conditions for which the tabulated data are reported, suggest an explanation.\r\n\r\n[caption id=\"attachment_5380\" align=\"aligncenter\" width=\"1300\"]<img class=\"size-full wp-image-5380\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033707\/CNX_Chem_05_01_OxyacTorch1.jpg\" alt=\"Two pictures are shown and labeled a and b. Picture a shows a metal railroad tie being cut with the flame of an acetylene torch. Picture b shows a chemical cold pack containing ammonium nitrate.\" width=\"1300\" height=\"556\" \/> Figure 6. (a) An oxyacetylene torch. (b) A cold pack. (credit a: modification of work by \u201cSkatebiker\u201d\/Wikimedia commons)[\/caption]<\/li>\r\n \t<li>How much heat is produced by burning 4.00 moles of acetylene under standard state conditions?<\/li>\r\n \t<li>How much heat is produced by combustion of 125 g of methanol under standard state conditions?<\/li>\r\n \t<li>How many moles of isooctane must be burned to produce 100 kJ of heat under standard state conditions?<\/li>\r\n \t<li>What mass of carbon monoxide must be burned to produce 175 kJ of heat under standard state conditions?<\/li>\r\n \t<li>When 2.50 g of methane burns in oxygen, 125 kJ of heat is produced. What is the enthalpy of combustion per mole of methane under these conditions?<\/li>\r\n \t<li>How much heat is produced when 100 mL of 0.250 M HCl (density, 1.00 g\/mL) and 200 mL of 0.150 M NaOH (density, 1.00 g\/mL) are mixed?[latex]\\text{HCl}\\left(aq\\right)+\\text{NaOH}\\left(aq\\right)\\rightarrow\\text{NaCl}\\left(aq\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta{H}_{298}^{\\circ }=-58\\text{kJ}[\/latex] If both solutions are at the same temperature and the heat capacity of the products is 4.19 J\/g \u00b0C, how much will the temperature increase? What assumption did you make in your calculation?<\/li>\r\n \t<li>A sample of 0.562 g of carbon is burned in oxygen in a bomb calorimeter, producing carbon dioxide. Assume both the reactants and products are under standard state conditions, and that the heat released is directly proportional to the enthalpy of combustion of graphite. The temperature of the calorimeter increases from 26.74 \u00b0C to 27.93 \u00b0C. What is the heat capacity of the calorimeter and its contents?<\/li>\r\n \t<li>Before the introduction of chlorofluorocarbons, sulfur dioxide (enthalpy of vaporization, 6.00 kcal\/mol) was used in household refrigerators. What mass of SO<sub>2<\/sub> must be evaporated to remove as much heat as evaporation of 1.00 kg of CCl<sub>2<\/sub>F<sub>2<\/sub> (enthalpy of vaporization is 17.4 kJ\/mol)? The vaporization reactions for SO<sub>2<\/sub> and CCl<sub>2<\/sub>F<sub>2<\/sub> are [latex]{\\text{SO}}_{2}\\left(l\\right)\\rightarrow{\\text{SO}}_{2}\\left(g\\right)[\/latex] and [latex]{\\text{CCl}}_{2}\\text{F}\\left(l\\right)\\rightarrow{\\text{CCl}}_{2}{\\text{F}}_{2}\\left(g\\right),[\/latex] respectively.<\/li>\r\n \t<li>Homes may be heated by pumping hot water through radiators. What mass of water will provide the same amount of heat when cooled from 95.0 to 35.0 \u00b0C, as the heat provided when 100 g of steam is cooled from 110 \u00b0C to 100 \u00b0C.<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"427747\"]Show Selected Answers[\/reveal-answer]\r\n[hidden-answer a=\"427747\"]\r\n\r\n2. The heat of combustion is -1301.1 as given in Table 1.\r\n<p style=\"text-align: center;\">heat released = 4.00 mol \u00d7 (-1301.1 kJ\/mol) = 5204.4 kJ<\/p>\r\n4. The value of \u0394<em>H<\/em><sub>comb<\/sub> = -5461 kJ\/mol. To produce 100 kJ requires:\r\n<p style=\"text-align: center;\">[latex]\\frac{100\\text{kJ}}{5461\\text{kJ}{\\text{mol}}^{-1}}=1.83\\times {10}^{-2}\\text{mol}.[\/latex]<\/p>\r\n6. The molar mass of CH<sub>4<\/sub> is 16.04 g\/mol.\u00a0Find the mole of CH<sub>4<\/sub> present:\r\n<p style=\"text-align: center;\">[latex]\\frac{2.50\\cancel{\\text{g}}}{16.04\\cancel{\\text{g}}{\\text{mol}}^{-1}}=0.15586\\text{mol}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\Delta{H}_{\\text{comb}}=\\frac{125\\text{kJ}}{0.15586\\text{mol}}=802\\text{kJ}{\\text{mol}}^{-1}.[\/latex]<\/p>\r\n8. The heat produced is found from the enthalpy of combustion:\r\n<p style=\"text-align: center;\">[latex]\\frac{0.562\\cancel{\\text{g}}\\cancel{^{\\circ C}}}{12.011\\cancel{\\text{g}}{\\text{mol}}^{-1}\\cancel{^{\\circ C}}}=-393.5\\text{kJ}{\\text{mol}}^{-1}=-18.4\\text{kJ}.[\/latex]<\/p>\r\nThis is the heat released.\r\n<p style=\"text-align: center;\"><em>q<\/em> = heat capacity \u00d7 \u0394<em>T<\/em><\/p>\r\n<p style=\"text-align: center;\">18.4 kJ = heat capacity \u00d7 (27.93 \u00baC - 26.74 \u00baC) = specific heat \u00d7 1.19 \u00baC<\/p>\r\n<p style=\"text-align: center;\">specific heat = 15.5 kJ\/\u00baC<\/p>\r\n10. <em>q<\/em> = <em>mc<\/em>\u2206<em>T<\/em>. The amount of heat transferred from steam is:\r\n\r\n<em>q<\/em><sub>steam<\/sub> = 100 g \u00d7 1.864 J\/(g \u00b0C) \u00d7 (110 - 100) \u00b0C = 1864 J\r\n<em>q<\/em><sub>water<\/sub> = <em>m<\/em><sub>water<\/sub> \u00d7 4.184 J\/(g \u00b0C) \u00d7 (95 - 35) \u00b0C = <em>m<\/em><sub>water<\/sub> \u00d7 251.04 J\/g = <em>q<\/em><sub>steam<\/sub> = 1864 J\r\n[latex]{m}_{\\text{water}}=\\frac{1864\\cancel{\\text{J}}}{251.01\\cancel{\\text{J}}\\text{\/g}}=7.43\\text{g}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2 data-type=\"title\">Standard Enthalpy of Formation<\/h2>\r\nA <strong>standard enthalpy of formation<\/strong> [latex]\\Delta{H}_{\\text{f}}^{\\circ}[\/latex] is an enthalpy change for a reaction in which exactly 1 mole of a pure substance is formed from free elements in their most stable states under standard state conditions. These values are especially useful for computing or predicting enthalpy changes for chemical reactions that are impractical or dangerous to carry out, or for processes for which it is difficult to make measurements. If we have values for the appropriate standard enthalpies of formation, we can determine the enthalpy change for any reaction, which we will practice in the next section on Hess\u2019s law.\r\n\r\nThe standard enthalpy of formation of CO<sub>2<\/sub>(<em>g<\/em>) is \u2212393.5 kJ\/mol. This is the enthalpy change for the exothermic reaction:\r\n<p style=\"text-align: center;\">[latex]\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)\\Delta{H}_{\\text{f}}^{\\circ }=\\Delta{H}_{298}^{\\circ }=-393.5\\text{kJ}[\/latex]<\/p>\r\nstarting with the reactants at a pressure of 1 atm and 25\u00b0C (with the carbon present as graphite, the most stable form of carbon under these conditions) and ending with one mole of CO<sub>2<\/sub>, also at 1 atm and 25\u00b0C. For nitrogen dioxide, NO<sub>2<\/sub>(<em>g<\/em>), [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] is 33.2 kJ\/mol. This is the enthalpy change for the reaction:\r\n<p style=\"text-align: center;\">[latex]\\frac{1}{2}{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{NO}}_{2}\\left(g\\right)\\Delta{H}_{\\text{f}}^{\\circ }=\\Delta{H}_{\\text{298}}^{\\circ }=\\text{+33.2}\\text{kJ}[\/latex]<\/p>\r\nA reaction equation with [latex]\\frac{1}{2}[\/latex] mole of N<sub>2<\/sub> and 1 mole of O<sub>2<\/sub> is correct in this case because the standard enthalpy of formation always refers to 1 mole of product, NO<sub>2<\/sub>(<em>g<\/em>).\r\n\r\nYou will find a table of standard enthalpies of formation of many common substances in <a class=\"target-chapter\" title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>. These values indicate that formation reactions range from highly exothermic (such as \u22122984 kJ\/mol for the formation of P<sub>4<\/sub>O<sub>10<\/sub>) to strongly endothermic (such as +226.7 kJ\/mol for the formation of acetylene, C<sub>2<\/sub>H<sub>2<\/sub>). By definition, the standard enthalpy of formation of an element in its most stable form is equal to zero under standard conditions, which is 1 atm for gases and 1 M for solutions.\r\n<div class=\"textbox examples\">\r\n<h3>Example 4:\u00a0<strong>Evaluating an Enthalpy of Formation<\/strong><\/h3>\r\nOzone, O<sub>3<\/sub>(<em>g<\/em>), forms from oxygen, O<sub>2<\/sub>(<em>g<\/em>), by an endothermic process. Ultraviolet radiation is the source of the energy that drives this reaction in the upper atmosphere. Assuming that both the reactants and products of the reaction are in their standard states, determine the standard enthalpy of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ}[\/latex] of ozone from the following information:\r\n<p style=\"text-align: center;\">[latex]3{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{O}}_{3}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=\\text{+286}\\text{kJ}[\/latex]<\/p>\r\n[reveal-answer q=\"296678\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"296678\"]\r\n<p id=\"fs-idp166467632\">[latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] is the enthalpy change for the formation of one mole of a substance in its standard state from the elements in their standard states. Thus, [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] for O<sub>3<\/sub>(<em>g<\/em>) is the enthalpy change for the reaction:<\/p>\r\n<p style=\"text-align: center;\">[latex]\\frac{3}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{O}}_{3}\\left(g\\right)[\/latex]<\/p>\r\nFor the formation of 2 mol of O<sub>3<\/sub>(<em>g<\/em>), [latex]\\Delta{H}_{\\text{298}}^{\\circ }=\\text{+286 kJ}[\/latex]. This ratio, [latex]\\left(\\frac{286\\text{kJ}}{2\\text{ mol }{\\text{O}}_{3}}\\right)[\/latex], can be used as a conversion factor to find the heat produced when 1 mole of O<sub>3<\/sub>(<em>g<\/em>) is formed, which is the enthalpy of formation for O<sub>3<\/sub>(<em>g<\/em>):\r\n<p style=\"text-align: center;\">[latex]\\Delta\\text{H}^{\\circ }\\text{for }1\\text{mole of }{\\text{O}}_{3}\\left(g\\right)=1\\cancel{\\text{ mol }{\\text{O}}_{3}}\\times \\frac{286\\text{kJ}}{2\\cancel{\\text{ mol }{\\text{O}}_{3}}}=143\\text{kJ}[\/latex]<\/p>\r\nTherefore, [latex]\\Delta{H}_{\\text{f}}^{\\circ }\\left[{\\text{O}}_{3}\\left(g\\right)\\right]=\\text{+143}\\text{kJ\/mol}.[\/latex]\r\n\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp167644640\"><strong>Check Your Learning<\/strong><\/h4>\r\nHydrogen gas, H<sub>2<\/sub>, reacts explosively with gaseous chlorine, Cl<sub>2<\/sub>, to form hydrogen chloride, HCl(<em>g<\/em>). What is the enthalpy change for the reaction of 1 mole of H<sub>2<\/sub>(<em>g<\/em>) with 1 mole of Cl<sub>2<\/sub>(<em>g<\/em>) if both the reactants and products are at standard state conditions? The standard enthalpy of formation of HCl(<em>g<\/em>) is -92.3 kJ\/mol.\r\n[reveal-answer q=\"500621\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"500621\"]For the reaction [latex]{\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow 2\\text{HCl}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-184.6\\text{kJ}[\/latex][\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>Example 5:\u00a0<strong>Writing Reaction Equations for [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] <\/strong><\/h3>\r\nWrite the heat of formation reaction equations for:\r\n<ol>\r\n \t<li>C<sub>2<\/sub>H<sub>5<\/sub>OH(<em>l<\/em>)<\/li>\r\n \t<li>Ca<sub>3<\/sub>(PO<sub>4<\/sub>)<sub>2<\/sub>(<em>s<\/em>)<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"931765\"]Show Answers[\/reveal-answer]\r\n[hidden-answer a=\"931765\"]\r\n\r\nRemembering that [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] reaction equations are for forming 1 mole of the compound from its constituent elements under standard conditions, we have:\r\n<ol>\r\n \t<li>[latex]2\\text{C}\\left(s,\\text{graphite}\\right)+3{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)[\/latex]<\/li>\r\n \t<li>[latex]3\\text{Ca}\\left(s\\right)+\\frac{1}{2}{\\text{P}}_{4}\\left(s\\right)+4{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Ca}}_{3}{{\\text{(PO}}_{4}\\text{)}}_{2}\\left(s\\right)[\/latex]<\/li>\r\n<\/ol>\r\nNote: The standard state of carbon is graphite, and phosphorus exists as P<sub>4<\/sub>.\r\n\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp166525568\"><strong>Check Your Learning<\/strong><\/h4>\r\nWrite the heat of formation reaction equations for:\r\n<ol>\r\n \t<li>C<sub>2<\/sub>H<sub>5<\/sub>OC<sub>2<\/sub>H<sub>5<\/sub>(<em>l<\/em>)<\/li>\r\n \t<li>Na<sub>2<\/sub>CO<sub>3<\/sub>(<em>s<\/em>)<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"539408\"]Show Answers[\/reveal-answer]\r\n[hidden-answer a=\"539408\"]\r\n<ol>\r\n \t<li>[latex]4\\text{C}\\left(s,\\text{graphite}\\right)+5{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{C}}_{2}{\\text{H}}_{5}{\\text{OC}}_{2}{\\text{H}}_{5}\\left(l\\right)[\/latex]<\/li>\r\n \t<li>[latex]2\\text{Na}\\left(s\\right)+\\text{C}\\left(s,\\text{graphite}\\right)+\\frac{3}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Na}}_{2}{\\text{CO}}_{3}\\left(s\\right)[\/latex]<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<ol>\r\n \t<li>Does the standard enthalpy of formation of H<sub>2<\/sub>O(<em>g<\/em>) differ from \u0394<em>H<\/em>\u00b0 for the reaction [latex]{\\text{2H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{H}}_{2}\\text{O}\\left(g\\right)?[\/latex]<\/li>\r\n \t<li>Joseph Priestly prepared oxygen in 1774 by heating red mercury(II) oxide with sunlight focused through a lens. How much heat is required to decompose exactly 1 mole of red HgO(<em>s<\/em>) to Hg(<em>l<\/em>) and O<sub>2<\/sub>(<em>g<\/em>) under standard conditions?<\/li>\r\n \t<li>How many kilojoules of heat will be released when exactly 1 mole of manganese, Mn, is burned to form Mn<sub>3<\/sub>O<sub>4<\/sub>(<em>s<\/em>) at standard state conditions?<\/li>\r\n \t<li>How many kilojoules of heat will be released when exactly 1 mole of iron, Fe, is burned to form Fe<sub>2<\/sub>O<sub>3<\/sub>(<em>s<\/em>) at standard state conditions?<\/li>\r\n \t<li>The following sequence of reactions occurs in the commercial production of aqueous nitric acid:[latex]4{\\text{NH}}_{3}\\left(g\\right)+5{\\text{O}}_{2}\\left(g\\right)\\rightarrow 4\\text{NO}\\left(g\\right)+6{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=-907\\text{kJ}[\/latex][latex]2\\text{NO}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta\\text{H}=-113\\text{kJ}[\/latex] [latex]3{\\text{NO}}_{2}+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow 2{\\text{HNO}}_{2}\\left(aq\\right)+\\text{NO}\\left(g\\right)\\Delta\\text{H}=-139\\text{kJ}[\/latex]\r\nDetermine the total energy change for the production of one mole of aqueous nitric acid by this process.<\/li>\r\n \t<li>Both graphite and diamond burn. [latex]\\text{C}\\left(s,\\text{diamond}\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)[\/latex] For the conversion of graphite to diamond:[latex]\\text{C}\\left(s,\\text{graphite}\\right)\\rightarrow\\text{C}\\left(s,\\text{diamond}\\right)\\Delta{H}_{298}^{\\circ }=1.90\\text{kJ}[\/latex] Which produces more heat, the combustion of graphite or the combustion of diamond?<\/li>\r\n \t<li>From the molar heats of formation in <a class=\"target-chapter\" title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, determine how much heat is required to evaporate one mole of water: [latex]{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(g\\right)[\/latex]<\/li>\r\n \t<li>Which produces more heat? [latex]\\text{Os}\\left(s\\right)\\rightarrow 2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{OsO}}_{4}\\left(s\\right)[\/latex] or [latex]\\text{Os}\\left(s\\right)\\rightarrow 2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{OsO}}_{4}\\left(g\\right)[\/latex] for the phase change [latex]{\\text{OsO}}_{4}\\left(s\\right)\\rightarrow{\\text{OsO}}_{4}\\left(g\\right)\\Delta\\text{H}=56.4\\text{kJ}[\/latex]<\/li>\r\n \t<li>Calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for the process [latex]\\text{Sb}\\left(s\\right)+\\frac{5}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{5}\\left(g\\right)[\/latex] from the following information: [latex]\\begin{array}{l}\\text{Sb}\\left(s\\right)+\\frac{3}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{3}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-314\\text{kJ}\\\\ {\\text{SbCl}}_{3}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{5}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-80\\text{kJ}\\end{array}[\/latex]<\/li>\r\n \t<li>Calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for the process [latex]\\text{Zn}\\left(s\\right)+\\text{S}\\left(s\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{ZnSO}}_{4}\\left(s\\right)[\/latex] from the following information: [latex]\\begin{array}{l}\\text{Zn}\\left(s\\right)+\\text{S}\\left(s\\right)\\rightarrow\\text{ZnS}\\left(s\\right)\\Delta{H}_{298}^{\\circ }=-206.0\\text{kJ}\\\\ \\text{ZnS}\\left(s\\right)+{\\text{2O}}_{\\text{2}}\\left(g\\right)\\rightarrow{\\text{ZnSO}}_{4}\\left(s\\right)\\Delta{H}_{298}^{\\circ }=-776.8\\text{kJ}\\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"93779\"]Show Selected Answers[\/reveal-answer]\r\n[hidden-answer a=\"93779\"]\r\n\r\n1. No. The standard enthalpy of formation can be determined for anything, including H<sub>2<\/sub>O(<em>g<\/em>), and water does not have to be liquid in this case, it\u2019s the gas-phase water that is the substance for which the heat of formation is to be found. However, the heat of this reaction is defined for two moles of H<sub>2<\/sub>O(<em>g<\/em>), thus the heat of formation is half of the heat of the reaction.\r\n\r\n3. This process requires 3 mol of Mn. For 1 mol, [latex]\\frac{1}{3}\\left(-1378.83\\text{kJ}\\right)=459.6\\text{kJ}.[\/latex]\r\n\r\n5. Enough material must be produced in each stage to proceed with the next. So [latex]\\frac{1}{2}[\/latex] of reaction 1 produces the NO required in reaction 2. But [latex]\\frac{3}{2}[\/latex] units of reaction 2 are required to provide enough NO<sub>2<\/sub> for reaction 3. Up to this stage, the heat produced is [latex]\\frac{3}{2}\\left[\\frac{1}{2}\\left(-907\\right)+\\left(-113\\right)\\right]=\\frac{3}{2}\\left(-566.55\\right)=-850\\text{kJ}[\/latex] to have the material to proceed with reaction 3. Therefore, from beginning to end, \u2013850 + (\u2013139) = \u2013989 kJ are released. The question asks for the enthalpy change for 1 mole. Therefore, division of the last answer by 2 gives -495 kJ\/mol.\r\n\r\n7. The heat of formation of H<sub>2<\/sub>O(<em>l<\/em>) is -285.83 kJ\/mol. The heat of formation of H<sub>2<\/sub>O(<em>g<\/em>) is -241.82 kJ\/mol. For the reaction:\r\n[latex]{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(g\\right),[\/latex]\r\n\r\nthe enthalpy of the reaction is the difference of heats of formation of the reactant and the product; thus, it is -241.82 - (-285.83) = 44.01 kJ\/mol.\r\n\r\n9. Add the two equations and their heat together.\r\n\r\n[latex]\\begin{array}{lll}\\text{Sb}\\left(s\\right)+\\frac{3}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{3}\\left(g\\right)\\hfill &amp; \\hfill &amp; \\Delta{H}_{298}^{\\circ }=-314\\text{kJ}\\hfill \\\\ \\frac{{\\text{SbCl}}_{3}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{5}\\left(g\\right)}{\\text{Sb}\\left(s\\right)+\\frac{\\text{5}}{\\text{2}}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{5}\\left(g\\right)}\\hfill &amp; \\hfill &amp; \\frac{\\Delta{H}_{298}^{\\circ }=-80\\text{kJ}}{\\Delta{H}_{298}^{\\circ }=-394\\text{kJ}}\\hfill \\end{array}[\/latex]\r\n\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2 data-type=\"title\">Hess\u2019s Law<\/h2>\r\nThere are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally determined enthalpy changes. Some reactions are difficult, if not impossible, to investigate and make accurate measurements for experimentally. And even when a reaction is not hard to perform or measure, it is convenient to be able to determine the heat involved in a reaction without having to perform an experiment.\r\n\r\nThis type of calculation usually involves the use of <strong>Hess\u2019s law<\/strong>, which states: <em>If a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps<\/em>. Hess\u2019s law is valid because enthalpy is a state function: Enthalpy changes depend only on where a chemical process starts and ends, but not on the path it takes from start to finish. For example, we can think of the reaction of carbon with oxygen to form carbon dioxide as occurring either directly or by a two-step process. The direct process is written:\r\n<p style=\"text-align: center;\">[latex]\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-394\\text{kJ}[\/latex]<\/p>\r\nIn the two-step process, first carbon monoxide is formed:\r\n<p style=\"text-align: center;\">[latex]\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-111\\text{kJ}[\/latex]<\/p>\r\nThen, carbon monoxide reacts further to form carbon dioxide:\r\n<p style=\"text-align: center;\">[latex]\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-283\\text{kJ}[\/latex]<\/p>\r\nThe equation describing the overall reaction is the sum of these two chemical changes:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}\\\\ \\text{Step 1: }\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)\\\\ \\underline{\\text{Step 2: }\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)}\\\\ \\text{Sum: }\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)+\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)+{\\text{CO}}_{2}\\left(g\\right)\\end{array}[\/latex]<\/p>\r\nBecause the CO produced in Step 1 is consumed in Step 2, the net change is:\r\n<p style=\"text-align: center;\">[latex]\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)[\/latex]<\/p>\r\nAccording to Hess\u2019s law, the enthalpy change of the reaction will equal the sum of the enthalpy changes of the steps. We can apply the data from the experimental enthalpies of combustion in Table 1 to find the enthalpy change of the entire reaction from its two steps:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)\\hfill &amp; \\Delta{H}_{298}^{\\circ }=-111\\text{kJ}\\hfill \\\\ \\frac{\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)}{\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)}\\hfill &amp; \\frac{\\Delta{H}_{298}^{\\circ }=-283\\text{kJ}}{\\Delta{H}_{298}^{\\circ }=-394\\text{kJ}}\\hfill \\end{array}[\/latex]<\/p>\r\nThe result is shown in Figure 7. We see that \u0394<em>H<\/em> of the overall reaction is the same whether it occurs in one step or two. This finding (overall \u0394<em>H<\/em> for the reaction = sum of \u0394<em>H<\/em> values for reaction \u201csteps\u201d in the overall reaction) is true in general for chemical and physical processes.\r\n\r\n[caption id=\"attachment_5378\" align=\"aligncenter\" width=\"975\"]<img class=\"size-full wp-image-5378\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033420\/CNX_Chem_05_03_HessCO21.jpg\" alt=\"A diagram is shown. A long arrow faces upward on the left with the phrase \u201cH increasing.\u201d A horizontal line at the bottom of the diagram is shown with the formula \u201cC O subscript 2 (g)\u201d below it. A horizontal line at the top of the diagram has the formulas \u201cC (s) + O subscript 2 (g)\u201d above it. The top and bottom lines are connected by a downward facing arrow with the value \u201c\u0394 H = \u2013394 k J\u201d written beside it. Below and to the right of the top horizontal line is a second horizontal line with the equations \u201cC O (g) + one half O subscript 2 (g)\u201d above it. This line and the bottom line are connected by a downward facing arrow with the value \u201c\u0394 H = \u2013283 k J\u201d written beside it. The same line and the top line are connected by a downward facing arrow with the value \u201c\u0394 H = \u2013111 k J\u201d written beside it. There are three brackets to the right of the diagram. The first bracket runs from the top horizontal line to the second horizontal line. It is labeled, \u201cEnthalpy of reactants.\u201d The second bracket runs from the second horizontal line to the bottom horizontal line. It is labeled, \u201cEnthalpy of products.\u201d Both of these brackets are included in the third bracket which runs from the top to the bottom of the diagram. It is labeled, \u201cEnthalpy change of exothermic reaction in 1 or 2 steps.\u201d\" width=\"975\" height=\"537\" \/> Figure 7. The formation of CO<sub>2<\/sub>(<em>g<\/em>) from its elements can be thought of as occurring in two steps, which sum to the overall reaction, as described by Hess\u2019s law. The horizontal blue lines represent enthalpies. For an exothermic process, the products are at lower enthalpy than are the reactants.[\/caption]\r\n\r\nBefore we further practice using Hess\u2019s law, let us recall two important features of \u0394<em>H<\/em>.\r\n<ol id=\"fs-idp167198464\" data-number-style=\"arabic\">\r\n \t<li>\u0394<em>H<\/em> is directly proportional to the quantities of reactants or products. For example, the enthalpy change for the reaction forming 1 mole of NO<sub>2<\/sub>(<em>g<\/em>) is +33.2 kJ:\r\n<p style=\"text-align: center;\">[latex]\\frac{1}{2}{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{NO}}_{2}\\left(g\\right)\\Delta\\text{H}=\\text{+33.2}\\text{kJ}[\/latex]<\/p>\r\nWhen 2 moles of NO<sub>2<\/sub> (twice as much) are formed, the \u0394<em>H<\/em> will be twice as large:\r\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta\\text{H}=\\text{+66.4}\\text{kJ}[\/latex]<\/p>\r\nIn general, if we multiply or divide an equation by a number, then the enthalpy change should also be multiplied or divided by the same number.<\/li>\r\n \t<li>\u0394<em>H<\/em> for a reaction in one direction is equal in magnitude and opposite in sign to \u0394<em>H<\/em> for the reaction in the reverse direction. For example, given that:\r\n<p style=\"text-align: center;\">[latex]{\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow 2\\text{HCl}\\left(g\\right)\\Delta\\text{H}=-184.6\\text{kJ}[\/latex]<\/p>\r\nThen, for the \u201creverse\u201d reaction, the enthalpy change is also \u201creversed:\u201d\r\n<p style=\"text-align: center;\">[latex]2\\text{HCl}\\left(g\\right)\\rightarrow{\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\Delta\\text{H}=\\text{+184.6}\\text{kJ}[\/latex]<\/p>\r\n<\/li>\r\n<\/ol>\r\n<div class=\"textbox examples\">\r\n<h3>Example 6:\u00a0<strong>Stepwise Calculation of [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] Using Hess\u2019s Law<\/strong><\/h3>\r\nDetermine the enthalpy of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex], of FeCl<sub>3<\/sub>(<em>s<\/em>) from the enthalpy changes of the following two-step process that occurs under standard state conditions:\r\n<p style=\"text-align: center;\">[latex]\\text{Fe}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{2}\\left(s\\right)\\Delta\\text{H}^{\\circ }=-341.8\\text{kJ}[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]{\\text{FeCl}}_{2}\\left(s\\right)+\\frac{1}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{3}\\left(s\\right)\\Delta\\text{H}^{\\circ }=-57.7\\text{kJ}[\/latex]<\/p>\r\n[reveal-answer q=\"783173\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"783173\"]\r\n\r\nWe are trying to find the standard enthalpy of formation of FeCl<sub>3<\/sub>(<em>s<\/em>), which is equal to \u0394<em>H<\/em>\u00b0 for the reaction:\r\n<p style=\"text-align: center;\">[latex]\\text{Fe}\\left(s\\right)+\\frac{3}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{3}\\left(s\\right)\\Delta{H}_{\\text{f}}^{\\circ }=?[\/latex]<\/p>\r\nLooking at the reactions, we see that the reaction for which we want to find \u0394<em>H<\/em>\u00b0 is the sum of the two reactions with known \u0394<em>H<\/em> values, so we must sum their \u0394<em>H<\/em>s:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{lll}\\text{Fe}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{\\text{2}}\\left(s\\right)\\hfill &amp; \\hfill &amp; \\Delta H^{\\circ }=-341.8\\text{kJ}\\hfill \\\\ \\frac{{\\text{FeCl}}_{\\text{2}}\\left(s\\right)+\\frac{1}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{\\text{3}}\\left(s\\right)}{\\text{Fe}\\left(s\\right)+\\frac{\\text{1}}{\\text{2}}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{\\text{3}}\\left(s\\right)}\\hfill &amp; \\hfill &amp; \\frac{\\Delta H^{\\circ }=-57.7\\text{kJ}}{\\Delta H^{\\circ }=-399.5\\text{kJ}}\\hfill \\end{array}[\/latex]<\/p>\r\nThe enthalpy of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex], of FeCl<sub>3<\/sub>(<em>s<\/em>) is \u2212399.5 kJ\/mol.\r\n\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp149511040\"><strong>Check Your Learning<\/strong><\/h4>\r\nCalculate \u0394<em>H<\/em> for the process:\r\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)[\/latex]<\/p>\r\nfrom the following information:\r\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2\\text{NO}\\left(g\\right)\\Delta\\text{H}=180.5\\text{kJ}[\/latex]\r\n[latex]\\text{NO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{NO}}_{2}\\left(g\\right)\\Delta\\text{H}=-57.06\\text{kJ}[\/latex]<\/p>\r\n[reveal-answer q=\"16353\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"16353\"]66.4 kJ[\/hidden-answer]\r\n\r\n<\/div>\r\nHere is a less straightforward example that illustrates the thought process involved in solving many Hess\u2019s law problems. It shows how we can find many standard enthalpies of formation (and other values of \u0394<em>H<\/em>) if they are difficult to determine experimentally.\r\n<div class=\"textbox examples\">\r\n<h3>Example 7:\u00a0<strong>A More Challenging Problem Using Hess\u2019s Law<\/strong><\/h3>\r\nChlorine monofluoride can react with fluorine to form chlorine trifluoride:\r\n\r\n<em>(i)<\/em> [latex]\\text{ClF}\\left(g\\right)+{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{ClF}}_{3}\\left(g\\right)\\Delta\\text{H}^{\\circ }=?[\/latex]\r\n\r\nUse the reactions here to determine the \u0394<em>H<\/em>\u00b0 for reaction <em>(i)<\/em>:\r\n\r\n<em>(ii)<\/em> [latex]2{\\text{OF}}_{2}\\left(g\\right)\\rightarrow{\\text{O}}_{2}\\left(g\\right)+2{\\text{F}}_{2}\\left(g\\right)\\Delta{H}_{\\left(ii\\right)}^{\\circ }=-49.4\\text{kJ}[\/latex]\r\n\r\n<em>(iii)<\/em> [latex]2\\text{ClF}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+{\\text{OF}}_{2}\\left(g\\right)\\Delta{H}_{\\left(iii\\right)}^{\\circ }=\\text{+205.6}\\text{kJ}[\/latex]\r\n\r\n<em>(iv)<\/em> [latex]{\\text{ClF}}_{3}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{3}{2}{\\text{OF}}_{2}\\left(g\\right)\\Delta{H}_{\\left(iv\\right)}^{\\circ }=\\text{+266.7}\\text{kJ}[\/latex]\r\n[reveal-answer q=\"122087\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"122087\"]\r\n\r\nOur goal is to manipulate and combine reactions <em>(ii)<\/em>, <em>(iii)<\/em>, and <em>(iv)<\/em> such that they add up to reaction <em>(i)<\/em>. Going from left to right in <em>(i)<\/em>, we first see that ClF(<em>g<\/em>) is needed as a reactant. This can be obtained by multiplying reaction <em>(iii)<\/em> by [latex]\\frac{1}{2},[\/latex] which means that the \u0394<em>H\u00b0<\/em>\u00a0change is also multiplied by [latex]\\frac{1}{2}\\text{:}[\/latex]\r\n\r\n[latex]\\text{ClF}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{1}{2}{\\text{OF}}_{2}\\left(g\\right)\\Delta\\text{H}^{\\circ }=\\frac{1}{2}\\left(205.6\\right)=\\text{+102.8}\\text{kJ}[\/latex]\r\n\r\nNext, we see that F<sub>2<\/sub> is also needed as a reactant. To get this, reverse and halve reaction <em>(ii)<\/em>, which means that the \u0394<em>H<\/em>\u00b0 changes sign and is halved:\r\n\r\n[latex]\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)+{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{OF}}_{2}\\left(g\\right)\\Delta\\text{H}^{\\circ }=\\text{+24.7}\\text{kJ}[\/latex]\r\n\r\nTo get ClF<sub>3<\/sub> as a product, reverse <em>(iv)<\/em>, changing the sign of \u0394<em>H<\/em>\u00b0:\r\n\r\n[latex]\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{3}{2}{\\text{OF}}_{2}\\left(g\\right)\\rightarrow{\\text{ClF}}_{3}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\Delta\\text{H}^{\\circ }=\\text{+266.7}\\text{kJ}[\/latex]\r\n\r\nNow check to make sure that these reactions add up to the reaction we want:\r\n\r\n[latex]\\begin{array}{lll}\\text{ClF}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{1}{2}{\\text{OF}}_{2}\\left(g\\right)\\hfill &amp; \\hfill &amp; \\Delta H^{\\circ }=\\text{+102.8}\\text{kJ}\\hfill \\\\ \\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)+{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{OF}}_{2}\\left(g\\right)\\hfill &amp; \\hfill &amp; \\Delta H^{\\circ }=\\text{+24.7}\\text{kJ}\\hfill \\\\ \\frac{\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{3}{2}{\\text{OF}}_{2}\\left(g\\right)\\rightarrow{\\text{ClF}}_{3}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)}{\\text{ClF}\\left(g\\right)+{\\text{F}}_{2}\\rightarrow{\\text{ClF}}_{3}\\left(g\\right)\\phantom{\\rule{8em}{0ex}}}\\hfill &amp; \\hfill &amp; \\frac{\\Delta H^{\\circ }=-266.7\\text{kJ}}{\\Delta H^{\\circ }=-139.2\\text{kJ}}\\hfill \\end{array}[\/latex]\r\n\r\nReactants [latex]\\frac{1}{2}{\\text{O}}_{2}[\/latex] and [latex]\\frac{1}{2}{\\text{O}}_{2}[\/latex] cancel out product O<sub>2<\/sub>; product [latex]\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}[\/latex] cancels reactant [latex]\\frac{1}{2}{\\text{Cl}}_{2}\\text{O;}[\/latex] and reactant [latex]\\frac{3}{2}{\\text{OF}}_{2}[\/latex] is cancelled by products [latex]\\frac{1}{2}{\\text{OF}}_{2}[\/latex] and OF<sub>2<\/sub>. This leaves only reactants ClF(<em>g<\/em>) and F<sub>2<\/sub>(<em>g<\/em>) and product ClF<sub>3<\/sub>(<em>g<\/em>), which are what we want. Since summing these three modified reactions yields the reaction of interest, summing the three modified \u0394<em>H<\/em>\u00b0 values will give the desired \u0394<em>H<\/em>\u00b0:\r\n\r\n[latex]\\Delta H^{\\circ }=\\left(+102.8\\text{kJ}\\right)+\\left(24.7\\text{kJ}\\right)+\\left(-266.7\\text{kJ}\\right)=-139.2\\text{kJ}[\/latex]\r\n\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp154380128\"><strong>Check Your Learning<\/strong><\/h4>\r\nAluminum chloride can be formed from its elements:\r\n\r\n<em>(i)<\/em> [latex]2\\text{Al}\\left(s\\right)+3{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow 2{\\text{AlCl}}_{3}\\left(s\\right)\\Delta H^{\\circ }=?[\/latex]\r\n\r\nUse the reactions here to determine the \u0394<em>H<\/em>\u00b0 for reaction <em>(i)<\/em>:\r\n\r\n<em>(ii)<\/em> [latex]\\text{HCl}\\left(g\\right)\\rightarrow\\text{HCl}\\left(aq\\right)\\Delta{H}_{\\left(ii\\right)}^{\\circ }=-74.8\\text{kJ}[\/latex]\r\n\r\n<em>(iii)<\/em> [latex]{\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow 2\\text{HCl}\\left(g\\right)\\Delta{H}_{\\left(iii\\right)}^{\\circ }=-185\\text{kJ}[\/latex]\r\n\r\n<em>(iv)<\/em> [latex]{\\text{AlCl}}_{3}\\left(aq\\right)\\rightarrow{\\text{AlCl}}_{3}\\left(s\\right)\\Delta{H}_{\\left(iv\\right)}^{\\circ }=+323\\text{kJ\/mol}[\/latex]\r\n\r\n<em>(v)<\/em> [latex]\\text{2Al}\\left(s\\right)+6\\text{HCl}\\left(aq\\right)\\rightarrow 2{\\text{AlCl}}_{3}\\left(aq\\right)+3{\\text{H}}_{2}\\left(g\\right)\\Delta{H}_{\\left(v\\right)}^{\\circ }=-1049\\text{kJ}[\/latex]\r\n[reveal-answer q=\"15946\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"15946\"]\u20131407 kJ[\/hidden-answer]\r\n\r\n<\/div>\r\nWe also can use <strong>Hess\u2019s law<\/strong> to determine the enthalpy change of any reaction if the corresponding enthalpies of formation of the reactants and products are available. The stepwise reactions we consider are: (i) decompositions of the reactants into their component elements (for which the enthalpy changes are proportional to the negative of the enthalpies of formation of the reactants), followed by (ii) re-combinations of the elements to give the products (with the enthalpy changes proportional to the enthalpies of formation of the products). The standard enthalpy change of the overall reaction is therefore equal to: (ii) the sum of the standard enthalpies of formation of all the products plus (i) the sum of the negatives of the standard enthalpies of formation of the reactants. This is usually rearranged slightly to be written as follows, with \u2211 representing \u201cthe sum of\u201d and <em>n<\/em> standing for the stoichiometric coefficients:\r\n<p style=\"text-align: center;\">[latex]\\Delta{H}_{\\text{reaction}}^{\\circ }=\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left(\\text{products}\\right)-\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left(\\text{reactants}\\right)[\/latex]<\/p>\r\nThe following example shows in detail why this equation is valid, and how to use it to calculate the enthalpy change for a reaction of interest.\r\n<div class=\"textbox examples\">\r\n<h3>Example 8:\u00a0<strong>Using Hess\u2019s Law<\/strong><\/h3>\r\nWhat is the standard enthalpy change for the reaction:\r\n<p style=\"text-align: center;\">[latex]3{\\text{NO}}_{2}\\left(g\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow 2{\\text{HNO}}_{3}\\left(aq\\right)+\\text{NO}\\left(g\\right)\\Delta\\text{H}^{\\circ }=?[\/latex]<\/p>\r\nThere are two possible solutions for this reaction. The first solution supports why the general equation is valid, the second solution uses the equation.\r\n[reveal-answer q=\"511660\"]Show Solution 1[\/reveal-answer]\r\n[hidden-answer a=\"511660\"]\r\n<h4 id=\"fs-idp134564208\">Solution 1 (Supporting Why the General Equation Is Valid)<\/h4>\r\nWe can write this reaction as the sum of the decompositions of 3NO<sub>2<\/sub>(<em>g<\/em>) and 1H<sub>2<\/sub>O(<em>l<\/em>) into their constituent elements, and the formation of 2HNO<sub>3<\/sub>(<em>aq<\/em>) and 1NO(<em>g<\/em>) from their constituent elements. Writing out these reactions, and noting their relationships to the [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] values for these compounds (from <a title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>), we have:\r\n<p style=\"text-align: center;\">[latex]3{\\text{NO}}_{2}\\left(g\\right)\\rightarrow{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\Delta{H}_{1}^{\\circ }=99.6\\text{kJ}[\/latex]\r\n[latex]{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\Delta{H}_{2}^{\\circ }=\\text{+285.8}\\text{kJ}\\left[-1\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left({\\text{H}}_{2}\\text{O}\\right)\\right][\/latex]\r\n[latex]{\\text{H}}_{2}\\left(g\\right)+{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{HNO}}_{3}\\left(aq\\right)\\Delta{H}_{3}^{\\circ }=414.8\\text{kJ}\\left[2\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left({\\text{HNO}}_{3}\\right)\\right][\/latex]\r\n[latex]\\frac{1}{2}{\\text{N}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{NO}\\left(g\\right)\\Delta{H}_{4}^{\\circ }=\\text{+90.2}\\text{kJ}\\left[1\\times \\left(\\text{NO}\\right)\\right][\/latex]<\/p>\r\nSumming these reaction equations gives the reaction we are interested in:\r\n<p style=\"text-align: center;\">[latex]{\\text{3NO}}_{2}\\left(g\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow 2{\\text{HNO}}_{3}\\left(aq\\right)+\\text{NO}\\left(g\\right)[\/latex]<\/p>\r\nSumming their enthalpy changes gives the value we want to determine:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{cc}\\hfill \\Delta{H}_{\\text{rxn}}^{\\circ }&amp; =\\Delta{H}_{1}^{\\circ }+\\Delta{H}_{2}^{\\circ }+\\Delta{H}_{3}^{\\circ }+\\Delta{H}_{4}^{\\circ }=\\left(-99.6\\text{kJ}\\right)+\\left(\\text{+285.8}\\text{kJ}\\right)+\\left(-414.8\\text{kJ}\\right)+\\left(\\text{+90.2}\\text{kJ}\\right)\\hfill \\\\ &amp; =-138.4\\text{kJ.}\\hfill \\end{array}[\/latex]<\/p>\r\nSo the standard enthalpy change for this reaction is \u0394<em>H<\/em>\u00b0 = \u2212138.4 kJ.\r\n\r\nNote that this result was obtained by (1) multiplying the [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of each product by its stoichiometric coefficient and summing those values, (2) multiplying the [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of each reactant by its stoichiometric coefficient and summing those values, and then (3) subtracting the result found in (2) from the result found in (1). This is also the procedure in using the general equation, as shown.\r\n\r\n[\/hidden-answer]\r\n[reveal-answer q=\"565595\"]Show Solution 2[\/reveal-answer]\r\n[hidden-answer a=\"565595\"]\r\n<h4 id=\"fs-idp146127120\">Solution 2 (Using the Equation)<\/h4>\r\nAlternatively, we could use the special form of Hess\u2019s law given previously:\r\n<p style=\"text-align: center;\">[latex]\\Delta{H}_{\\text{reaction}}^{\\circ }=\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\text{(products)}-\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left(\\text{reactants}\\right)[\/latex]<\/p>\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}\\\\ =\\left[2\\cancel{\\text{mol}{\\text{HNO}}_{3}}\\times \\frac{-207.4\\text{kJ}}{\\cancel{\\text{mol}{\\text{HNO}}_{3}\\left(aq\\right)}}+1\\cancel{\\text{mol}\\text{NO}\\left(g\\right)}\\times \\frac{\\text{+90.2}\\text{kJ}}{\\cancel{\\text{mol}\\text{NO}\\left(g\\right)}}\\right]\\\\ -\\left[3\\cancel{\\text{mol}{\\text{NO}}_{2}\\left(g\\right)}\\times \\frac{\\text{+33.2}\\text{kJ}}{\\cancel{\\text{mol}{\\text{NO}}_{2}\\left(g\\right)}}+1\\cancel{\\text{mol}{\\text{H}}_{2}\\text{O}\\left(l\\right)}\\times \\frac{-285.8\\text{kJ}}{\\cancel{\\text{mol}{\\text{H}}_{2}\\text{O}\\left(l\\right)}}\\right]\\\\ =2\\left(-207.4\\text{kJ}\\right)+1\\left(\\text{+90.2}\\text{kJ}\\right)-3\\left(\\text{+33.2}\\text{kJ}\\right)-1\\left(-285.8\\text{kJ}\\right)\\\\ =-138.4\\text{kJ}\\end{array}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n<h4 id=\"fs-idp165556368\"><strong>Check Your Learning<\/strong><\/h4>\r\nCalculate the heat of combustion of 1 mole of ethanol, C<sub>2<\/sub>H<sub>5<\/sub>OH(<em>l<\/em>), when H<sub>2<\/sub>O(<em>l<\/em>) and CO<sub>2<\/sub>(<em>g<\/em>) are formed. Use the following enthalpies of formation: C<sub>2<\/sub>H<sub>5<\/sub>OH(<em>l<\/em>), \u2212278 kJ\/mol; H<sub>2<\/sub>O(<em>l<\/em>), \u2212286 kJ\/mol; and CO<sub>2<\/sub>(<em>g<\/em>), \u2212394 kJ\/mol.\r\n\r\n[reveal-answer q=\"509110\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"509110\"]\u20131368 kJ\/mol[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<ol>\r\n \t<li>Calculate the standard molar enthalpy of formation of NO(<em>g<\/em>) from the following data: [latex]\\begin{array}{l}{\\text{N}}_{2}\\left(g\\right)+2{\\text{O}}_{2}\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=66.4\\text{kJ}\\\\ \\text{2NO}\\left(g\\right)+{\\text{O}}_{2}\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-114.1\\text{kJ}\\end{array}[\/latex]<\/li>\r\n \t<li>Using the data in <a class=\"target-chapter\" title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, calculate the standard enthalpy change for each of the following reactions:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2\\text{NO}\\left(g\\right)[\/latex]<\/li>\r\n \t<li>[latex]\\text{Si}\\left(s\\right)+2{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SiCl}}_{4}\\left(g\\right)[\/latex]<\/li>\r\n \t<li>[latex]{\\text{Fe}}_{2}\\text{O}\\left(s\\right)+3{\\text{H}}_{2}\\left(g\\right)\\rightarrow 2\\text{Fe}\\left(s\\right)+3{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/li>\r\n \t<li>[latex]2\\text{LiOH}\\left(s\\right)+{\\text{CO}}_{2}\\left(g\\right)\\rightarrow{\\text{Li}}_{2}{\\text{CO}}_{3}\\left(s\\right)+{\\text{H}}_{2}\\text{O}\\left(g\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Using the data in <a class=\"target-chapter\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\">Standard Thermodynamic Properties for Selected Substances<\/a>, calculate the standard enthalpy change for each of the following reactions:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\\text{Si}\\left(s\\right)+2{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{SiF}}_{4}\\left(g\\right)[\/latex]<\/li>\r\n \t<li>[latex]2\\text{C}\\left(s\\right)+2{\\text{H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CH}}_{3}{\\text{CO}}_{2}\\text{H}\\left(l\\right)[\/latex]<\/li>\r\n \t<li>[latex]{\\text{CH}}_{4}\\left(g\\right)+{\\text{N}}_{2}\\left(g\\right)\\rightarrow\\text{HCN}\\left(g\\right){\\text{+NH}}_{3}\\left(g\\right)\\text{;}[\/latex]<\/li>\r\n \t<li>[latex]{\\text{Cs}}_{2}\\left(g\\right)+3{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{CCl}}_{4}\\left(g\\right){\\text{+S}}_{2}{\\text{Cl}}_{2}\\left(g\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>The following reactions can be used to prepare samples of metals. Determine the enthalpy change under standard state conditions for each.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]2{\\text{Ag}}_{2}\\text{O}\\left(s\\right)\\rightarrow 4\\text{Ag}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)[\/latex]<\/li>\r\n \t<li>[latex]\\text{SnO}\\left(s\\right)+\\text{CO}\\left(g\\right)\\rightarrow\\text{Sn}\\left(s\\right)+{\\text{CO}}_{2}\\left(g\\right)[\/latex]<\/li>\r\n \t<li>[latex]{\\text{Cr}}_{2}{\\text{O}}_{3}\\left(s\\right)+3{\\text{H}}_{2}\\left(g\\right)\\rightarrow 2\\text{Cr}\\left(s\\right)+3{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/li>\r\n \t<li>[latex]2\\text{Al}\\left(s\\right)+{\\text{Fe}}_{2}{\\text{O}}_{3}\\left(s\\right)\\rightarrow{\\text{Al}}_{2}{\\text{O}}_{3}\\left(s\\right)+2\\text{Fe}\\left(s\\right)[\/latex]<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>The decomposition of hydrogen peroxide, H<sub>2<\/sub>O<sub>2<\/sub>, has been used to provide thrust in the control jets of various space vehicles. Using the data in <a class=\"target-chapter\" title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, determine how much heat is produced by the decomposition of exactly 1 mole of H<sub>2<\/sub>O<sub>2<\/sub> under standard conditions. [latex]2{\\text{H}}_{2}{\\text{O}}_{2}\\left(l\\right)\\rightarrow 2{\\text{H}}_{2}\\text{O}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)[\/latex]<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"835105\"]Show Selected Answers[\/reveal-answer]\r\n[hidden-answer a=\"835105\"]\r\n\r\n1. Hess\u2019s law can be applied to the two equations by reversing the direction of the second equation. The first equation is a formation reaction and is so indicated by writing [latex]\\Delta{H}_{298}^{\\circ }[\/latex].\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}{\\text{N}}_{2}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=66.4\\text{kJ}\\\\ 2{\\text{NO}}_{\\text{2}}\\left(g\\right)\\rightarrow 2\\text{NO}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\Delta H^{\\circ }=114.1\\text{kJ}\\end{array}[\/latex]<\/p>\r\nAdding the equations yields:\r\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2\\text{NO}\\left(g\\right)\\Delta{H}^{\\circ }=180.5\\text{kJ}.[\/latex]<\/p>\r\nThis is the heat of formation of 2 mol of NO. For 1 mol,\r\n<p style=\"text-align: center;\">[latex]\\Delta{H}_{298}^{\\circ }=\\frac{180.5\\text{kJ}}{2}=90.3{\\text{mol}}^{-1}\\text{of}\\text{NO}.[\/latex]<\/p>\r\n3. The standard enthalpy changes are as follows:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>[latex]\\text{Si}\\left(s\\right)+2{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{SiF}}_{4}\\left(g\\right)[\/latex]\r\n[latex]\\begin{array}{rll} \\\\ \\Delta{H}_{\\text{reaction}}^{\\circ }&amp;=&amp;\\Delta{H}_{\\text{products}}^{\\circ }-\\Delta{H}_{\\text{reactants}}^{\\circ }\\\\ &amp;=&amp;\\Delta{H}_{{\\text{SiF}}_{4}\\left(g\\right)}^{\\circ }-\\Delta{H}_{\\text{Si}\\left(s\\right)}^{\\circ }-2\\Delta{H}_{{\\text{F}}_{2}\\left(g\\right)}^{\\circ }\\\\ &amp;=&amp;-1614.9-\\left(0\\right)-2\\left(0\\right)=-1615.0\\text{kJ}{\\text{mol}}^{-1}\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]2\\text{C}\\left(s\\right)+2{\\text{H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CH}}_{3}{\\text{CO}}_{2}\\text{H}\\left(l\\right)[\/latex]\r\n[latex]\\begin{array}{rll} \\\\ \\Delta{H}_{\\text{reaction}}^{\\circ }&amp;=&amp;\\Delta{H}_{\\text{products}}^{\\circ }-\\Delta{H}_{\\text{reactants}}^{\\circ }\\\\ &amp;=&amp;\\Delta{H}_{{\\text{CH}}_{3}{\\text{CO}}_{2}\\text{H}\\left(l\\right)}^{\\circ }-2\\Delta{H}_{\\text{C}\\left(s\\right)}^{\\circ }-2\\Delta{H}_{{\\text{H}}_{2}\\left(g\\right)}^{\\circ }-\\Delta{H}_{{\\text{O}}_{2}\\left(g\\right)}^{\\circ }\\\\ &amp;=&amp;-484.5-2\\left(0\\right)-2\\left(0\\right)-\\left(0\\right)=-484.3\\text{kJ}{\\text{mol}}^{-1}\\end{array}[\/latex]<\/li>\r\n \t<li>[latex]{\\text{CH}}_{\\text{4}}\\left(g\\right)\\rightarrow\\text{C}\\left(s\\right)+2{\\text{H}}_{2}\\left(g\\right)\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\Delta{H}_{1}^{\\circ }=-\\left(-74.6\\text{kJ}\\right)[\/latex]\r\n[latex]\\begin{array}{lll} \\\\ \\frac{\\text{1}}{\\text{2}}{\\text{H}}_{\\text{2}}\\left(g\\right)+\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{N}}_{2}\\left(g\\right)\\rightarrow\\text{HCN}\\left(g\\right)\\hfill &amp; \\hfill &amp; \\Delta{H}_{2}^{\\circ }=135.5\\text{kJ}\\hfill \\\\ \\frac{\\frac{\\text{1}}{\\text{2}}{\\text{N}}_{\\text{2}}\\left(g\\right)+\\frac{3}{2}{\\text{H}}_{2}\\left(g\\right)\\rightarrow{\\text{NH}}_{3}\\left(g\\right)}{{\\text{CH}}_{4}\\left(g\\right)+{\\text{N}}_{2}\\left(g\\right)\\rightarrow\\text{HCN}\\left(g\\right)+{\\text{NH}}_{3}\\left(g\\right)}\\hfill &amp; \\hfill &amp; \\frac{\\Delta{H}_{3}^{\\circ }=-45.9\\text{kJ}}{\\Delta H^{\\circ }=164.2\\text{kJ}}\\hfill \\end{array}[\/latex]<\/li>\r\n \t<li>[latex]{\\text{CS}}_{\\text{2}}\\left(g\\right)\\rightarrow\\text{C}\\left(s\\right)+2S\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\Delta{H}_{1}^{\\circ }=-\\left(116.9\\text{kJ}\\right)[\/latex]\r\n[latex]\\begin{array}{lll} \\\\ \\text{C}\\left(s\\right)+2{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{CCl}}_{\\text{4}}\\left(g\\right)\\hfill &amp; \\hfill &amp; \\Delta{H}_{2}^{\\circ }=-95.7\\text{kJ}\\hfill \\\\ \\frac{2\\text{S}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{S}}_{2}{\\text{Cl}}_{2}\\left(g\\right)}{{\\text{CS}}_{2}\\left(g\\right)+3{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{CCl}}_{4}\\left(g\\right)+{\\text{S}}_{\\text{2}}{\\text{Cl}}_{2}\\left(g\\right)}\\hfill &amp; \\hfill &amp; \\frac{\\Delta{H}_{3}^{\\circ }=-19.50\\text{kJ}}{\\Delta H^{\\circ }=-232.1\\text{kJ}}\\hfill \\end{array}[\/latex]<\/li>\r\n<\/ol>\r\n5. To determine how much heat is produced, we use the following equation:\r\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\Delta{H}_{\\text{reaction}}^{\\circ }&amp; =&amp; \\Delta{H}_{\\text{products}}^{\\circ }-\\Delta{H}_{\\text{reactants}}^{\\circ }\\hfill \\\\ &amp; =&amp; 2\\Delta{H}_{{\\text{H}}_{2}\\text{O}\\left(g\\right)}^{\\circ }+\\Delta{H}_{{\\text{O}}_{2}\\left(g\\right)}^{\\circ }-2\\Delta{H}_{{\\text{H}}_{2}{\\text{O}}_{2}\\left(l\\right)}^{\\circ }\\hfill \\\\ &amp; =&amp; 2\\left(-241.82\\right)+0-2\\left(-187.78\\right)=-108.08\\text{kJ}\\hfill \\end{array}[\/latex]<\/p>\r\nThe value relates to the decomposition of 2 mol of hydrogen peroxide. For 1 mol,\r\n<p style=\"text-align: center;\">[latex]\\frac{-108.0}{2}=-54.04\\text{kJ}{\\text{mol}}^{-1}[\/latex]<\/p>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Concepts and Summary<\/h3>\r\nIf a chemical change is carried out at constant pressure and the only work done is caused by expansion or contraction, <em>q<\/em> for the change is called the enthalpy change with the symbol \u0394<em>H<\/em>, or [latex]\\Delta{H}_{\\text{298}}^{\\circ }[\/latex] for reactions occurring under standard state conditions. The value of \u0394<em>H<\/em> for a reaction in one direction is equal in magnitude, but opposite in sign, to \u0394<em>H<\/em> for the reaction in the opposite direction, and \u0394<em>H<\/em> is directly proportional to the quantity of reactants and products. Examples of enthalpy changes include enthalpy of combustion, enthalpy of fusion, enthalpy of vaporization, and standard enthalpy of formation. The standard enthalpy of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ },[\/latex] is the enthalpy change accompanying the formation of 1 mole of a substance from the elements in their most stable states at 1 bar (standard state). Many of the processes are carried out at 298.15 K. If the enthalpies of formation are available for the reactants and products of a reaction, the enthalpy change can be calculated using Hess\u2019s law: If a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps.\r\n<h4>Key Equations<\/h4>\r\n<ul>\r\n \t<li>[latex]\\Delta U=q+w[\/latex]<\/li>\r\n \t<li>[latex]\\Delta{H}_{\\text{reaction}}^{\\circ }=\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\text{(products)}-\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left(\\text{reactants}\\right)[\/latex]<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<ol>\r\n \t<li>Which of the enthalpies of combustion in Table 1 are also standard enthalpies of formation?<\/li>\r\n \t<li>Calculate \u0394<em>H<\/em> for the process [latex]{\\text{Hg}}_{2}{\\text{Cl}}_{2}\\left(s\\right)\\rightarrow 2\\text{Hg}\\left(l\\right)+{\\text{Cl}}_{2}\\left(g\\right)[\/latex] from the following information:[latex]\\begin{array}{l}\\\\ \\text{Hg}\\left(l\\right)+{\\text{Cl}}_{\\text{2}}\\left(g\\right)\\rightarrow{\\text{HgCl}}_{\\text{2}}\\left(s\\right)\\Delta H=-224\\text{kJ}\\\\ \\text{Hg}\\left(l\\right)+{\\text{HgCl}}_{\\text{2}}\\left(s\\right)\\rightarrow{\\text{Hg}}_{\\text{2}}{\\text{Cl}}_{2}\\left(s\\right)\\Delta H=-41.2\\text{kJ}\\end{array}[\/latex]<\/li>\r\n \t<li>Calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for the process [latex]{\\text{Co}}_{3}{\\text{O}}_{4}\\left(s\\right)\\rightarrow 3\\text{Co}\\left(s\\right)+2{\\text{O}}_{2}\\left(g\\right)[\/latex] from the following information: [latex]\\begin{array}{l}\\\\ \\text{Co}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CoO}\\left(s\\right)\\Delta{H}_{298}^{\\circ }=-237.9\\text{kJ}\\\\ \\text{3Co}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Co}}_{3}{\\text{O}}_{4}\\left(s\\right)\\Delta{H}_{298}^{\\circ }=-177.5\\text{kJ}\\end{array}[\/latex]<\/li>\r\n \t<li>Calculate the enthalpy of combustion of propane, C<sub>3<\/sub>H<sub>8<\/sub>(<em>g<\/em>), for the formation of H<sub>2<\/sub>O(<em>g<\/em>) and CO<sub>2<\/sub>(<em>g<\/em>). The enthalpy of formation of propane is \u2212104 kJ\/mol.<\/li>\r\n \t<li>Calculate the enthalpy of combustion of butane, C<sub>4<\/sub>H<sub>10<\/sub>(<em>g<\/em>) for the formation of H<sub>2<\/sub>O(<em>g<\/em>) and CO<sub>2<\/sub>(<em>g<\/em>). The enthalpy of formation of butane is \u2212126 kJ\/mol.<\/li>\r\n \t<li>Both propane and butane are used as gaseous fuels. Which compound produces more heat per gram when burned?<\/li>\r\n \t<li>The white pigment TiO<sub>2<\/sub> is prepared by the reaction of titanium tetrachloride, TiCl<sub>4<\/sub>, with water vapor in the gas phase: [latex]{\\text{TiCl}}_{4}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow{\\text{TiO}}_{2}\\left(s\\right)+4\\text{HCl}\\left(g\\right)[\/latex]. How much heat is evolved in the production of exactly 1 mole of TiO<sub>2<\/sub>(<em>s<\/em>) under standard state conditions?<\/li>\r\n \t<li>Water gas, a mixture of H<sub>2<\/sub> and CO, is an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon: [latex]\\text{C}\\left(s\\right)+{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)+{\\text{H}}_{2}\\left(g\\right).[\/latex]\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Assuming that coke has the same enthalpy of formation as graphite, calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for this reaction.<\/li>\r\n \t<li>Methanol, a liquid fuel that could possibly replace gasoline, can be prepared from water gas and additional hydrogen at high temperature and pressure in the presence of a suitable catalyst: [latex]2{\\text{H}}_{2}\\left(g\\right)+\\text{CO}\\left(g\\right)\\rightarrow{\\text{CH}}_{3}\\text{OH}\\left(g\\right)[\/latex]. Under the conditions of the reaction, methanol forms as a gas. Calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for this reaction and for the condensation of gaseous methanol to liquid methanol.<\/li>\r\n \t<li>Calculate the heat of combustion of 1 mole of liquid methanol to H<sub>2<\/sub>O(<em>g<\/em>) and CO<sub>2<\/sub>(<em>g<\/em>).<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>In the early days of automobiles, illumination at night was provided by burning acetylene, C<sub>2<\/sub>H<sub>2<\/sub>. Though no longer used as auto headlamps, acetylene is still used as a source of light by some cave explorers. The acetylene is (was) prepared in the lamp by the reaction of water with calcium carbide, CaC<sub>2<\/sub>: [latex]{\\text{CaC}}_{2}\\left(s\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow\\text{Ca}{\\left(\\text{OH}\\right)}_{2}\\left(s\\right)+{\\text{C}}_{2}{\\text{H}}_{2}\\left(g\\right).[\/latex] Calculate the standard enthalpy of the reaction. The [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of CaC<sub>2<\/sub> is \u221215.14 kcal\/mol.<\/li>\r\n \t<li>From the data in Table 1, determine which of the following fuels produces the greatest amount of heat per gram when burned under standard conditions: CO(<em>g<\/em>), CH<sub>4<\/sub>(<em>g<\/em>), or C<sub>2<\/sub>H<sub>2<\/sub>(<em>g<\/em>).<\/li>\r\n \t<li>The enthalpy of combustion of hard coal averages \u221235 kJ\/g, that of gasoline, 1.28 \u00d7 10<sup>5<\/sup> kJ\/gal. How many kilograms of hard coal provide the same amount of heat as is available from 1.0 gallon of gasoline? Assume that the density of gasoline is 0.692 g\/mL (the same as the density of isooctane).<\/li>\r\n \t<li>Ethanol, C<sub>2<\/sub>H<sub>5<\/sub>OH, is used as a fuel for motor vehicles, particularly in Brazil.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Write the balanced equation for the combustion of ethanol to CO<sub>2<\/sub>(<em>g<\/em>) and H<sub>2<\/sub>O(<em>g<\/em>), and, using the data in <a class=\"target-chapter\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, calculate the enthalpy of combustion of 1 mole of ethanol.<\/li>\r\n \t<li>The density of ethanol is 0.7893 g\/mL. Calculate the enthalpy of combustion of exactly 1 L of ethanol.<\/li>\r\n \t<li>Assuming that an automobile\u2019s mileage is directly proportional to the heat of combustion of the fuel, calculate how much farther an automobile could be expected to travel on 1 L of gasoline than on 1 L of ethanol. Assume that gasoline has the heat of combustion and the density of n\u2013octane, C<sub>8<\/sub>H<sub>18<\/sub> [latex]\\left(\\Delta{H}_{\\text{f}}^{\\circ }=-208.4\\text{kJ\/mol}\\right)[\/latex] density = 0.7025 g\/mL).<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Among the substances that react with oxygen and that have been considered as potential rocket fuels are diborane [B<sub>2<\/sub>H<sub>6<\/sub>, produces B<sub>2<\/sub>O<sub>3<\/sub>(<em>s<\/em>) and H<sub>2<\/sub>O(<em>g<\/em>)], methane [CH<sub>4<\/sub>, produces CO<sub>2<\/sub>(<em>g<\/em>) and H<sub>2<\/sub>O(<em>g<\/em>)], and hydrazine [N<sub>2<\/sub>H<sub>4<\/sub>, produces N<sub>2<\/sub>(<em>g<\/em>) and H<sub>2<\/sub>O(<em>g<\/em>)]. On the basis of the heat released by 1.00 g of each substance in its reaction with oxygen, which of these compounds offers the best possibility as a rocket fuel? The [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of B<sub>2<\/sub>H<sub>6<\/sub>(<em>g<\/em>), CH<sub>4<\/sub>(<em>g<\/em>), and N<sub>2<\/sub>H<sub>4<\/sub>(<em>l<\/em>) may be found in <a class=\"target-chapter\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>.<\/li>\r\n \t<li>How much heat is produced when 1.25 g of chromium metal reacts with oxygen gas under standard conditions?<\/li>\r\n \t<li>Ethylene, C<sub>2<\/sub>H<sub>2<\/sub>, a byproduct from the fractional distillation of petroleum, is fourth among the 50 chemical compounds produced commercially in the largest quantities. About 80% of synthetic ethanol is manufactured from ethylene by its reaction with water in the presence of a suitable catalyst. [latex]{\\text{C}}_{2}{\\text{H}}_{4}\\left(g\\right)+{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)[\/latex] Using the data in the table in <a class=\"target-chapter\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, calculate \u0394<em>H<\/em>\u00b0 for the reaction.<\/li>\r\n \t<li>The oxidation of the sugar glucose, C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>, is described by the following equation: [latex]{\\text{C}}_{6}{\\text{H}}_{12}{\\text{O}}_{6}\\left(s\\right)+6{\\text{O}}_{2}\\left(g\\right)\\rightarrow 6{\\text{CO}}_{2}\\left(g\\right)+6{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=-2816\\text{kJ}[\/latex] The metabolism of glucose gives the same products, although the glucose reacts with oxygen in a series of steps in the body.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>How much heat in kilojoules can be produced by the metabolism of 1.0 g of glucose?<\/li>\r\n \t<li>How many Calories can be produced by the metabolism of 1.0 g of glucose?<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Propane, C<sub>3<\/sub>H<sub>8<\/sub>, is a hydrocarbon that is commonly used as a fuel.\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Write a balanced equation for the complete combustion of propane gas.<\/li>\r\n \t<li>Calculate the volume of air at 25 \u00b0C and 1.00 atmosphere that is needed to completely combust 25.0 grams of propane. Assume that air is 21.0 percent O<sub>2<\/sub> by volume. (Hint: we will see how to do this calculation in a later chapter on gases\u2014for now use the information that 1.00 L of air at 25 \u00b0C and 1.00 atm contains 0.275 g of O<sub>2<\/sub> per liter.)<\/li>\r\n \t<li>The heat of combustion of propane is -2,219.2 kJ\/mol. Calculate the heat of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of propane given that [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of H<sub>2<\/sub>O(<em>l<\/em>) = \u2212285.8 kJ\/mol and [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of CO<sub>2<\/sub>(<em>g<\/em>) = \u2212393.5 kJ\/mol.<\/li>\r\n \t<li>Assuming that all of the heat released in burning 25.0 grams of propane is transferred to 4.00 kilograms of water, calculate the increase in temperature of the water.<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>During a recent winter month in Sheboygan, Wisconsin, it was necessary to obtain 3500 kWh of heat provided by a natural gas furnace with 89% efficiency to keep a small house warm (the efficiency of a gas furnace is the percent of the heat produced by combustion that is transferred into the house).\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>Assume that natural gas is pure methane and determine the volume of natural gas in cubic feet that was required to heat the house. The average temperature of the natural gas was 56 \u00b0F; at this temperature and a pressure of 1 atm, natural gas has a density of 0.681 g\/L.<\/li>\r\n \t<li>How many gallons of LPG (liquefied petroleum gas) would be required to replace the natural gas used? Assume the LPG is liquid propane [C<sub>3<\/sub>H<sub>8<\/sub>: density, 0.5318 g\/mL; enthalpy of combustion, 2219 kJ\/mol for the formation of CO<sub>2<\/sub>(<em>g<\/em>) and H<sub>2<\/sub>O(<em>l<\/em>)] and the furnace used to burn the LPG has the same efficiency as the gas furnace.<\/li>\r\n \t<li>What mass of carbon dioxide is produced by combustion of the methane used to heat the house?<\/li>\r\n \t<li>What mass of water is produced by combustion of the methane used to heat the house?<\/li>\r\n \t<li>What volume of air is required to provide the oxygen for the combustion of the methane used to heat the house? Air contains 23% oxygen by mass. The average density of air during the month was 1.22 g\/L.<\/li>\r\n \t<li>How many kilowatt\u2013hours (1 kWh = 3.6 \u00d7 10<sup>6<\/sup> J) of electricity would be required to provide the heat necessary to heat the house? Note electricity is 100% efficient in producing heat inside a house.<\/li>\r\n \t<li>Although electricity is 100% efficient in producing heat inside a house, production and distribution of electricity is not 100% efficient. The efficiency of production and distribution of electricity produced in a coal-fired power plant is about 40%. A certain type of coal provides 2.26 kWh per pound upon combustion. What mass of this coal in kilograms will be required to produce the electrical energy necessary to heat the house if the efficiency of generation and distribution is 40%?<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"659342\"]Show Selected Answers[\/reveal-answer]\r\n[hidden-answer a=\"659342\"]\r\n\r\n2. Reverse the direction of both equations and add the new equations and enthalpies.\r\n\r\n[latex]\\begin{array}{lll}{\\text{HgCl}}_{2}\\rightarrow\\text{Hg}\\left(l\\right)+{\\text{Cl}}_{2}\\left(l\\right)\\hfill &amp; \\hfill &amp; \\Delta H=224\\text{kJ}\\hfill \\\\ \\frac{{\\text{Hg}}_{\\text{2}}{\\text{Cl}}_{2}\\left(s\\right)\\rightarrow\\text{Hg}\\left(l\\right)+{\\text{HgCl}}_{2}\\left(s\\right)}{{\\text{Hg}}_{\\text{2}}{\\text{Cl}}_{2}\\left(s\\right)\\rightarrow 2\\text{Hg}\\left(l\\right)+{\\text{Cl}}_{2}\\left(g\\right)}\\hfill &amp; \\hfill &amp; \\frac{\\Delta H=41.2\\text{kJ}}{\\Delta H=265\\text{kJ}}\\hfill \\end{array}[\/latex]\r\n\r\n5. The enthalpy\u00a0can be found through the following steps:\r\n\r\n[latex]\\begin{array}{llll}\\text{Step}1:\\hfill &amp; 4\\left[\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)\\right]\\hfill &amp; \\hfill &amp; \\Delta H^{\\circ }=4\\left(-394\\text{kJ}{\\text{mol}}^{-1}\\right)\\hfill \\\\ \\text{Step}2:\\hfill &amp; 5\\left[{\\text{H}}_{\\text{2}}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{H}}_{\\text{2}}\\text{O}\\left(g\\right)\\right]\\hfill &amp; \\hfill &amp; \\Delta H^{\\circ }=5\\left(-242\\text{kJ}{\\text{mol}}^{-1}\\right)\\hfill \\\\ \\text{Step}\\text{3:}\\hfill &amp; \\underline{{\\text{C}}_{\\text{4}}{\\text{H}}_{10}\\rightarrow 4\\text{C}\\left(s\\right)+5{\\text{H}}_{2}\\left(g\\right)}\\hfill &amp; \\hfill &amp; \\underline{\\Delta H^{\\circ }=+126\\text{kJ}{\\text{mol}}^{-1}}\\hfill \\\\ \\text{Sum:}\\hfill &amp; {\\text{C}}_{\\text{4}}{\\text{H}}_{10}+\\frac{13}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow 4{\\text{CO}}_{2}\\left(g\\right)+5{\\text{H}}_{2}\\text{O}\\left(l\\right)\\hfill &amp; \\hfill &amp; \\Delta{H}_{298}^{\\circ }=-2660\\text{kJ}{\\text{mol}}^{-1}\\hfill \\end{array}[\/latex]\r\n\r\n7.\u00a0The heat\u00a0can be found through the following steps:\r\n\r\n[latex]\\begin{array}{lllllll}{\\text{TiCl}}_{4}\\left(g\\right)\\rightarrow\\text{Ti}\\left(s\\right)+2{\\text{Cl}}_{2}\\left(g\\right)\\hfill &amp; &amp; &amp; &amp; &amp; &amp; \\Delta{H}_{1}^{\\circ }=-\\left(-763.2\\text{kJ}\\right)\\hfill \\\\ 2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow 2{\\text{H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(s\\right)\\hfill &amp; &amp; &amp; &amp; &amp; &amp; \\Delta{H}_{2}^{\\circ }=-2\\text{(}-241.82\\text{kJ)}=483.6\\text{kJ}\\hfill \\\\ \\text{Ti}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{TiO}}_{2}\\left(s\\right)\\hfill &amp; &amp; &amp; &amp; &amp; &amp; \\Delta{H}_{3}^{\\circ }=-944.7\\text{kJ}\\hfill \\\\ \\underline{2{\\text{H}}_{2}\\left(g\\right)\\rightarrow 2{\\text{Cl}}_{2}\\left(g\\right)+4\\text{HCl}\\left(s\\right)}\\hfill &amp; &amp; &amp; &amp; &amp; &amp; \\underline{\\Delta{H}_{4}^{\\circ }=4\\text{(}-92.3\\text{kJ)}=-369.2\\text{kJ}}\\hfill \\\\ {\\text{TiCl}}_{4}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow{\\text{TiO}}_{2}\\left(s\\right)+4\\text{HCl}\\left(g\\right)\\hfill &amp; &amp; &amp; &amp; &amp; &amp; \\Delta{H}_{298}^{\\circ }=-67.1\\text{kJ}\\hfill \\end{array}[\/latex]\r\nThus, 67.1 kJ of heat is evolved.\r\n\r\n9. Convert \u221215.14 kcal to kJ:\u00a0\u221215.14 kcal \u00d7 4.184 kJ\/kcal = 63.35 kJ\/mol\r\n\r\n[latex]\\begin{array}{ll}\\hfill \\Delta{H}_{\\text{reaction}}^{\\circ }&amp; =\\Delta{H}_{\\text{products}}^{\\circ }-\\Delta{H}_{\\text{reactants}}^{\\circ }\\hfill \\\\ &amp; =\\Delta{H}_{\\text{Ca}{\\left(\\text{OH}\\right)}_{2}\\left(s\\right)}^{\\circ }+\\Delta{H}_{{\\text{C}}_{2}{\\text{H}}_{2}\\left(g\\right)}^{\\circ }-\\Delta{H}_{{\\text{CaC}}_{2}\\left(s\\right)}^{\\circ }-2\\Delta{H}_{{\\text{H}}_{2}{\\text{O}}_{2}\\left(l\\right)}^{\\circ }\\hfill \\\\ &amp; =-985.2+227.4-63.35-2\\left(-285.83\\right)=-249.5\\text{kJ}\\hfill \\end{array}[\/latex]\r\n\r\n11. the amount of heat produced by burning of 1.0 gallon of gasoline is:\r\n<em>q<\/em> = 1.0 gallon \u00d7 (\u20131.28 \u00d7 10<sup>5<\/sup> kJ\/gal) = -1.28 \u00d7 10<sup>5<\/sup> kJ\r\nMass \u00d7 (-35 kJ\/g) = -1.28 \u00d7 10<sup>5<\/sup> kJ\r\nMass = 3657 g or 3.7 kg\r\n\r\n13. Write the balanced equation for each reaction.\r\n[latex]\\begin{array}{l}{\\text{B}}_{2}{\\text{H}}_{6}\\left(g\\right)+3{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{B}}_{2}{\\text{O}}_{3}\\left(s\\right)+3{\\text{H}}_{2}\\text{O}\\left(g\\right)\\\\ {\\text{CH}}_{4}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\\\ {\\text{N}}_{2}{\\text{H}}_{4}\\left(l\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{N}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\end{array}[\/latex]\r\n\r\nCalculate the heat released per mole; then, calculate the heat per gram.\r\n\r\n[latex]\\begin{array}{l}\\Delta{H}_{\\text{rxn}}^{\\circ }=\\Delta{H}_{\\text{P}}^{\\circ }-\\Delta{H}_{\\text{R}}^{\\circ }\\\\ \\Delta{H}_{\\text{comb}}^{\\circ }=-1273.5+3\\left(-241.82\\right)+36.4=-1962.6\\text{kJ}{\\text{mol}}^{-1}\\\\ \\Delta{H}_{\\text{comb}}^{\\circ }=-393.51+2\\left(-241.82\\right)-\\left(-74.6\\right)=-802.6\\text{kJ}{\\text{mol}}^{-1}\\\\ \\Delta{H}_{\\text{comb}}^{\\circ }=2\\left(-241.82\\right)-\\left(50.63\\right)=-534.27\\text{kJ}{\\text{mol}}^{-1}\\end{array}[\/latex]\r\n\r\nCalculate the heat per mole released per gram.\r\n\r\nFor B<sub>2<\/sub>H<sub>6<\/sub>: [latex]\\frac{-1912.26\\text{kJ}}{27.610\\text{g}}=-69.26\\text{kJ}{\\text{g}}^{-1}-\\frac{1962.6}{27.67}=-70.93[\/latex]\r\n\r\nFor CH<sub>4<\/sub>: [latex]\\frac{-802.34\\text{kJ}}{16.043\\text{g}}=-50.012\\text{kJ}{\\text{g}}^{-1}-\\frac{802.6}{16.043}=-50.03[\/latex]\r\n\r\nFor N<sub>2<\/sub>H<sub>4<\/sub>: [latex]\\frac{-534.27\\text{kJ}}{32.0452\\text{g}}=16.67[\/latex]\r\n\r\nOn the assumption that the best rocket fuel is the one that gives off the most heat, B<sub>2<\/sub>H<sub>6<\/sub> is the prime candidate. Other things must be considered, however. For example, the moles of gaseous product formed are related to the specific impulse of the fuel, toxicity of products, cost, and ability to contain original fuel (stability and corrosiveness).\r\n\r\n15. [latex]\\begin{array}{cc}\\hfill \\Delta{H}_{\\text{rxn}}^{\\circ }&amp; =\\Delta{H}_{{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)}^{\\circ }-\\Delta{H}_{{\\text{H}}_{2}\\text{O}\\left(g\\right)}^{\\circ }-\\Delta{H}_{{\\text{C}}_{2}{\\text{H}}_{4}\\left(g\\right)}^{\\circ }\\hfill \\\\ &amp; =-277.7-\\left(-241.82\\right)-\\left(52.4\\right)\\hfill \\\\ &amp; =-88.2\\text{kJ}\\hfill \\end{array}[\/latex]\r\n\r\n17. The answers are as follows:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>(a) [latex]{\\text{C}}_{3}{\\text{H}}_{8}\\left(g\\right)+5{\\text{O}}_{2}\\left(g\\right)\\rightarrow 3{\\text{CO}}_{2}\\left(g\\right)+4{\\text{H}}_{2}\\text{O}\\left(l\\right);[\/latex]<\/li>\r\n \t<li>(b) Determine the number of moles of O<sub>2<\/sub> required and from that the number of grams. Then use the density to find the volume.\r\n[latex]\\begin{array}{lll}\\\\ \\hfill \\text{Mass}{\\text{O}}_{2}&amp; =&amp; 25.0\\cancel{\\text{g}{\\text{C}}_{3}{\\text{H}}_{8}}\\times \\frac{1\\cancel{\\text{mol}{\\text{C}}_{3}{\\text{H}}_{8}}}{44.097\\cancel{\\text{g}}}\\times \\frac{5\\cancel{\\text{mol}{\\text{O}}_{2}}}{1\\cancel{\\text{mol}{\\text{C}}_{3}{\\text{H}}_{8}\\left(g\\right)}}\\times \\frac{31.999\\text{g}}{1\\cancel{\\text{mol}{\\text{O}}_{2}}}\\\\ &amp; =&amp; 90.7\\text{g}\\\\ \\text{Volume}{\\text{O}}_{2}&amp; =&amp; \\frac{90.7\\cancel{\\text{g}}}{0.275\\cancel{\\text{g}}{\\text{L}}^{-1}}=330\\text{L}\\end{array}[\/latex]<\/li>\r\n \t<li>(c) [latex]\\begin{array}{ccc}\\hfill \\Delta{H}_{\\text{comb}}^{\\circ }\\left({\\text{C}}_{3}{\\text{H}}_{6}\\left(g\\right)\\right)&amp; =&amp; -2219.2\\text{kJ}{\\text{mol}}^{-1}=3\\Delta{H}_{\\text{f}}^{\\circ }\\text{(}{\\text{CO}}_{2}\\left(g\\right)\\text{)}+4\\Delta{H}_{\\text{f}}^{\\circ }\\text{(}{\\text{H}}_{2}\\text{O}\\left(l\\right)\\text{)}-\\Delta{H}_{\\text{f}}^{\\circ }\\text{(}{\\text{C}}_{3}{\\text{H}}_{6}\\left(g\\right)\\text{)}\\hfill \\\\ \\hfill \\Delta{H}_{\\text{f}}^{\\circ }\\left({\\text{C}}_{3}{\\text{H}}_{6}\\left(g\\right)\\right)&amp; =&amp; \\left[2220.1+3\\left(-393.5\\right)+4\\left(-285.8\\right)\\right]\\text{kJ}{\\text{mol}}^{-1}\\hfill \\\\ &amp; =&amp; -104.5\\text{kJ}{\\text{mol}}^{-1}\\hfill \\end{array}[\/latex]<\/li>\r\n \t<li>(d) [latex]\\frac{25.0\\cancel{\\text{g}}}{44.097\\cancel{\\text{g}}{\\text{mol}}^{-1}}\\times 2219.2\\text{kJ}{\\text{mol}}^{-1}=1258\\text{kJ}=1.26\\times {10}^{6}\\text{J}[\/latex]\r\nHeat = 1.26 \u00d7 10<sup>6<\/sup> J = 4.18 J g<sup>-1<\/sup> \u00b0C<sup>-1<\/sup> \u00d7 4.00 \u00d7 10<sup>3<\/sup> \u00d7 \u0394<em>T\r\n<\/em>\u0394<em>T<\/em> = 75.4 \u00b0C<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Glossary<\/h2>\r\n<strong>chemical thermodynamics: <\/strong>area of science that deals with the relationships between heat, work, and all forms of energy associated with chemical and physical processes\r\n\r\n<strong>enthalpy (<em>H<\/em>): <\/strong>sum of a system\u2019s internal energy and the mathematical product of its pressure and volume\r\n\r\n<strong>enthalpy change (\u0394<em>H<\/em>): <\/strong>heat released or absorbed by a system under constant pressure during a chemical or physical process\r\n\r\n<strong>expansion work (pressure-volume work): <\/strong>work done as a system expands or contracts against external pressure\r\n\r\n<strong>first law of thermodynamics: <\/strong>internal energy of a system changes due to heat flow in or out of the system or work done on or by the system\r\n\r\n<strong>Hess\u2019s law: <\/strong>if a process can be represented as the sum of several steps, the enthalpy change of the process equals the sum of the enthalpy changes of the steps\r\n\r\n<strong>hydrocarbon: <\/strong>compound composed only of hydrogen and carbon; the major component of fossil fuels\r\n\r\n<strong>internal energy (<em>U<\/em>): <\/strong>total of all possible kinds of energy present in a substance or substances\r\n\r\n<strong>standard enthalpy of combustion [latex]\\text{(}\\Delta{H}_{\\text{c}}^{\\circ }\\text{)}[\/latex]: <\/strong>heat released when one mole of a compound undergoes complete combustion under standard conditions\r\n\r\n<strong>standard enthalpy of formation [latex]\\text{(}\\Delta{H}_{\\text{f}}^{\\circ }\\text{)}[\/latex]: <\/strong>enthalpy change of a chemical reaction in which 1 mole of a pure substance is formed from its elements in their most stable states under standard state conditions\r\n\r\n<strong>standard state: <\/strong>set of physical conditions as accepted as common reference conditions for reporting thermodynamic properties; 1 bar of pressure, and solutions at 1 molar concentrations, usually at a temperature of 298.15 K\r\n\r\n<strong>state function: <\/strong>property depending only on the state of a system, and not the path taken to reach that state","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>State the first law of thermodynamics<\/li>\n<li>Define enthalpy and explain its classification as a state function<\/li>\n<li>Write and balance thermochemical equations<\/li>\n<li>Calculate enthalpy changes for various chemical reactions<\/li>\n<li>Explain Hess\u2019s law and use it to compute reaction enthalpies<\/li>\n<\/ul>\n<\/div>\n<p>Thermochemistry is a branch of <strong>chemical thermodynamics<\/strong>, the science that deals with the relationships between heat, work, and other forms of energy in the context of chemical and physical processes. As we concentrate on thermochemistry in this chapter, we need to consider some widely used concepts of thermodynamics.<\/p>\n<p>Substances act as reservoirs of energy, meaning that energy can be added to them or removed from them. Energy is stored in a substance when the kinetic energy of its atoms or molecules is raised. The greater kinetic energy may be in the form of increased translations (travel or straight-line motions), vibrations, or rotations of the atoms or molecules. When thermal energy is lost, the intensities of these motions decrease and the kinetic energy falls. The total of all possible kinds of energy present in a substance is called the<strong> internal energy (<em>U<\/em>)<\/strong>, sometimes symbolized as <em>E<\/em>.<\/p>\n<p>As a system undergoes a change, its internal energy can change, and energy can be transferred from the system to the surroundings, or from the surroundings to the system. Energy is transferred into a system when it absorbs heat (<em>q<\/em>) from the surroundings or when the surroundings do work (<em>w<\/em>) on the system. For example, energy is transferred into room-temperature metal wire if it is immersed in hot water (the wire absorbs heat from the water), or if you rapidly bend the wire back and forth (the wire becomes warmer because of the work done on it). Both processes increase the internal energy of the wire, which is reflected in an increase in the wire\u2019s temperature. Conversely, energy is transferred out of a system when heat is lost from the system, or when the system does work on the surroundings.<\/p>\n<p>The relationship between internal energy, heat, and work can be represented by the equation:<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta U=q+w[\/latex]<\/p>\n<p>as shown in Figure 1. This is one version of the <strong>first law of thermodynamics<\/strong>, and it shows that the internal energy of a system changes through heat flow into or out of the system (positive <em>q<\/em> is heat flow in; negative <em>q<\/em> is heat flow out) or work done on or by the system. The work, <em>w<\/em>, is positive if it is done on the system and negative if it is done by the system.<\/p>\n<div id=\"attachment_5369\" style=\"width: 660px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5369\" class=\"wp-image-5369 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09032607\/CNX_Chem_05_03_Systemqw1.jpg\" alt=\"A rectangular diagram is shown. A green oval lies in the center of a tan field inside of a gray box. The tan field is labeled \u201cSurroundings\u201d and the equation \u201c\u0394 U = q + w\u201d is written at the bottom of the diagram. Two arrows face into the green oval and are labeled \u201cq subscript in\u201d and \u201cw subscript on\u201d while two more arrows face away from the oval and are labeled \u201cq subscript out\u201d and \u201cw subscript by.\u201d The center of the oval contains the terms \u201c\u0394 U &lt; 0\u201d, \u201cSystem,\u201d and \u201c\u0394 U &gt; 0.\u201d\" width=\"650\" height=\"437\" \/><\/p>\n<p id=\"caption-attachment-5369\" class=\"wp-caption-text\">Figure 1. The internal energy, U, of a system can be changed by heat flow and work. If heat flows into the system, qin, or work is done on the system, won, its internal energy increases, \u0394U &lt; 0. If heat flows out of the system, qout, or work is done by the system, wby, its internal energy decreases, \u0394U &gt; 0.<\/p>\n<\/div>\n<p>A type of work called<strong> expansion work (or pressure-volume work)<\/strong> occurs when a system pushes back the surroundings against a restraining pressure, or when the surroundings compress the system. An example of this occurs during the operation of an internal combustion engine. The reaction of gasoline and oxygen is exothermic. Some of this energy is given off as heat, and some does work pushing the piston in the cylinder. The substances involved in the reaction are the system, and the engine and the rest of the universe are the surroundings. The system loses energy by both heating and doing work on the surroundings, and its internal energy decreases. (The engine is able to keep the car moving because this process is repeated many times per second while the engine is running.) We will consider how to determine the amount of work involved in a chemical or physical change in the chapter on thermodynamics.<\/p>\n<div class=\"textbox\">This view of <a href=\"http:\/\/auto.howstuffworks.com\/engine1.htm\" target=\"_blank\">an internal combustion engine on How Stuff Works<\/a> illustrates the conversion of energy produced by the exothermic combustion reaction of a fuel such as gasoline into energy of motion.<\/div>\n<p>As discussed, the relationship between internal energy, heat, and work can be represented as \u0394<em>U<\/em> = <em>q<\/em> + <em>w<\/em>. Internal energy is a type of quantity known as a <strong>state function<\/strong> (or state variable), whereas heat and work are not state functions. The value of a state function depends only on the state that a system is in, and not on how that state is reached. If a quantity is not a state function, then its value <em>does<\/em> depend on how the state is reached. An example of a state function is altitude or elevation. If you stand on the summit of Mt. Kilimanjaro, you are at an altitude of 5895 m, and it does not matter whether you hiked there or parachuted there. The distance you traveled to the top of Kilimanjaro, however, is not a state function. You could climb to the summit by a direct route or by a more roundabout, circuitous path (Figure 2). The distances traveled would differ (distance is not a state function) but the elevation reached would be the same (altitude is a state function).<\/p>\n<div id=\"attachment_5371\" style=\"width: 985px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5371\" class=\"wp-image-5371 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09032807\/CNX_Chem_05_03_Summit1.jpg\" alt=\"An aerial photo depicts a view of Mount Kilimanjaro. A straight, green arrow labeled X is drawn from the term \u201cbase,\u201d written at the bottom of the mountain, to the term \u201cSummit,\u201d written at the top of the mountain. Another arrow labeled Y is draw from the base to the summit alongside the green arrow, but this arrow is pink and has three large S-shaped curves along its length.\" width=\"975\" height=\"525\" \/><\/p>\n<p id=\"caption-attachment-5371\" class=\"wp-caption-text\">Figure 2. Paths X and Y represent two different routes to the summit of Mt. Kilimanjaro. Both have the same change in elevation (altitude or elevation on a mountain is a state function; it does not depend on path), but they have very different distances traveled (distance walked is not a state function; it depends on the path). (credit: modification of work by Paul Shaffner)<\/p>\n<\/div>\n<p>Chemists ordinarily use a property known as <strong>enthalpy (<em>H<\/em>)<\/strong> to describe the thermodynamics of chemical and physical processes. Enthalpy is defined as the sum of a system\u2019s internal energy (<em>U<\/em>) and the mathematical product of its pressure (<em>P<\/em>) and volume (<em>V<\/em>):<\/p>\n<p style=\"text-align: center;\">[latex]H=U+PV[\/latex]<\/p>\n<p>Since it is derived from three state functions (<em>U<\/em>, <em>P<\/em>, and <em>V<\/em>), enthalpy is also a state function. Enthalpy values for specific substances cannot be measured directly; only enthalpy <em>changes<\/em> for chemical or physical processes can be determined. For processes that take place at constant pressure (a common condition for many chemical and physical changes), the <strong>enthalpy change (\u0394<em>H<\/em>)<\/strong> is:<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta H=\\Delta U+P\\Delta V[\/latex]<\/p>\n<p>The mathematical product <em>P<\/em>\u0394<em>V<\/em> represents work (<em>w<\/em>), namely, expansion or pressure-volume work as noted. By their definitions, the arithmetic signs of \u0394<em>V<\/em> and <em>w<\/em> will always be opposite:<\/p>\n<p style=\"text-align: center;\">[latex]P\\Delta V=-w[\/latex]<\/p>\n<p>Substituting this equation and the definition of internal energy into the enthalpy-change equation yields:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rll}\\Delta H&=&\\Delta U+P\\Delta V\\\\&=&{q}_{\\text{p}}+w-w\\\\&=&{q}_{\\text{p}}\\end{array}[\/latex]<\/p>\n<p>where <em>q<sub>p<\/sub><\/em> is the heat of reaction under conditions of constant pressure.<\/p>\n<p>And so, if a chemical or physical process is carried out at constant pressure with the only work done caused by expansion or contraction, then the heat flow (<em>q<sub>p<\/sub><\/em>) and enthalpy change (\u0394<em>H<\/em>) for the process are equal.<\/p>\n<p>The heat given off when you operate a Bunsen burner is equal to the enthalpy change of the methane combustion reaction that takes place, since it occurs at the essentially constant pressure of the atmosphere. On the other hand, the heat produced by a reaction measured in a bomb calorimeter is not equal to \u0394<em>H<\/em>, because the closed, constant-volume metal container prevents expansion work from occurring. Chemists usually perform experiments under normal atmospheric conditions, at constant external pressure with <em>q<\/em> = \u0394<em>H<\/em>, which makes enthalpy the most convenient choice for determining heat.<\/p>\n<p>The following conventions apply when we use \u0394<em>H<\/em>:<\/p>\n<ol id=\"fs-idm49861360\" data-number-style=\"arabic\">\n<li>Chemists use a thermochemical equation to represent the changes in both matter and energy. In a thermochemical equation, the enthalpy change of a reaction is shown as a \u0394<em>H<\/em> value following the equation for the reaction. This \u0394<em>H<\/em> value indicates the amount of heat associated with the reaction involving the number of moles of reactants and products <em>as shown in the chemical equation<\/em>. For example, consider this equation:\n<p style=\"text-align: center;\">[latex]{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=-286\\text{kJ}[\/latex]<\/p>\n<p>This equation indicates that when 1 mole of hydrogen gas and [latex]\\frac{1}{2}[\/latex] mole of oxygen gas at some temperature and pressure change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released to the surroundings. If the coefficients of the chemical equation are multiplied by some factor, the enthalpy change must be multiplied by that same factor (\u0394<em>H<\/em> is an extensive property):<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}\\left(\\text{two-fold increase in amounts}\\right)\\\\ 2{\\text{H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=2\\times \\left(-286\\text{kJ}\\right)=-572\\text{kJ}\\\\ \\left(\\text{two-fold decrease in amounts}\\right)\\\\ \\frac{1}{2}{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{4}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\frac{1}{2}{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=\\frac{1}{2}\\times \\left(-286\\text{kJ}\\right)=-143\\text{kJ}\\end{array}[\/latex]<\/p>\n<\/li>\n<li>The enthalpy change of a reaction depends on the physical state of the reactants and products of the reaction (whether we have gases, liquids, solids, or aqueous solutions), so these must be shown. For example, when 1 mole of hydrogen gas and [latex]\\frac{1}{2}[\/latex] mole of oxygen gas change to 1 mole of liquid water at the same temperature and pressure, 286 kJ of heat are released. If gaseous water forms, only 242 kJ of heat are released.\n<p style=\"text-align: center;\">[latex]{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(g\\right)\\Delta\\text{H}=-242\\text{kJ}[\/latex]<\/p>\n<\/li>\n<li>A negative value of an enthalpy change, \u0394<em>H<\/em>, indicates an exothermic reaction; a positive value of \u0394<em>H<\/em> indicates an endothermic reaction. If the direction of a chemical equation is reversed, the arithmetic sign of its \u0394<em>H<\/em> is changed (a process that is endothermic in one direction is exothermic in the opposite direction).<\/li>\n<\/ol>\n<div class=\"textbox examples\">\n<h3>Example 1:\u00a0<strong>Measurement of an Enthalpy Change<\/strong><\/h3>\n<p>When 0.0500 mol of HCl(<em>aq<\/em>) reacts with 0.0500 mol of NaOH(<em>aq<\/em>) to form 0.0500 mol of NaCl(<em>aq<\/em>), 2.9 kJ of heat are produced. What is \u0394<em>H<\/em>, the enthalpy change, per mole of acid reacting, for the acid-base reaction run under the conditions described in <a href=\".\/chapter\/calorimetry\/\" target=\"_blank\">Example 3 of Calorimetry<\/a>?<\/p>\n<p style=\"text-align: center;\">[latex]\\text{HCl}\\left(aq\\right)+\\text{NaOH}\\left(aq\\right)\\rightarrow\\text{NaCl}\\left(aq\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q755793\">Show Answer<\/span><\/p>\n<div id=\"q755793\" class=\"hidden-answer\" style=\"display: none\">\n<p>For the reaction of 0.0500 mol acid (HCl), <em>q<\/em> = -2.9 kJ. This ratio [latex]\\frac{-2.9\\text{kJ}}{0.0500\\text{mol}\\text{HCl}}[\/latex] can be used as a conversion factor to find the heat produced when 1 mole of HCl reacts:<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta\\text{H}=1\\cancel{\\text{mol}\\text{HCl}}\\times \\frac{-2.9\\text{kJ}}{0.0500\\cancel{\\text{mol}\\text{HCl}}}=-58\\text{kJ}[\/latex]<\/p>\n<p>The enthalpy change when 1 mole of HCl reacts is \u221258 kJ. Since that is the number of moles in the chemical equation, we write the thermochemical equation as:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{HCl}\\left(aq\\right)+\\text{NaOH}\\left(aq\\right)\\rightarrow\\text{NaCl}\\left(aq\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=-58\\text{kJ}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp6958160\"><strong>Check Your Learning<\/strong><\/h4>\n<p>When 1.34 g Zn(<em>s<\/em>) reacts with 60.0 mL of 0.750 M HCl(<em>aq<\/em>), 3.14 kJ of heat are produced. Determine the enthalpy change per mole of zinc reacting for the reaction:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Zn}\\left(s\\right)+2\\text{HCl}\\left(aq\\right)\\rightarrow{\\text{ZnCl}}_{2}\\left(aq\\right)+{\\text{H}}_{2}\\left(g\\right)[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q227263\">Show Answer<\/span><\/p>\n<div id=\"q227263\" class=\"hidden-answer\" style=\"display: none\">\u0394H = \u2013153 kJ<\/div>\n<\/div>\n<\/div>\n<p>Be sure to take both stoichiometry and limiting reactants into account when determining the \u0394<em>H<\/em> for a chemical reaction.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 2:\u00a0<strong>Another Example of the Measurement of an Enthalpy Change<\/strong><\/h3>\n<p>A gummy bear contains 2.67 g sucrose, C<sub>12<\/sub>H<sub>22<\/sub>O<sub>11<\/sub>. When it reacts with 7.19 g potassium chlorate, KClO<sub>3<\/sub>, 43.7 kJ of heat are produced. Determine the enthalpy change for the reaction<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}\\left(aq\\right)+8{\\text{KClO}}_{3}\\left(aq\\right)\\rightarrow 12{\\text{CO}}_{2}\\left(g\\right)+11{\\text{H}}_{2}\\text{O}\\left(l\\right)+8\\text{KCl}\\left(aq\\right)[\/latex]<\/p>\n<p id=\"fs-idm42247408\">\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q908763\">Show Answer<\/span><\/p>\n<div id=\"q908763\" class=\"hidden-answer\" style=\"display: none\">\n<p>We have [latex]2.67\\cancel{\\text{g}}\\times \\frac{1\\text{ mol}}{342.3\\cancel{\\text{g}}}=0.00780\\text{ mol }{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}[\/latex] available, and [latex]7.19\\cancel{\\text{g}}\\times \\frac{1\\text{ mol}}{122.5\\cancel{\\text{g}}}=0.0587\\text{ mol }{\\text{KClO}}_{3}[\/latex] available. Since [latex]0.0587\\text{ mol }{\\text{KClO}}_{3}\\times \\frac{1\\text{ mol }{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}}{8\\text{ mol }{\\text{KClO}}_{3}}=0.00734\\text{ mol }{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}[\/latex] is needed, C<sub>12<\/sub>H<sub>22<\/sub>O<sub>11<\/sub> is the excess reactant and KClO<sub>3<\/sub> is the limiting reactant.<\/p>\n<p>The reaction uses 8 mol KClO<sub>3<\/sub>, and the conversion factor is [latex]\\frac{-43.7\\text{kJ}}{0.0587\\text{ mol }{\\text{KClO}}_{3}},[\/latex] so we have<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta\\text{H}=8\\text{mol}\\times \\frac{-43.7\\text{kJ}}{0.0587\\text{ mol }{\\text{KClO}}_{3}}=-5960\\text{kJ}[\/latex]<\/p>\n<p>The enthalpy change for this reaction is -5960 kJ, and the thermochemical equation is:<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{C}}_{12}{\\text{H}}_{22}{\\text{O}}_{11}+8{\\text{KClO}}_{3}\\rightarrow 12{\\text{CO}}_{2}+11{\\text{H}}_{2}\\text{O}+8\\text{KCl}\\Delta\\text{H}=-5960\\text{ kJ}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp82549456\"><strong>Check Your Learning<\/strong><\/h4>\n<p>When 1.42 g of iron reacts with 1.80 g of chlorine, 3.22 g of FeCl<sub>2<\/sub>(<em>s<\/em>) and 8.60 kJ of heat is produced. What is the enthalpy change for the reaction when 1 mole of FeCl<sub>2<\/sub>(<em>s<\/em>) is produced?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q608658\">Show Answer<\/span><\/p>\n<div id=\"q608658\" class=\"hidden-answer\" style=\"display: none\">\u0394H = \u2013338 kJ<\/div>\n<\/div>\n<\/div>\n<p>Enthalpy changes are typically tabulated for reactions in which both the reactants and products are at the same conditions. A <strong>standard state <\/strong>is a commonly accepted set of conditions used as a reference point for the determination of properties under other different conditions. For chemists, the IUPAC standard state refers to materials under a pressure of 1 bar and solutions at 1 M, and does not specify a temperature. Many thermochemical tables list values with a standard state of 1 atm. Because the \u0394<em>H<\/em> of a reaction changes very little with such small changes in pressure (1 bar = 0.987 atm), \u0394<em>H<\/em> values (except for the most precisely measured values) are essentially the same under both sets of standard conditions. We will include a superscripted \u201co\u201d in the enthalpy change symbol to designate standard state. Since the usual (but not technically standard) temperature is 298.15 K, we will use a subscripted \u201c298\u201d to designate this temperature. Thus, the symbol [latex]\\left(\\Delta{H}_{298}^{\\circ}\\right)[\/latex] is used to indicate an enthalpy change for a process occurring under these conditions. (The symbol \u0394<em>H<\/em> is used to indicate an enthalpy change for a reaction occurring under nonstandard conditions.)<\/p>\n<p>The enthalpy changes for many types of chemical and physical processes are available in the reference literature, including those for combustion reactions, phase transitions, and formation reactions. As we discuss these quantities, it is important to pay attention to the <em>extensive<\/em> nature of enthalpy and enthalpy changes. Since the enthalpy change for a given reaction is proportional to the amounts of substances involved, it may be reported on that basis (i.e., as the \u0394<em>H<\/em> for specific amounts of reactants). However, we often find it more useful to divide one extensive property (\u0394<em>H<\/em>) by another (amount of substance), and report a per-amount <em>intensive<\/em> value of \u0394<em>H<\/em>, often \u201cnormalized\u201d to a per-mole basis. (Note that this is similar to determining the intensive property specific heat from the extensive property heat capacity, as seen previously.)<\/p>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<ol>\n<li>Explain how the heat measured in <a href=\".\/chapter\/calorimetry\" target=\"_blank\">Example 3 of Calorimetry<\/a> differs from the enthalpy change for the exothermic reaction described by the following equation: [latex]\\text{HCl}\\left(aq\\right)+\\text{NaOH}\\left(aq\\right)\\rightarrow\\text{NaCl}\\left(aq\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/li>\n<li>Using the data in the check your learning section of <a href=\".chapter\/calorimetry-6-formula-errors\/\" target=\"_blank\">Example 3 of Calorimetry<\/a>, calculate \u0394H in kJ\/mol of AgNO3(aq) for the reaction: [latex]\\text{NaCl(}aq\\text{)}+{\\text{AgNO}}_{3}\\text{(}aq\\text{)}\\rightarrow\\text{AgCl}\\text{(}s\\text{)}+{\\text{NaNO}}_{3}\\text{(}aq\\text{).}[\/latex]<\/li>\n<li>Calculate the enthalpy of solution (\u0394<em>H<\/em> for the dissolution) per mole of NH<sub>4<\/sub>NO<sub>3<\/sub> under the conditions described in <a href=\"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-admin\/.chapter\/calorimetry-6-formula-errors\" target=\"_blank\">Figure 6\u00a0in\u00a0Calorimetry<\/a>.<\/li>\n<li>Calculate \u0394<em>H<\/em> for the reaction described by the equation. [latex]\\text{Ba}{\\left(\\text{OH}\\right)}_{2}\\cdot 8{\\text{H}}_{2}\\text{O}\\left(s\\right)+2{\\text{NH}}_{4}\\text{SCN}\\left(aq\\right)\\rightarrow\\text{Ba}{\\left(\\text{SCN}\\right)}_{2}\\left(aq\\right)+2{\\text{NH}}_{3}\\left(aq\\right)+10{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/li>\n<li>Calculate the enthalpy of solution (\u0394<em>H<\/em> for the dissolution) per mole of CaCl<sub>2<\/sub>.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q631741\">Show Selected Answers<\/span><\/p>\n<div id=\"q631741\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. The enthalpy change of the indicated reaction is for exactly 1 mol HCL and 1 mol NaOH; the heat in the example is produced by 0.0500 mol HCl and 0.0500 mol NaOH.<\/p>\n<p>3. The molar mass of NH<sub>4<\/sub>NO<sub>3<\/sub> is 80.0423 g\/mol. From the example, 1000 J is required to dissolve 3.21 g of NH<sub>4<\/sub>NO<sub>3<\/sub>.<\/p>\n<p>One mole under the same conditions would require<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{80.0432\\cancel{\\text{g}}{\\text{ mol}}^{-1}}{3.21\\cancel{\\text{g}}}\\times 1000\\text{ J}=25\\text{ kJ}{\\text{ mol}}^{-1}.[\/latex]<\/p>\n<p>(The heat of solution is positive because the process is endothermic.)<\/p>\n<p>5. The molar mass of CaCl<sub>2<\/sub> is 40.078 + 2(35.4572) = 110.992 g\/mol. In the previous section, 3.0 g of CaCl<sub>2<\/sub> dissolved in water releases a heat of 2.2 kJ. Therefore,<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{rcl}\\frac{3.0\\cancel{\\text{g}}}{110.992\\cancel{\\text{ g }}{\\text{mol}}^{-1}}&=&0.027\\text{ mol}\\\\ \\frac{2.2\\text{kJ}}{0.027\\text{ mol}}&=&81\\text{ kJ }{\\text{ mol}}^{-1}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2 data-type=\"title\">Enthalpy of Combustion<\/h2>\n<p><strong>Standard enthalpy of combustion<\/strong> [latex]\\left(\\Delta{H}_{C}^{\\circ }\\right)[\/latex] is the enthalpy change when 1 mole of a substance burns (combines vigorously with oxygen) under standard state conditions; it is sometimes called \u201cheat of combustion.\u201d For example, the enthalpy of combustion of ethanol, -1366.8 kJ\/mol, is the amount of heat produced when one mole of ethanol undergoes complete combustion at 25 \u00b0C and 1 atmosphere pressure, yielding products also at 25 \u00b0C and 1 atm.<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)+3{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{CO}}_{2}+3{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta{H}_{298}^{\\circ }=\\text{-1366.8}\\text{kJ}[\/latex]<\/p>\n<p>Enthalpies of combustion for many substances have been measured; a few of these are listed in Table 1. Many readily available substances with large enthalpies of combustion are used as fuels, including hydrogen, carbon (as coal or charcoal), and hydrocarbons (compounds containing only hydrogen and carbon), such as methane, propane, and the major components of gasoline.<\/p>\n<table id=\"fs-idp98710048\" summary=\"A data table is shown that has three columns and eleven rows. The header row reads \u201cSubstance,\u201d \u201cCombustion reaction,\u201d and \u201cEnthalpy of Combustion, \u0394 H subscript C superscript degree symbol (k J\/ mol at 25 \u00b0 C).\u201d The first column contains entries reading \u201ccarbon,\u201d \u201chydrogen,\u201d \u201cmagnesium,\u201d \u201csulfur,\u201d \u201ccarbon monoxide,\u201d \u201cmethane,\u201d \u201cacetylene,\u201d \u201cethanol,\u201d \u201cmethanol,\u201d and \u201cisooctane.\u201d The second column contains the equations \u201cC (s) + O (g) right-facing arrow C O subscript 2 (g),\u201d \u201cH subscript 2 (g) + one half O subscript 2 (g) right-facing arrow H subscript 2 O (l),\u201d \u201cM g (s) + one half O subscript 2 (g) right-facing arrow M g O (s),\u201d \u201cS (s) + O subscript 2 (g) right-facing arrow S O subscript 2 (g),\u201d \u201cC O (g) + one half O subscript 2 (g) right-facing arrow C O subscript 2 (g),\u201d \u201cC H subscript 4 (g) + 2 O subscript 2 (g) right-facing arrow C O subscript 2 (g) + 2 H subscript 2 O (g),\u201d \u201cC subscript 2 H subscript 2 (g) + five halves O subscript 2 (g) right-facing arrow 2 C O subscript 2 (g) + H subscript 2 O (l),\u201d \u201cC subscript 2 H subscript 5 O H (l) + 2 O subscript 2 (g) right-facing arrow C O subscript 2 (g) + 3 H subscript 2 O (l),\u201d \u201cC H subscript 3 O H (l) + three halves O subscript 2 (g) right-facing arrow C O subscript 2 (g) + 2 H subscript 2 O (l),\u201d and \u201cC subscript 8 H subscript 18 (l) + twenty five halves O subscript 2 (g) right-facing arrow 8 C O subscript 2 (g) + 9 H subscript 2 O (l).\u201d The final column contains the values \u201c\u2013393.5,\u201d \u201c\u2013285.8,\u201d \u201c\u2013601.6,\u201d \u201c\u2013296.8,\u201d \u201c\u2013283.0,\u201d \u201c\u2013890.8,\u201d \u201c\u20131301.1,\u201d \u201c\u20131366.8,\u201d \u201c\u2013726.1,\u201d and \u201c\u20135461.\u201d\">\n<thead>\n<tr>\n<th colspan=\"3\">Table 1. Standard Molar Enthalpies of Combustion<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<th style=\"width: 20%;\">Substance<\/th>\n<th style=\"width: 40%;\">Combustion Reaction<\/th>\n<th style=\"width: 40%;\">Enthalpy of Combustion, [latex]\\Delta{H}_{c}^{\\circ }[\/latex] [latex]\\left(\\frac{\\text{kJ}}{\\text{mol}}\\text{ at }25^{\\circ}\\text{ C}\\right)[\/latex]<\/th>\n<\/tr>\n<tr valign=\"top\">\n<td>carbon<\/td>\n<td>[latex]\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)[\/latex]<\/td>\n<td>\u2212393.5<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>hydrogen<\/td>\n<td>[latex]{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>\u2212285.8<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>magnesium<\/td>\n<td>[latex]\\text{Mg}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{MgO}\\left(s\\right)[\/latex]<\/td>\n<td>\u2212601.6<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>sulfur<\/td>\n<td>[latex]\\text{S}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{SO}}_{2}\\left(g\\right)[\/latex]<\/td>\n<td>\u2212296.8<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>carbon monoxide<\/td>\n<td>[latex]\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)[\/latex]<\/td>\n<td>\u2212283.0<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>methane<\/td>\n<td>[latex]{\\text{CH}}_{4}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>\u2212890.8<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>acetylene<\/td>\n<td>[latex]{\\text{C}}_{2}{\\text{H}}_{2}\\left(g\\right)+\\frac{5}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{CO}}_{2}\\left(g\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>\u22121301.1<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>ethanol<\/td>\n<td>[latex]{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)+3{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>\u22121366.8<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>methanol<\/td>\n<td>[latex]{\\text{CH}}_{3}\\text{OH}\\left(l\\right)+\\frac{3}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>\u2212726.1<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>isooctane<\/td>\n<td>[latex]{\\text{C}}_{8}{\\text{H}}_{18}\\left(l\\right)+\\frac{25}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow 8{\\text{CO}}_{2}\\left(g\\right)+9{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/td>\n<td>\u22125461<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div class=\"textbox examples\">\n<h3>Example 3:\u00a0<strong>Using Enthalpy of Combustion<\/strong><\/h3>\n<p>As Figure 3 suggests, the combustion of gasoline is a highly exothermic process. Let us determine the approximate amount of heat produced by burning 1.00 L of gasoline, assuming the enthalpy of combustion of gasoline is the same as that of isooctane, a common component of gasoline. The density of isooctane is 0.692 g\/mL.<\/p>\n<div id=\"attachment_5374\" style=\"width: 1210px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5374\" class=\"wp-image-5374 size-full\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033040\/CNX_Chem_05_03_GasBurning1.jpg\" alt=\"A picture shows a large ball of fire burning on a road. A fire truck and fireman are shown in the foreground.\" width=\"1200\" height=\"313\" \/><\/p>\n<p id=\"caption-attachment-5374\" class=\"wp-caption-text\">Figure 3. The combustion of gasoline is very exothermic. (credit: modification of work by \u201cAlexEagle\u201d\/Flickr)<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q583919\">Show Answer<\/span><\/p>\n<div id=\"q583919\" class=\"hidden-answer\" style=\"display: none\">\n<p>Starting with a known amount (1.00 L of isooctane), we can perform conversions between units until we arrive at the desired amount of heat or energy. The enthalpy of combustion of isooctane provides one of the necessary conversions. Table 1 gives this value as \u22125460 kJ per 1 mole of isooctane (C<sub>8<\/sub>H<sub>18<\/sub>).<\/p>\n<p>Using these data,<\/p>\n<p style=\"text-align: center;\">[latex]1.00\\cancel{\\text{L }{\\text{C}}_{8}{\\text{H}}_{18}}\\times \\frac{1000\\cancel{\\text{mL }{\\text{C}}_{8}{\\text{H}}_{18}}}{1\\cancel{\\text{L }{\\text{C}}_{8}{\\text{H}}_{18}}}\\times \\frac{0.692\\cancel{\\text{g }{\\text{C}}_{8}{\\text{H}}_{18}}}{1\\cancel{\\text{mL }{\\text{C}}_{8}{\\text{H}}_{18}}}\\times \\frac{1\\cancel{\\text{mol}{\\text{C}}_{8}{\\text{H}}_{18}}}{114\\cancel{\\text{g}{\\text{C}}_{8}{\\text{H}}_{18}}}\\times \\frac{-5460\\text{kJ}}{1\\cancel{\\text{mol}{\\text{C}}_{8}{\\text{H}}_{18}}}=-3.31\\times {10}^{4}\\text{kJ}[\/latex]<\/p>\n<p>The combustion of 1.00 L of isooctane produces 33,100 kJ of heat. (This amount of energy is enough to melt 99.2 kg, or about 218 lbs, of ice.)<\/p>\n<p>Note: If you do this calculation one step at a time, you would find:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}\\\\ 1.00\\text{L }{\\text{C}}_{8}{\\text{H}}_{18}\\rightarrow 1.00\\times {10}^{3}\\text{mL }{\\text{C}}_{8}{\\text{H}}_{18}\\\\ 1.00\\times {10}^{3}\\text{mL }{\\text{C}}_{8}{\\text{H}}_{18}\\rightarrow 692\\text{g}{\\text{C}}_{8}{\\text{H}}_{18}\\\\ 692\\text{g}{\\text{C}}_{8}{\\text{H}}_{18}\\rightarrow 6.07\\text{mol}{\\text{C}}_{8}{\\text{H}}_{18}\\\\ 692\\text{g}{\\text{C}}_{8}{\\text{H}}_{18}\\rightarrow-3.31\\times {10}^{4}\\text{kJ}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp49733232\"><strong>Check Your Learning<\/strong><\/h4>\n<p>How much heat is produced by the combustion of 125 g of acetylene?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q413251\">Show Answer<\/span><\/p>\n<div id=\"q413251\" class=\"hidden-answer\" style=\"display: none\">6.25 \u00d7 10<sup>3<\/sup> kJ<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<h3 style=\"text-align: left;\">Emerging Algae-Based Energy Technologies (Biofuels)<\/h3>\n<p>As reserves of fossil fuels diminish and become more costly to extract, the search is ongoing for replacement fuel sources for the future. Among the most promising biofuels are those derived from algae (Figure 4). The species of algae used are nontoxic, biodegradable, and among the world\u2019s fastest growing organisms. About 50% of algal weight is oil, which can be readily converted into fuel such as biodiesel. Algae can yield 26,000 gallons of biofuel per hectare\u2014much more energy per acre than other crops. Some strains of algae can flourish in brackish water that is not usable for growing other crops. Algae can produce biodiesel, biogasoline, ethanol, butanol, methane, and even jet fuel.<\/p>\n<div id=\"attachment_5376\" style=\"width: 1210px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5376\" class=\"size-full wp-image-5376\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033150\/CNX_Chem_05_03_AlgalFuel11.jpg\" alt=\"Three pictures are shown and labeled a, b, and c. Picture a shows a microscopic view of algal organisms. They are brown, multipart strands and net-like structures on a background of light violet. Picture b shows five large tubs full of a brown liquid containing these algal organisms. Picture c depicts a cylinder full of green liquid in the foreground and a poster in the background that has the title \u201cFrom Field to Fleet.\u201d\" width=\"1200\" height=\"425\" \/><\/p>\n<p id=\"caption-attachment-5376\" class=\"wp-caption-text\">Figure 4. (a) Tiny algal organisms can be (b) grown in large quantities and eventually (c) turned into a useful fuel such as biodiesel. (credit a: modification of work by Micah Sittig; credit b: modification of work by Robert Kerton; credit c: modification of work by John F. Williams)<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>According to the US Department of Energy, only 39,000 square kilometers (about 0.4% of the land mass of the US or less than [latex]\\frac{1}{7}[\/latex] of the area used to grow corn) can produce enough algal fuel to replace all the petroleum-based fuel used in the US. The cost of algal fuels is becoming more competitive\u2014for instance, the US Air Force is producing jet fuel from algae at a total cost of under $5 per gallon. The process used to produce algal fuel is as follows: grow the algae (which use sunlight as their energy source and CO<sub>2<\/sub> as a raw material); harvest the algae; extract the fuel compounds (or precursor compounds); process as necessary (e.g., perform a transesterification reaction to make biodiesel); purify; and distribute (Figure 5).<\/p>\n<div id=\"attachment_5377\" style=\"width: 1018px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5377\" class=\"size-full wp-image-5377\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033252\/CNX_Chem_05_03_AlgalFuel21.jpg\" alt=\"A flowchart is shown that contains pictures and words. Reading from left to right, the terms \u201cGrow,\u201d \u201cHarvest,\u201d \u201cExtract,\u201d \u201cProcess and purify,\u201d and \u201cJet fuel gasoline diesel\u201d are shown with right-facing arrows in between each. Above each term, respectively, are diagrams of three containers, three cylinders lying side-by-side, a pyramid-like container with liquid inside, a factory, and a fuel pump. In the space above all of the diagrams and to the left of the images is a diagram of the sun.\" width=\"1008\" height=\"365\" \/><\/p>\n<p id=\"caption-attachment-5377\" class=\"wp-caption-text\">Figure 5. Algae convert sunlight and carbon dioxide into oil that is harvested, extracted, purified, and transformed into a variety of renewable fuels.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<p>Watch this video to learn more about the process of creating algae biofuel.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Algae for Fuel - a QUEST Nebraska Feature\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/q9X7UNLRbds?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<ol>\n<li>Although the gas used in an oxyacetylene torch (Figure 6) is essentially pure acetylene, the heat produced by combustion of one mole of acetylene in such a torch is likely not equal to the enthalpy of combustion of acetylene listed in Table 1. Considering the conditions for which the tabulated data are reported, suggest an explanation.\n<div id=\"attachment_5380\" style=\"width: 1310px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5380\" class=\"size-full wp-image-5380\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033707\/CNX_Chem_05_01_OxyacTorch1.jpg\" alt=\"Two pictures are shown and labeled a and b. Picture a shows a metal railroad tie being cut with the flame of an acetylene torch. Picture b shows a chemical cold pack containing ammonium nitrate.\" width=\"1300\" height=\"556\" \/><\/p>\n<p id=\"caption-attachment-5380\" class=\"wp-caption-text\">Figure 6. (a) An oxyacetylene torch. (b) A cold pack. (credit a: modification of work by \u201cSkatebiker\u201d\/Wikimedia commons)<\/p>\n<\/div>\n<\/li>\n<li>How much heat is produced by burning 4.00 moles of acetylene under standard state conditions?<\/li>\n<li>How much heat is produced by combustion of 125 g of methanol under standard state conditions?<\/li>\n<li>How many moles of isooctane must be burned to produce 100 kJ of heat under standard state conditions?<\/li>\n<li>What mass of carbon monoxide must be burned to produce 175 kJ of heat under standard state conditions?<\/li>\n<li>When 2.50 g of methane burns in oxygen, 125 kJ of heat is produced. What is the enthalpy of combustion per mole of methane under these conditions?<\/li>\n<li>How much heat is produced when 100 mL of 0.250 M HCl (density, 1.00 g\/mL) and 200 mL of 0.150 M NaOH (density, 1.00 g\/mL) are mixed?[latex]\\text{HCl}\\left(aq\\right)+\\text{NaOH}\\left(aq\\right)\\rightarrow\\text{NaCl}\\left(aq\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta{H}_{298}^{\\circ }=-58\\text{kJ}[\/latex] If both solutions are at the same temperature and the heat capacity of the products is 4.19 J\/g \u00b0C, how much will the temperature increase? What assumption did you make in your calculation?<\/li>\n<li>A sample of 0.562 g of carbon is burned in oxygen in a bomb calorimeter, producing carbon dioxide. Assume both the reactants and products are under standard state conditions, and that the heat released is directly proportional to the enthalpy of combustion of graphite. The temperature of the calorimeter increases from 26.74 \u00b0C to 27.93 \u00b0C. What is the heat capacity of the calorimeter and its contents?<\/li>\n<li>Before the introduction of chlorofluorocarbons, sulfur dioxide (enthalpy of vaporization, 6.00 kcal\/mol) was used in household refrigerators. What mass of SO<sub>2<\/sub> must be evaporated to remove as much heat as evaporation of 1.00 kg of CCl<sub>2<\/sub>F<sub>2<\/sub> (enthalpy of vaporization is 17.4 kJ\/mol)? The vaporization reactions for SO<sub>2<\/sub> and CCl<sub>2<\/sub>F<sub>2<\/sub> are [latex]{\\text{SO}}_{2}\\left(l\\right)\\rightarrow{\\text{SO}}_{2}\\left(g\\right)[\/latex] and [latex]{\\text{CCl}}_{2}\\text{F}\\left(l\\right)\\rightarrow{\\text{CCl}}_{2}{\\text{F}}_{2}\\left(g\\right),[\/latex] respectively.<\/li>\n<li>Homes may be heated by pumping hot water through radiators. What mass of water will provide the same amount of heat when cooled from 95.0 to 35.0 \u00b0C, as the heat provided when 100 g of steam is cooled from 110 \u00b0C to 100 \u00b0C.<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q427747\">Show Selected Answers<\/span><\/p>\n<div id=\"q427747\" class=\"hidden-answer\" style=\"display: none\">\n<p>2. The heat of combustion is -1301.1 as given in Table 1.<\/p>\n<p style=\"text-align: center;\">heat released = 4.00 mol \u00d7 (-1301.1 kJ\/mol) = 5204.4 kJ<\/p>\n<p>4. The value of \u0394<em>H<\/em><sub>comb<\/sub> = -5461 kJ\/mol. To produce 100 kJ requires:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{100\\text{kJ}}{5461\\text{kJ}{\\text{mol}}^{-1}}=1.83\\times {10}^{-2}\\text{mol}.[\/latex]<\/p>\n<p>6. The molar mass of CH<sub>4<\/sub> is 16.04 g\/mol.\u00a0Find the mole of CH<sub>4<\/sub> present:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{2.50\\cancel{\\text{g}}}{16.04\\cancel{\\text{g}}{\\text{mol}}^{-1}}=0.15586\\text{mol}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta{H}_{\\text{comb}}=\\frac{125\\text{kJ}}{0.15586\\text{mol}}=802\\text{kJ}{\\text{mol}}^{-1}.[\/latex]<\/p>\n<p>8. The heat produced is found from the enthalpy of combustion:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{0.562\\cancel{\\text{g}}\\cancel{^{\\circ C}}}{12.011\\cancel{\\text{g}}{\\text{mol}}^{-1}\\cancel{^{\\circ C}}}=-393.5\\text{kJ}{\\text{mol}}^{-1}=-18.4\\text{kJ}.[\/latex]<\/p>\n<p>This is the heat released.<\/p>\n<p style=\"text-align: center;\"><em>q<\/em> = heat capacity \u00d7 \u0394<em>T<\/em><\/p>\n<p style=\"text-align: center;\">18.4 kJ = heat capacity \u00d7 (27.93 \u00baC &#8211; 26.74 \u00baC) = specific heat \u00d7 1.19 \u00baC<\/p>\n<p style=\"text-align: center;\">specific heat = 15.5 kJ\/\u00baC<\/p>\n<p>10. <em>q<\/em> = <em>mc<\/em>\u2206<em>T<\/em>. The amount of heat transferred from steam is:<\/p>\n<p><em>q<\/em><sub>steam<\/sub> = 100 g \u00d7 1.864 J\/(g \u00b0C) \u00d7 (110 &#8211; 100) \u00b0C = 1864 J<br \/>\n<em>q<\/em><sub>water<\/sub> = <em>m<\/em><sub>water<\/sub> \u00d7 4.184 J\/(g \u00b0C) \u00d7 (95 &#8211; 35) \u00b0C = <em>m<\/em><sub>water<\/sub> \u00d7 251.04 J\/g = <em>q<\/em><sub>steam<\/sub> = 1864 J<br \/>\n[latex]{m}_{\\text{water}}=\\frac{1864\\cancel{\\text{J}}}{251.01\\cancel{\\text{J}}\\text{\/g}}=7.43\\text{g}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2 data-type=\"title\">Standard Enthalpy of Formation<\/h2>\n<p>A <strong>standard enthalpy of formation<\/strong> [latex]\\Delta{H}_{\\text{f}}^{\\circ}[\/latex] is an enthalpy change for a reaction in which exactly 1 mole of a pure substance is formed from free elements in their most stable states under standard state conditions. These values are especially useful for computing or predicting enthalpy changes for chemical reactions that are impractical or dangerous to carry out, or for processes for which it is difficult to make measurements. If we have values for the appropriate standard enthalpies of formation, we can determine the enthalpy change for any reaction, which we will practice in the next section on Hess\u2019s law.<\/p>\n<p>The standard enthalpy of formation of CO<sub>2<\/sub>(<em>g<\/em>) is \u2212393.5 kJ\/mol. This is the enthalpy change for the exothermic reaction:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)\\Delta{H}_{\\text{f}}^{\\circ }=\\Delta{H}_{298}^{\\circ }=-393.5\\text{kJ}[\/latex]<\/p>\n<p>starting with the reactants at a pressure of 1 atm and 25\u00b0C (with the carbon present as graphite, the most stable form of carbon under these conditions) and ending with one mole of CO<sub>2<\/sub>, also at 1 atm and 25\u00b0C. For nitrogen dioxide, NO<sub>2<\/sub>(<em>g<\/em>), [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] is 33.2 kJ\/mol. This is the enthalpy change for the reaction:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{1}{2}{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{NO}}_{2}\\left(g\\right)\\Delta{H}_{\\text{f}}^{\\circ }=\\Delta{H}_{\\text{298}}^{\\circ }=\\text{+33.2}\\text{kJ}[\/latex]<\/p>\n<p>A reaction equation with [latex]\\frac{1}{2}[\/latex] mole of N<sub>2<\/sub> and 1 mole of O<sub>2<\/sub> is correct in this case because the standard enthalpy of formation always refers to 1 mole of product, NO<sub>2<\/sub>(<em>g<\/em>).<\/p>\n<p>You will find a table of standard enthalpies of formation of many common substances in <a class=\"target-chapter\" title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>. These values indicate that formation reactions range from highly exothermic (such as \u22122984 kJ\/mol for the formation of P<sub>4<\/sub>O<sub>10<\/sub>) to strongly endothermic (such as +226.7 kJ\/mol for the formation of acetylene, C<sub>2<\/sub>H<sub>2<\/sub>). By definition, the standard enthalpy of formation of an element in its most stable form is equal to zero under standard conditions, which is 1 atm for gases and 1 M for solutions.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 4:\u00a0<strong>Evaluating an Enthalpy of Formation<\/strong><\/h3>\n<p>Ozone, O<sub>3<\/sub>(<em>g<\/em>), forms from oxygen, O<sub>2<\/sub>(<em>g<\/em>), by an endothermic process. Ultraviolet radiation is the source of the energy that drives this reaction in the upper atmosphere. Assuming that both the reactants and products of the reaction are in their standard states, determine the standard enthalpy of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ}[\/latex] of ozone from the following information:<\/p>\n<p style=\"text-align: center;\">[latex]3{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{O}}_{3}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=\\text{+286}\\text{kJ}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q296678\">Show Answer<\/span><\/p>\n<div id=\"q296678\" class=\"hidden-answer\" style=\"display: none\">\n<p id=\"fs-idp166467632\">[latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] is the enthalpy change for the formation of one mole of a substance in its standard state from the elements in their standard states. Thus, [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] for O<sub>3<\/sub>(<em>g<\/em>) is the enthalpy change for the reaction:<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{3}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{O}}_{3}\\left(g\\right)[\/latex]<\/p>\n<p>For the formation of 2 mol of O<sub>3<\/sub>(<em>g<\/em>), [latex]\\Delta{H}_{\\text{298}}^{\\circ }=\\text{+286 kJ}[\/latex]. This ratio, [latex]\\left(\\frac{286\\text{kJ}}{2\\text{ mol }{\\text{O}}_{3}}\\right)[\/latex], can be used as a conversion factor to find the heat produced when 1 mole of O<sub>3<\/sub>(<em>g<\/em>) is formed, which is the enthalpy of formation for O<sub>3<\/sub>(<em>g<\/em>):<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta\\text{H}^{\\circ }\\text{for }1\\text{mole of }{\\text{O}}_{3}\\left(g\\right)=1\\cancel{\\text{ mol }{\\text{O}}_{3}}\\times \\frac{286\\text{kJ}}{2\\cancel{\\text{ mol }{\\text{O}}_{3}}}=143\\text{kJ}[\/latex]<\/p>\n<p>Therefore, [latex]\\Delta{H}_{\\text{f}}^{\\circ }\\left[{\\text{O}}_{3}\\left(g\\right)\\right]=\\text{+143}\\text{kJ\/mol}.[\/latex]<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp167644640\"><strong>Check Your Learning<\/strong><\/h4>\n<p>Hydrogen gas, H<sub>2<\/sub>, reacts explosively with gaseous chlorine, Cl<sub>2<\/sub>, to form hydrogen chloride, HCl(<em>g<\/em>). What is the enthalpy change for the reaction of 1 mole of H<sub>2<\/sub>(<em>g<\/em>) with 1 mole of Cl<sub>2<\/sub>(<em>g<\/em>) if both the reactants and products are at standard state conditions? The standard enthalpy of formation of HCl(<em>g<\/em>) is -92.3 kJ\/mol.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q500621\">Show Answer<\/span><\/p>\n<div id=\"q500621\" class=\"hidden-answer\" style=\"display: none\">For the reaction [latex]{\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow 2\\text{HCl}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-184.6\\text{kJ}[\/latex]<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>Example 5:\u00a0<strong>Writing Reaction Equations for [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] <\/strong><\/h3>\n<p>Write the heat of formation reaction equations for:<\/p>\n<ol>\n<li>C<sub>2<\/sub>H<sub>5<\/sub>OH(<em>l<\/em>)<\/li>\n<li>Ca<sub>3<\/sub>(PO<sub>4<\/sub>)<sub>2<\/sub>(<em>s<\/em>)<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q931765\">Show Answers<\/span><\/p>\n<div id=\"q931765\" class=\"hidden-answer\" style=\"display: none\">\n<p>Remembering that [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] reaction equations are for forming 1 mole of the compound from its constituent elements under standard conditions, we have:<\/p>\n<ol>\n<li>[latex]2\\text{C}\\left(s,\\text{graphite}\\right)+3{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)[\/latex]<\/li>\n<li>[latex]3\\text{Ca}\\left(s\\right)+\\frac{1}{2}{\\text{P}}_{4}\\left(s\\right)+4{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Ca}}_{3}{{\\text{(PO}}_{4}\\text{)}}_{2}\\left(s\\right)[\/latex]<\/li>\n<\/ol>\n<p>Note: The standard state of carbon is graphite, and phosphorus exists as P<sub>4<\/sub>.<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp166525568\"><strong>Check Your Learning<\/strong><\/h4>\n<p>Write the heat of formation reaction equations for:<\/p>\n<ol>\n<li>C<sub>2<\/sub>H<sub>5<\/sub>OC<sub>2<\/sub>H<sub>5<\/sub>(<em>l<\/em>)<\/li>\n<li>Na<sub>2<\/sub>CO<sub>3<\/sub>(<em>s<\/em>)<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q539408\">Show Answers<\/span><\/p>\n<div id=\"q539408\" class=\"hidden-answer\" style=\"display: none\">\n<ol>\n<li>[latex]4\\text{C}\\left(s,\\text{graphite}\\right)+5{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{C}}_{2}{\\text{H}}_{5}{\\text{OC}}_{2}{\\text{H}}_{5}\\left(l\\right)[\/latex]<\/li>\n<li>[latex]2\\text{Na}\\left(s\\right)+\\text{C}\\left(s,\\text{graphite}\\right)+\\frac{3}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Na}}_{2}{\\text{CO}}_{3}\\left(s\\right)[\/latex]<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<ol>\n<li>Does the standard enthalpy of formation of H<sub>2<\/sub>O(<em>g<\/em>) differ from \u0394<em>H<\/em>\u00b0 for the reaction [latex]{\\text{2H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{H}}_{2}\\text{O}\\left(g\\right)?[\/latex]<\/li>\n<li>Joseph Priestly prepared oxygen in 1774 by heating red mercury(II) oxide with sunlight focused through a lens. How much heat is required to decompose exactly 1 mole of red HgO(<em>s<\/em>) to Hg(<em>l<\/em>) and O<sub>2<\/sub>(<em>g<\/em>) under standard conditions?<\/li>\n<li>How many kilojoules of heat will be released when exactly 1 mole of manganese, Mn, is burned to form Mn<sub>3<\/sub>O<sub>4<\/sub>(<em>s<\/em>) at standard state conditions?<\/li>\n<li>How many kilojoules of heat will be released when exactly 1 mole of iron, Fe, is burned to form Fe<sub>2<\/sub>O<sub>3<\/sub>(<em>s<\/em>) at standard state conditions?<\/li>\n<li>The following sequence of reactions occurs in the commercial production of aqueous nitric acid:[latex]4{\\text{NH}}_{3}\\left(g\\right)+5{\\text{O}}_{2}\\left(g\\right)\\rightarrow 4\\text{NO}\\left(g\\right)+6{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=-907\\text{kJ}[\/latex][latex]2\\text{NO}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta\\text{H}=-113\\text{kJ}[\/latex] [latex]3{\\text{NO}}_{2}+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow 2{\\text{HNO}}_{2}\\left(aq\\right)+\\text{NO}\\left(g\\right)\\Delta\\text{H}=-139\\text{kJ}[\/latex]<br \/>\nDetermine the total energy change for the production of one mole of aqueous nitric acid by this process.<\/li>\n<li>Both graphite and diamond burn. [latex]\\text{C}\\left(s,\\text{diamond}\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)[\/latex] For the conversion of graphite to diamond:[latex]\\text{C}\\left(s,\\text{graphite}\\right)\\rightarrow\\text{C}\\left(s,\\text{diamond}\\right)\\Delta{H}_{298}^{\\circ }=1.90\\text{kJ}[\/latex] Which produces more heat, the combustion of graphite or the combustion of diamond?<\/li>\n<li>From the molar heats of formation in <a class=\"target-chapter\" title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, determine how much heat is required to evaporate one mole of water: [latex]{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(g\\right)[\/latex]<\/li>\n<li>Which produces more heat? [latex]\\text{Os}\\left(s\\right)\\rightarrow 2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{OsO}}_{4}\\left(s\\right)[\/latex] or [latex]\\text{Os}\\left(s\\right)\\rightarrow 2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{OsO}}_{4}\\left(g\\right)[\/latex] for the phase change [latex]{\\text{OsO}}_{4}\\left(s\\right)\\rightarrow{\\text{OsO}}_{4}\\left(g\\right)\\Delta\\text{H}=56.4\\text{kJ}[\/latex]<\/li>\n<li>Calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for the process [latex]\\text{Sb}\\left(s\\right)+\\frac{5}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{5}\\left(g\\right)[\/latex] from the following information: [latex]\\begin{array}{l}\\text{Sb}\\left(s\\right)+\\frac{3}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{3}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-314\\text{kJ}\\\\ {\\text{SbCl}}_{3}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{5}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-80\\text{kJ}\\end{array}[\/latex]<\/li>\n<li>Calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for the process [latex]\\text{Zn}\\left(s\\right)+\\text{S}\\left(s\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{ZnSO}}_{4}\\left(s\\right)[\/latex] from the following information: [latex]\\begin{array}{l}\\text{Zn}\\left(s\\right)+\\text{S}\\left(s\\right)\\rightarrow\\text{ZnS}\\left(s\\right)\\Delta{H}_{298}^{\\circ }=-206.0\\text{kJ}\\\\ \\text{ZnS}\\left(s\\right)+{\\text{2O}}_{\\text{2}}\\left(g\\right)\\rightarrow{\\text{ZnSO}}_{4}\\left(s\\right)\\Delta{H}_{298}^{\\circ }=-776.8\\text{kJ}\\end{array}[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q93779\">Show Selected Answers<\/span><\/p>\n<div id=\"q93779\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. No. The standard enthalpy of formation can be determined for anything, including H<sub>2<\/sub>O(<em>g<\/em>), and water does not have to be liquid in this case, it\u2019s the gas-phase water that is the substance for which the heat of formation is to be found. However, the heat of this reaction is defined for two moles of H<sub>2<\/sub>O(<em>g<\/em>), thus the heat of formation is half of the heat of the reaction.<\/p>\n<p>3. This process requires 3 mol of Mn. For 1 mol, [latex]\\frac{1}{3}\\left(-1378.83\\text{kJ}\\right)=459.6\\text{kJ}.[\/latex]<\/p>\n<p>5. Enough material must be produced in each stage to proceed with the next. So [latex]\\frac{1}{2}[\/latex] of reaction 1 produces the NO required in reaction 2. But [latex]\\frac{3}{2}[\/latex] units of reaction 2 are required to provide enough NO<sub>2<\/sub> for reaction 3. Up to this stage, the heat produced is [latex]\\frac{3}{2}\\left[\\frac{1}{2}\\left(-907\\right)+\\left(-113\\right)\\right]=\\frac{3}{2}\\left(-566.55\\right)=-850\\text{kJ}[\/latex] to have the material to proceed with reaction 3. Therefore, from beginning to end, \u2013850 + (\u2013139) = \u2013989 kJ are released. The question asks for the enthalpy change for 1 mole. Therefore, division of the last answer by 2 gives -495 kJ\/mol.<\/p>\n<p>7. The heat of formation of H<sub>2<\/sub>O(<em>l<\/em>) is -285.83 kJ\/mol. The heat of formation of H<sub>2<\/sub>O(<em>g<\/em>) is -241.82 kJ\/mol. For the reaction:<br \/>\n[latex]{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow{\\text{H}}_{2}\\text{O}\\left(g\\right),[\/latex]<\/p>\n<p>the enthalpy of the reaction is the difference of heats of formation of the reactant and the product; thus, it is -241.82 &#8211; (-285.83) = 44.01 kJ\/mol.<\/p>\n<p>9. Add the two equations and their heat together.<\/p>\n<p>[latex]\\begin{array}{lll}\\text{Sb}\\left(s\\right)+\\frac{3}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{3}\\left(g\\right)\\hfill & \\hfill & \\Delta{H}_{298}^{\\circ }=-314\\text{kJ}\\hfill \\\\ \\frac{{\\text{SbCl}}_{3}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{5}\\left(g\\right)}{\\text{Sb}\\left(s\\right)+\\frac{\\text{5}}{\\text{2}}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SbCl}}_{5}\\left(g\\right)}\\hfill & \\hfill & \\frac{\\Delta{H}_{298}^{\\circ }=-80\\text{kJ}}{\\Delta{H}_{298}^{\\circ }=-394\\text{kJ}}\\hfill \\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<h2 data-type=\"title\">Hess\u2019s Law<\/h2>\n<p>There are two ways to determine the amount of heat involved in a chemical change: measure it experimentally, or calculate it from other experimentally determined enthalpy changes. Some reactions are difficult, if not impossible, to investigate and make accurate measurements for experimentally. And even when a reaction is not hard to perform or measure, it is convenient to be able to determine the heat involved in a reaction without having to perform an experiment.<\/p>\n<p>This type of calculation usually involves the use of <strong>Hess\u2019s law<\/strong>, which states: <em>If a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps<\/em>. Hess\u2019s law is valid because enthalpy is a state function: Enthalpy changes depend only on where a chemical process starts and ends, but not on the path it takes from start to finish. For example, we can think of the reaction of carbon with oxygen to form carbon dioxide as occurring either directly or by a two-step process. The direct process is written:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-394\\text{kJ}[\/latex]<\/p>\n<p>In the two-step process, first carbon monoxide is formed:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-111\\text{kJ}[\/latex]<\/p>\n<p>Then, carbon monoxide reacts further to form carbon dioxide:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-283\\text{kJ}[\/latex]<\/p>\n<p>The equation describing the overall reaction is the sum of these two chemical changes:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}\\\\ \\text{Step 1: }\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)\\\\ \\underline{\\text{Step 2: }\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)}\\\\ \\text{Sum: }\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)+\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)+{\\text{CO}}_{2}\\left(g\\right)\\end{array}[\/latex]<\/p>\n<p>Because the CO produced in Step 1 is consumed in Step 2, the net change is:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)[\/latex]<\/p>\n<p>According to Hess\u2019s law, the enthalpy change of the reaction will equal the sum of the enthalpy changes of the steps. We can apply the data from the experimental enthalpies of combustion in Table 1 to find the enthalpy change of the entire reaction from its two steps:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ll}\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)\\hfill & \\Delta{H}_{298}^{\\circ }=-111\\text{kJ}\\hfill \\\\ \\frac{\\text{CO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)}{\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)}\\hfill & \\frac{\\Delta{H}_{298}^{\\circ }=-283\\text{kJ}}{\\Delta{H}_{298}^{\\circ }=-394\\text{kJ}}\\hfill \\end{array}[\/latex]<\/p>\n<p>The result is shown in Figure 7. We see that \u0394<em>H<\/em> of the overall reaction is the same whether it occurs in one step or two. This finding (overall \u0394<em>H<\/em> for the reaction = sum of \u0394<em>H<\/em> values for reaction \u201csteps\u201d in the overall reaction) is true in general for chemical and physical processes.<\/p>\n<div id=\"attachment_5378\" style=\"width: 985px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5378\" class=\"size-full wp-image-5378\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/219\/2016\/08\/09033420\/CNX_Chem_05_03_HessCO21.jpg\" alt=\"A diagram is shown. A long arrow faces upward on the left with the phrase \u201cH increasing.\u201d A horizontal line at the bottom of the diagram is shown with the formula \u201cC O subscript 2 (g)\u201d below it. A horizontal line at the top of the diagram has the formulas \u201cC (s) + O subscript 2 (g)\u201d above it. The top and bottom lines are connected by a downward facing arrow with the value \u201c\u0394 H = \u2013394 k J\u201d written beside it. Below and to the right of the top horizontal line is a second horizontal line with the equations \u201cC O (g) + one half O subscript 2 (g)\u201d above it. This line and the bottom line are connected by a downward facing arrow with the value \u201c\u0394 H = \u2013283 k J\u201d written beside it. The same line and the top line are connected by a downward facing arrow with the value \u201c\u0394 H = \u2013111 k J\u201d written beside it. There are three brackets to the right of the diagram. The first bracket runs from the top horizontal line to the second horizontal line. It is labeled, \u201cEnthalpy of reactants.\u201d The second bracket runs from the second horizontal line to the bottom horizontal line. It is labeled, \u201cEnthalpy of products.\u201d Both of these brackets are included in the third bracket which runs from the top to the bottom of the diagram. It is labeled, \u201cEnthalpy change of exothermic reaction in 1 or 2 steps.\u201d\" width=\"975\" height=\"537\" \/><\/p>\n<p id=\"caption-attachment-5378\" class=\"wp-caption-text\">Figure 7. The formation of CO<sub>2<\/sub>(<em>g<\/em>) from its elements can be thought of as occurring in two steps, which sum to the overall reaction, as described by Hess\u2019s law. The horizontal blue lines represent enthalpies. For an exothermic process, the products are at lower enthalpy than are the reactants.<\/p>\n<\/div>\n<p>Before we further practice using Hess\u2019s law, let us recall two important features of \u0394<em>H<\/em>.<\/p>\n<ol id=\"fs-idp167198464\" data-number-style=\"arabic\">\n<li>\u0394<em>H<\/em> is directly proportional to the quantities of reactants or products. For example, the enthalpy change for the reaction forming 1 mole of NO<sub>2<\/sub>(<em>g<\/em>) is +33.2 kJ:\n<p style=\"text-align: center;\">[latex]\\frac{1}{2}{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{NO}}_{2}\\left(g\\right)\\Delta\\text{H}=\\text{+33.2}\\text{kJ}[\/latex]<\/p>\n<p>When 2 moles of NO<sub>2<\/sub> (twice as much) are formed, the \u0394<em>H<\/em> will be twice as large:<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta\\text{H}=\\text{+66.4}\\text{kJ}[\/latex]<\/p>\n<p>In general, if we multiply or divide an equation by a number, then the enthalpy change should also be multiplied or divided by the same number.<\/li>\n<li>\u0394<em>H<\/em> for a reaction in one direction is equal in magnitude and opposite in sign to \u0394<em>H<\/em> for the reaction in the reverse direction. For example, given that:\n<p style=\"text-align: center;\">[latex]{\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow 2\\text{HCl}\\left(g\\right)\\Delta\\text{H}=-184.6\\text{kJ}[\/latex]<\/p>\n<p>Then, for the \u201creverse\u201d reaction, the enthalpy change is also \u201creversed:\u201d<\/p>\n<p style=\"text-align: center;\">[latex]2\\text{HCl}\\left(g\\right)\\rightarrow{\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\Delta\\text{H}=\\text{+184.6}\\text{kJ}[\/latex]<\/p>\n<\/li>\n<\/ol>\n<div class=\"textbox examples\">\n<h3>Example 6:\u00a0<strong>Stepwise Calculation of [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] Using Hess\u2019s Law<\/strong><\/h3>\n<p>Determine the enthalpy of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex], of FeCl<sub>3<\/sub>(<em>s<\/em>) from the enthalpy changes of the following two-step process that occurs under standard state conditions:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Fe}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{2}\\left(s\\right)\\Delta\\text{H}^{\\circ }=-341.8\\text{kJ}[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{FeCl}}_{2}\\left(s\\right)+\\frac{1}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{3}\\left(s\\right)\\Delta\\text{H}^{\\circ }=-57.7\\text{kJ}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q783173\">Show Answer<\/span><\/p>\n<div id=\"q783173\" class=\"hidden-answer\" style=\"display: none\">\n<p>We are trying to find the standard enthalpy of formation of FeCl<sub>3<\/sub>(<em>s<\/em>), which is equal to \u0394<em>H<\/em>\u00b0 for the reaction:<\/p>\n<p style=\"text-align: center;\">[latex]\\text{Fe}\\left(s\\right)+\\frac{3}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{3}\\left(s\\right)\\Delta{H}_{\\text{f}}^{\\circ }=?[\/latex]<\/p>\n<p>Looking at the reactions, we see that the reaction for which we want to find \u0394<em>H<\/em>\u00b0 is the sum of the two reactions with known \u0394<em>H<\/em> values, so we must sum their \u0394<em>H<\/em>s:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{lll}\\text{Fe}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{\\text{2}}\\left(s\\right)\\hfill & \\hfill & \\Delta H^{\\circ }=-341.8\\text{kJ}\\hfill \\\\ \\frac{{\\text{FeCl}}_{\\text{2}}\\left(s\\right)+\\frac{1}{2}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{\\text{3}}\\left(s\\right)}{\\text{Fe}\\left(s\\right)+\\frac{\\text{1}}{\\text{2}}{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{FeCl}}_{\\text{3}}\\left(s\\right)}\\hfill & \\hfill & \\frac{\\Delta H^{\\circ }=-57.7\\text{kJ}}{\\Delta H^{\\circ }=-399.5\\text{kJ}}\\hfill \\end{array}[\/latex]<\/p>\n<p>The enthalpy of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex], of FeCl<sub>3<\/sub>(<em>s<\/em>) is \u2212399.5 kJ\/mol.<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp149511040\"><strong>Check Your Learning<\/strong><\/h4>\n<p>Calculate \u0394<em>H<\/em> for the process:<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)[\/latex]<\/p>\n<p>from the following information:<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2\\text{NO}\\left(g\\right)\\Delta\\text{H}=180.5\\text{kJ}[\/latex]<br \/>\n[latex]\\text{NO}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{NO}}_{2}\\left(g\\right)\\Delta\\text{H}=-57.06\\text{kJ}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q16353\">Show Answer<\/span><\/p>\n<div id=\"q16353\" class=\"hidden-answer\" style=\"display: none\">66.4 kJ<\/div>\n<\/div>\n<\/div>\n<p>Here is a less straightforward example that illustrates the thought process involved in solving many Hess\u2019s law problems. It shows how we can find many standard enthalpies of formation (and other values of \u0394<em>H<\/em>) if they are difficult to determine experimentally.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 7:\u00a0<strong>A More Challenging Problem Using Hess\u2019s Law<\/strong><\/h3>\n<p>Chlorine monofluoride can react with fluorine to form chlorine trifluoride:<\/p>\n<p><em>(i)<\/em> [latex]\\text{ClF}\\left(g\\right)+{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{ClF}}_{3}\\left(g\\right)\\Delta\\text{H}^{\\circ }=?[\/latex]<\/p>\n<p>Use the reactions here to determine the \u0394<em>H<\/em>\u00b0 for reaction <em>(i)<\/em>:<\/p>\n<p><em>(ii)<\/em> [latex]2{\\text{OF}}_{2}\\left(g\\right)\\rightarrow{\\text{O}}_{2}\\left(g\\right)+2{\\text{F}}_{2}\\left(g\\right)\\Delta{H}_{\\left(ii\\right)}^{\\circ }=-49.4\\text{kJ}[\/latex]<\/p>\n<p><em>(iii)<\/em> [latex]2\\text{ClF}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+{\\text{OF}}_{2}\\left(g\\right)\\Delta{H}_{\\left(iii\\right)}^{\\circ }=\\text{+205.6}\\text{kJ}[\/latex]<\/p>\n<p><em>(iv)<\/em> [latex]{\\text{ClF}}_{3}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{3}{2}{\\text{OF}}_{2}\\left(g\\right)\\Delta{H}_{\\left(iv\\right)}^{\\circ }=\\text{+266.7}\\text{kJ}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q122087\">Show Answer<\/span><\/p>\n<div id=\"q122087\" class=\"hidden-answer\" style=\"display: none\">\n<p>Our goal is to manipulate and combine reactions <em>(ii)<\/em>, <em>(iii)<\/em>, and <em>(iv)<\/em> such that they add up to reaction <em>(i)<\/em>. Going from left to right in <em>(i)<\/em>, we first see that ClF(<em>g<\/em>) is needed as a reactant. This can be obtained by multiplying reaction <em>(iii)<\/em> by [latex]\\frac{1}{2},[\/latex] which means that the \u0394<em>H\u00b0<\/em>\u00a0change is also multiplied by [latex]\\frac{1}{2}\\text{:}[\/latex]<\/p>\n<p>[latex]\\text{ClF}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{1}{2}{\\text{OF}}_{2}\\left(g\\right)\\Delta\\text{H}^{\\circ }=\\frac{1}{2}\\left(205.6\\right)=\\text{+102.8}\\text{kJ}[\/latex]<\/p>\n<p>Next, we see that F<sub>2<\/sub> is also needed as a reactant. To get this, reverse and halve reaction <em>(ii)<\/em>, which means that the \u0394<em>H<\/em>\u00b0 changes sign and is halved:<\/p>\n<p>[latex]\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)+{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{OF}}_{2}\\left(g\\right)\\Delta\\text{H}^{\\circ }=\\text{+24.7}\\text{kJ}[\/latex]<\/p>\n<p>To get ClF<sub>3<\/sub> as a product, reverse <em>(iv)<\/em>, changing the sign of \u0394<em>H<\/em>\u00b0:<\/p>\n<p>[latex]\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{3}{2}{\\text{OF}}_{2}\\left(g\\right)\\rightarrow{\\text{ClF}}_{3}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\Delta\\text{H}^{\\circ }=\\text{+266.7}\\text{kJ}[\/latex]<\/p>\n<p>Now check to make sure that these reactions add up to the reaction we want:<\/p>\n<p>[latex]\\begin{array}{lll}\\text{ClF}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{1}{2}{\\text{OF}}_{2}\\left(g\\right)\\hfill & \\hfill & \\Delta H^{\\circ }=\\text{+102.8}\\text{kJ}\\hfill \\\\ \\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)+{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{OF}}_{2}\\left(g\\right)\\hfill & \\hfill & \\Delta H^{\\circ }=\\text{+24.7}\\text{kJ}\\hfill \\\\ \\frac{\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}\\left(g\\right)+\\frac{3}{2}{\\text{OF}}_{2}\\left(g\\right)\\rightarrow{\\text{ClF}}_{3}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)}{\\text{ClF}\\left(g\\right)+{\\text{F}}_{2}\\rightarrow{\\text{ClF}}_{3}\\left(g\\right)\\phantom{\\rule{8em}{0ex}}}\\hfill & \\hfill & \\frac{\\Delta H^{\\circ }=-266.7\\text{kJ}}{\\Delta H^{\\circ }=-139.2\\text{kJ}}\\hfill \\end{array}[\/latex]<\/p>\n<p>Reactants [latex]\\frac{1}{2}{\\text{O}}_{2}[\/latex] and [latex]\\frac{1}{2}{\\text{O}}_{2}[\/latex] cancel out product O<sub>2<\/sub>; product [latex]\\frac{1}{2}{\\text{Cl}}_{2}\\text{O}[\/latex] cancels reactant [latex]\\frac{1}{2}{\\text{Cl}}_{2}\\text{O;}[\/latex] and reactant [latex]\\frac{3}{2}{\\text{OF}}_{2}[\/latex] is cancelled by products [latex]\\frac{1}{2}{\\text{OF}}_{2}[\/latex] and OF<sub>2<\/sub>. This leaves only reactants ClF(<em>g<\/em>) and F<sub>2<\/sub>(<em>g<\/em>) and product ClF<sub>3<\/sub>(<em>g<\/em>), which are what we want. Since summing these three modified reactions yields the reaction of interest, summing the three modified \u0394<em>H<\/em>\u00b0 values will give the desired \u0394<em>H<\/em>\u00b0:<\/p>\n<p>[latex]\\Delta H^{\\circ }=\\left(+102.8\\text{kJ}\\right)+\\left(24.7\\text{kJ}\\right)+\\left(-266.7\\text{kJ}\\right)=-139.2\\text{kJ}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp154380128\"><strong>Check Your Learning<\/strong><\/h4>\n<p>Aluminum chloride can be formed from its elements:<\/p>\n<p><em>(i)<\/em> [latex]2\\text{Al}\\left(s\\right)+3{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow 2{\\text{AlCl}}_{3}\\left(s\\right)\\Delta H^{\\circ }=?[\/latex]<\/p>\n<p>Use the reactions here to determine the \u0394<em>H<\/em>\u00b0 for reaction <em>(i)<\/em>:<\/p>\n<p><em>(ii)<\/em> [latex]\\text{HCl}\\left(g\\right)\\rightarrow\\text{HCl}\\left(aq\\right)\\Delta{H}_{\\left(ii\\right)}^{\\circ }=-74.8\\text{kJ}[\/latex]<\/p>\n<p><em>(iii)<\/em> [latex]{\\text{H}}_{2}\\left(g\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow 2\\text{HCl}\\left(g\\right)\\Delta{H}_{\\left(iii\\right)}^{\\circ }=-185\\text{kJ}[\/latex]<\/p>\n<p><em>(iv)<\/em> [latex]{\\text{AlCl}}_{3}\\left(aq\\right)\\rightarrow{\\text{AlCl}}_{3}\\left(s\\right)\\Delta{H}_{\\left(iv\\right)}^{\\circ }=+323\\text{kJ\/mol}[\/latex]<\/p>\n<p><em>(v)<\/em> [latex]\\text{2Al}\\left(s\\right)+6\\text{HCl}\\left(aq\\right)\\rightarrow 2{\\text{AlCl}}_{3}\\left(aq\\right)+3{\\text{H}}_{2}\\left(g\\right)\\Delta{H}_{\\left(v\\right)}^{\\circ }=-1049\\text{kJ}[\/latex]<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q15946\">Show Answer<\/span><\/p>\n<div id=\"q15946\" class=\"hidden-answer\" style=\"display: none\">\u20131407 kJ<\/div>\n<\/div>\n<\/div>\n<p>We also can use <strong>Hess\u2019s law<\/strong> to determine the enthalpy change of any reaction if the corresponding enthalpies of formation of the reactants and products are available. The stepwise reactions we consider are: (i) decompositions of the reactants into their component elements (for which the enthalpy changes are proportional to the negative of the enthalpies of formation of the reactants), followed by (ii) re-combinations of the elements to give the products (with the enthalpy changes proportional to the enthalpies of formation of the products). The standard enthalpy change of the overall reaction is therefore equal to: (ii) the sum of the standard enthalpies of formation of all the products plus (i) the sum of the negatives of the standard enthalpies of formation of the reactants. This is usually rearranged slightly to be written as follows, with \u2211 representing \u201cthe sum of\u201d and <em>n<\/em> standing for the stoichiometric coefficients:<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta{H}_{\\text{reaction}}^{\\circ }=\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left(\\text{products}\\right)-\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left(\\text{reactants}\\right)[\/latex]<\/p>\n<p>The following example shows in detail why this equation is valid, and how to use it to calculate the enthalpy change for a reaction of interest.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 8:\u00a0<strong>Using Hess\u2019s Law<\/strong><\/h3>\n<p>What is the standard enthalpy change for the reaction:<\/p>\n<p style=\"text-align: center;\">[latex]3{\\text{NO}}_{2}\\left(g\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow 2{\\text{HNO}}_{3}\\left(aq\\right)+\\text{NO}\\left(g\\right)\\Delta\\text{H}^{\\circ }=?[\/latex]<\/p>\n<p>There are two possible solutions for this reaction. The first solution supports why the general equation is valid, the second solution uses the equation.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q511660\">Show Solution 1<\/span><\/p>\n<div id=\"q511660\" class=\"hidden-answer\" style=\"display: none\">\n<h4 id=\"fs-idp134564208\">Solution 1 (Supporting Why the General Equation Is Valid)<\/h4>\n<p>We can write this reaction as the sum of the decompositions of 3NO<sub>2<\/sub>(<em>g<\/em>) and 1H<sub>2<\/sub>O(<em>l<\/em>) into their constituent elements, and the formation of 2HNO<sub>3<\/sub>(<em>aq<\/em>) and 1NO(<em>g<\/em>) from their constituent elements. Writing out these reactions, and noting their relationships to the [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] values for these compounds (from <a title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>), we have:<\/p>\n<p style=\"text-align: center;\">[latex]3{\\text{NO}}_{2}\\left(g\\right)\\rightarrow{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\Delta{H}_{1}^{\\circ }=99.6\\text{kJ}[\/latex]<br \/>\n[latex]{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow{\\text{H}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\Delta{H}_{2}^{\\circ }=\\text{+285.8}\\text{kJ}\\left[-1\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left({\\text{H}}_{2}\\text{O}\\right)\\right][\/latex]<br \/>\n[latex]{\\text{H}}_{2}\\left(g\\right)+{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{HNO}}_{3}\\left(aq\\right)\\Delta{H}_{3}^{\\circ }=414.8\\text{kJ}\\left[2\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left({\\text{HNO}}_{3}\\right)\\right][\/latex]<br \/>\n[latex]\\frac{1}{2}{\\text{N}}_{2}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{NO}\\left(g\\right)\\Delta{H}_{4}^{\\circ }=\\text{+90.2}\\text{kJ}\\left[1\\times \\left(\\text{NO}\\right)\\right][\/latex]<\/p>\n<p>Summing these reaction equations gives the reaction we are interested in:<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{3NO}}_{2}\\left(g\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow 2{\\text{HNO}}_{3}\\left(aq\\right)+\\text{NO}\\left(g\\right)[\/latex]<\/p>\n<p>Summing their enthalpy changes gives the value we want to determine:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{cc}\\hfill \\Delta{H}_{\\text{rxn}}^{\\circ }& =\\Delta{H}_{1}^{\\circ }+\\Delta{H}_{2}^{\\circ }+\\Delta{H}_{3}^{\\circ }+\\Delta{H}_{4}^{\\circ }=\\left(-99.6\\text{kJ}\\right)+\\left(\\text{+285.8}\\text{kJ}\\right)+\\left(-414.8\\text{kJ}\\right)+\\left(\\text{+90.2}\\text{kJ}\\right)\\hfill \\\\ & =-138.4\\text{kJ.}\\hfill \\end{array}[\/latex]<\/p>\n<p>So the standard enthalpy change for this reaction is \u0394<em>H<\/em>\u00b0 = \u2212138.4 kJ.<\/p>\n<p>Note that this result was obtained by (1) multiplying the [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of each product by its stoichiometric coefficient and summing those values, (2) multiplying the [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of each reactant by its stoichiometric coefficient and summing those values, and then (3) subtracting the result found in (2) from the result found in (1). This is also the procedure in using the general equation, as shown.<\/p>\n<\/div>\n<\/div>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q565595\">Show Solution 2<\/span><\/p>\n<div id=\"q565595\" class=\"hidden-answer\" style=\"display: none\">\n<h4 id=\"fs-idp146127120\">Solution 2 (Using the Equation)<\/h4>\n<p>Alternatively, we could use the special form of Hess\u2019s law given previously:<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta{H}_{\\text{reaction}}^{\\circ }=\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\text{(products)}-\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left(\\text{reactants}\\right)[\/latex]<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}\\\\ =\\left[2\\cancel{\\text{mol}{\\text{HNO}}_{3}}\\times \\frac{-207.4\\text{kJ}}{\\cancel{\\text{mol}{\\text{HNO}}_{3}\\left(aq\\right)}}+1\\cancel{\\text{mol}\\text{NO}\\left(g\\right)}\\times \\frac{\\text{+90.2}\\text{kJ}}{\\cancel{\\text{mol}\\text{NO}\\left(g\\right)}}\\right]\\\\ -\\left[3\\cancel{\\text{mol}{\\text{NO}}_{2}\\left(g\\right)}\\times \\frac{\\text{+33.2}\\text{kJ}}{\\cancel{\\text{mol}{\\text{NO}}_{2}\\left(g\\right)}}+1\\cancel{\\text{mol}{\\text{H}}_{2}\\text{O}\\left(l\\right)}\\times \\frac{-285.8\\text{kJ}}{\\cancel{\\text{mol}{\\text{H}}_{2}\\text{O}\\left(l\\right)}}\\right]\\\\ =2\\left(-207.4\\text{kJ}\\right)+1\\left(\\text{+90.2}\\text{kJ}\\right)-3\\left(\\text{+33.2}\\text{kJ}\\right)-1\\left(-285.8\\text{kJ}\\right)\\\\ =-138.4\\text{kJ}\\end{array}[\/latex]<\/p>\n<\/div>\n<\/div>\n<h4 id=\"fs-idp165556368\"><strong>Check Your Learning<\/strong><\/h4>\n<p>Calculate the heat of combustion of 1 mole of ethanol, C<sub>2<\/sub>H<sub>5<\/sub>OH(<em>l<\/em>), when H<sub>2<\/sub>O(<em>l<\/em>) and CO<sub>2<\/sub>(<em>g<\/em>) are formed. Use the following enthalpies of formation: C<sub>2<\/sub>H<sub>5<\/sub>OH(<em>l<\/em>), \u2212278 kJ\/mol; H<sub>2<\/sub>O(<em>l<\/em>), \u2212286 kJ\/mol; and CO<sub>2<\/sub>(<em>g<\/em>), \u2212394 kJ\/mol.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q509110\">Show Answer<\/span><\/p>\n<div id=\"q509110\" class=\"hidden-answer\" style=\"display: none\">\u20131368 kJ\/mol<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<ol>\n<li>Calculate the standard molar enthalpy of formation of NO(<em>g<\/em>) from the following data: [latex]\\begin{array}{l}{\\text{N}}_{2}\\left(g\\right)+2{\\text{O}}_{2}\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=66.4\\text{kJ}\\\\ \\text{2NO}\\left(g\\right)+{\\text{O}}_{2}\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=-114.1\\text{kJ}\\end{array}[\/latex]<\/li>\n<li>Using the data in <a class=\"target-chapter\" title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, calculate the standard enthalpy change for each of the following reactions:\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2\\text{NO}\\left(g\\right)[\/latex]<\/li>\n<li>[latex]\\text{Si}\\left(s\\right)+2{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{SiCl}}_{4}\\left(g\\right)[\/latex]<\/li>\n<li>[latex]{\\text{Fe}}_{2}\\text{O}\\left(s\\right)+3{\\text{H}}_{2}\\left(g\\right)\\rightarrow 2\\text{Fe}\\left(s\\right)+3{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/li>\n<li>[latex]2\\text{LiOH}\\left(s\\right)+{\\text{CO}}_{2}\\left(g\\right)\\rightarrow{\\text{Li}}_{2}{\\text{CO}}_{3}\\left(s\\right)+{\\text{H}}_{2}\\text{O}\\left(g\\right)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>Using the data in <a class=\"target-chapter\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\">Standard Thermodynamic Properties for Selected Substances<\/a>, calculate the standard enthalpy change for each of the following reactions:\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\\text{Si}\\left(s\\right)+2{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{SiF}}_{4}\\left(g\\right)[\/latex]<\/li>\n<li>[latex]2\\text{C}\\left(s\\right)+2{\\text{H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CH}}_{3}{\\text{CO}}_{2}\\text{H}\\left(l\\right)[\/latex]<\/li>\n<li>[latex]{\\text{CH}}_{4}\\left(g\\right)+{\\text{N}}_{2}\\left(g\\right)\\rightarrow\\text{HCN}\\left(g\\right){\\text{+NH}}_{3}\\left(g\\right)\\text{;}[\/latex]<\/li>\n<li>[latex]{\\text{Cs}}_{2}\\left(g\\right)+3{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{CCl}}_{4}\\left(g\\right){\\text{+S}}_{2}{\\text{Cl}}_{2}\\left(g\\right)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>The following reactions can be used to prepare samples of metals. Determine the enthalpy change under standard state conditions for each.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]2{\\text{Ag}}_{2}\\text{O}\\left(s\\right)\\rightarrow 4\\text{Ag}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)[\/latex]<\/li>\n<li>[latex]\\text{SnO}\\left(s\\right)+\\text{CO}\\left(g\\right)\\rightarrow\\text{Sn}\\left(s\\right)+{\\text{CO}}_{2}\\left(g\\right)[\/latex]<\/li>\n<li>[latex]{\\text{Cr}}_{2}{\\text{O}}_{3}\\left(s\\right)+3{\\text{H}}_{2}\\left(g\\right)\\rightarrow 2\\text{Cr}\\left(s\\right)+3{\\text{H}}_{2}\\text{O}\\left(l\\right)[\/latex]<\/li>\n<li>[latex]2\\text{Al}\\left(s\\right)+{\\text{Fe}}_{2}{\\text{O}}_{3}\\left(s\\right)\\rightarrow{\\text{Al}}_{2}{\\text{O}}_{3}\\left(s\\right)+2\\text{Fe}\\left(s\\right)[\/latex]<\/li>\n<\/ol>\n<\/li>\n<li>The decomposition of hydrogen peroxide, H<sub>2<\/sub>O<sub>2<\/sub>, has been used to provide thrust in the control jets of various space vehicles. Using the data in <a class=\"target-chapter\" title=\"Standard Thermodynamic Properties for Selected Substances\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, determine how much heat is produced by the decomposition of exactly 1 mole of H<sub>2<\/sub>O<sub>2<\/sub> under standard conditions. [latex]2{\\text{H}}_{2}{\\text{O}}_{2}\\left(l\\right)\\rightarrow 2{\\text{H}}_{2}\\text{O}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)[\/latex]<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q835105\">Show Selected Answers<\/span><\/p>\n<div id=\"q835105\" class=\"hidden-answer\" style=\"display: none\">\n<p>1. Hess\u2019s law can be applied to the two equations by reversing the direction of the second equation. The first equation is a formation reaction and is so indicated by writing [latex]\\Delta{H}_{298}^{\\circ }[\/latex].<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{l}{\\text{N}}_{2}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2{\\text{NO}}_{2}\\left(g\\right)\\Delta{H}_{298}^{\\circ }=66.4\\text{kJ}\\\\ 2{\\text{NO}}_{\\text{2}}\\left(g\\right)\\rightarrow 2\\text{NO}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\Delta H^{\\circ }=114.1\\text{kJ}\\end{array}[\/latex]<\/p>\n<p>Adding the equations yields:<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow 2\\text{NO}\\left(g\\right)\\Delta{H}^{\\circ }=180.5\\text{kJ}.[\/latex]<\/p>\n<p>This is the heat of formation of 2 mol of NO. For 1 mol,<\/p>\n<p style=\"text-align: center;\">[latex]\\Delta{H}_{298}^{\\circ }=\\frac{180.5\\text{kJ}}{2}=90.3{\\text{mol}}^{-1}\\text{of}\\text{NO}.[\/latex]<\/p>\n<p>3. The standard enthalpy changes are as follows:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>[latex]\\text{Si}\\left(s\\right)+2{\\text{F}}_{2}\\left(g\\right)\\rightarrow{\\text{SiF}}_{4}\\left(g\\right)[\/latex]<br \/>\n[latex]\\begin{array}{rll} \\\\ \\Delta{H}_{\\text{reaction}}^{\\circ }&=&\\Delta{H}_{\\text{products}}^{\\circ }-\\Delta{H}_{\\text{reactants}}^{\\circ }\\\\ &=&\\Delta{H}_{{\\text{SiF}}_{4}\\left(g\\right)}^{\\circ }-\\Delta{H}_{\\text{Si}\\left(s\\right)}^{\\circ }-2\\Delta{H}_{{\\text{F}}_{2}\\left(g\\right)}^{\\circ }\\\\ &=&-1614.9-\\left(0\\right)-2\\left(0\\right)=-1615.0\\text{kJ}{\\text{mol}}^{-1}\\end{array}[\/latex]<\/li>\n<li>[latex]2\\text{C}\\left(s\\right)+2{\\text{H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CH}}_{3}{\\text{CO}}_{2}\\text{H}\\left(l\\right)[\/latex]<br \/>\n[latex]\\begin{array}{rll} \\\\ \\Delta{H}_{\\text{reaction}}^{\\circ }&=&\\Delta{H}_{\\text{products}}^{\\circ }-\\Delta{H}_{\\text{reactants}}^{\\circ }\\\\ &=&\\Delta{H}_{{\\text{CH}}_{3}{\\text{CO}}_{2}\\text{H}\\left(l\\right)}^{\\circ }-2\\Delta{H}_{\\text{C}\\left(s\\right)}^{\\circ }-2\\Delta{H}_{{\\text{H}}_{2}\\left(g\\right)}^{\\circ }-\\Delta{H}_{{\\text{O}}_{2}\\left(g\\right)}^{\\circ }\\\\ &=&-484.5-2\\left(0\\right)-2\\left(0\\right)-\\left(0\\right)=-484.3\\text{kJ}{\\text{mol}}^{-1}\\end{array}[\/latex]<\/li>\n<li>[latex]{\\text{CH}}_{\\text{4}}\\left(g\\right)\\rightarrow\\text{C}\\left(s\\right)+2{\\text{H}}_{2}\\left(g\\right)\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\, \\Delta{H}_{1}^{\\circ }=-\\left(-74.6\\text{kJ}\\right)[\/latex]<br \/>\n[latex]\\begin{array}{lll} \\\\ \\frac{\\text{1}}{\\text{2}}{\\text{H}}_{\\text{2}}\\left(g\\right)+\\text{C}\\left(s\\right)+\\frac{1}{2}{\\text{N}}_{2}\\left(g\\right)\\rightarrow\\text{HCN}\\left(g\\right)\\hfill & \\hfill & \\Delta{H}_{2}^{\\circ }=135.5\\text{kJ}\\hfill \\\\ \\frac{\\frac{\\text{1}}{\\text{2}}{\\text{N}}_{\\text{2}}\\left(g\\right)+\\frac{3}{2}{\\text{H}}_{2}\\left(g\\right)\\rightarrow{\\text{NH}}_{3}\\left(g\\right)}{{\\text{CH}}_{4}\\left(g\\right)+{\\text{N}}_{2}\\left(g\\right)\\rightarrow\\text{HCN}\\left(g\\right)+{\\text{NH}}_{3}\\left(g\\right)}\\hfill & \\hfill & \\frac{\\Delta{H}_{3}^{\\circ }=-45.9\\text{kJ}}{\\Delta H^{\\circ }=164.2\\text{kJ}}\\hfill \\end{array}[\/latex]<\/li>\n<li>[latex]{\\text{CS}}_{\\text{2}}\\left(g\\right)\\rightarrow\\text{C}\\left(s\\right)+2S\\left(s\\right)\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\,\\Delta{H}_{1}^{\\circ }=-\\left(116.9\\text{kJ}\\right)[\/latex]<br \/>\n[latex]\\begin{array}{lll} \\\\ \\text{C}\\left(s\\right)+2{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{CCl}}_{\\text{4}}\\left(g\\right)\\hfill & \\hfill & \\Delta{H}_{2}^{\\circ }=-95.7\\text{kJ}\\hfill \\\\ \\frac{2\\text{S}\\left(s\\right)+{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{S}}_{2}{\\text{Cl}}_{2}\\left(g\\right)}{{\\text{CS}}_{2}\\left(g\\right)+3{\\text{Cl}}_{2}\\left(g\\right)\\rightarrow{\\text{CCl}}_{4}\\left(g\\right)+{\\text{S}}_{\\text{2}}{\\text{Cl}}_{2}\\left(g\\right)}\\hfill & \\hfill & \\frac{\\Delta{H}_{3}^{\\circ }=-19.50\\text{kJ}}{\\Delta H^{\\circ }=-232.1\\text{kJ}}\\hfill \\end{array}[\/latex]<\/li>\n<\/ol>\n<p>5. To determine how much heat is produced, we use the following equation:<\/p>\n<p style=\"text-align: center;\">[latex]\\begin{array}{ccc}\\Delta{H}_{\\text{reaction}}^{\\circ }& =& \\Delta{H}_{\\text{products}}^{\\circ }-\\Delta{H}_{\\text{reactants}}^{\\circ }\\hfill \\\\ & =& 2\\Delta{H}_{{\\text{H}}_{2}\\text{O}\\left(g\\right)}^{\\circ }+\\Delta{H}_{{\\text{O}}_{2}\\left(g\\right)}^{\\circ }-2\\Delta{H}_{{\\text{H}}_{2}{\\text{O}}_{2}\\left(l\\right)}^{\\circ }\\hfill \\\\ & =& 2\\left(-241.82\\right)+0-2\\left(-187.78\\right)=-108.08\\text{kJ}\\hfill \\end{array}[\/latex]<\/p>\n<p>The value relates to the decomposition of 2 mol of hydrogen peroxide. For 1 mol,<\/p>\n<p style=\"text-align: center;\">[latex]\\frac{-108.0}{2}=-54.04\\text{kJ}{\\text{mol}}^{-1}[\/latex]<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Concepts and Summary<\/h3>\n<p>If a chemical change is carried out at constant pressure and the only work done is caused by expansion or contraction, <em>q<\/em> for the change is called the enthalpy change with the symbol \u0394<em>H<\/em>, or [latex]\\Delta{H}_{\\text{298}}^{\\circ }[\/latex] for reactions occurring under standard state conditions. The value of \u0394<em>H<\/em> for a reaction in one direction is equal in magnitude, but opposite in sign, to \u0394<em>H<\/em> for the reaction in the opposite direction, and \u0394<em>H<\/em> is directly proportional to the quantity of reactants and products. Examples of enthalpy changes include enthalpy of combustion, enthalpy of fusion, enthalpy of vaporization, and standard enthalpy of formation. The standard enthalpy of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ },[\/latex] is the enthalpy change accompanying the formation of 1 mole of a substance from the elements in their most stable states at 1 bar (standard state). Many of the processes are carried out at 298.15 K. If the enthalpies of formation are available for the reactants and products of a reaction, the enthalpy change can be calculated using Hess\u2019s law: If a process can be written as the sum of several stepwise processes, the enthalpy change of the total process equals the sum of the enthalpy changes of the various steps.<\/p>\n<h4>Key Equations<\/h4>\n<ul>\n<li>[latex]\\Delta U=q+w[\/latex]<\/li>\n<li>[latex]\\Delta{H}_{\\text{reaction}}^{\\circ }=\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\text{(products)}-\\sum n\\times \\Delta{H}_{\\text{f}}^{\\circ }\\left(\\text{reactants}\\right)[\/latex]<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<ol>\n<li>Which of the enthalpies of combustion in Table 1 are also standard enthalpies of formation?<\/li>\n<li>Calculate \u0394<em>H<\/em> for the process [latex]{\\text{Hg}}_{2}{\\text{Cl}}_{2}\\left(s\\right)\\rightarrow 2\\text{Hg}\\left(l\\right)+{\\text{Cl}}_{2}\\left(g\\right)[\/latex] from the following information:[latex]\\begin{array}{l}\\\\ \\text{Hg}\\left(l\\right)+{\\text{Cl}}_{\\text{2}}\\left(g\\right)\\rightarrow{\\text{HgCl}}_{\\text{2}}\\left(s\\right)\\Delta H=-224\\text{kJ}\\\\ \\text{Hg}\\left(l\\right)+{\\text{HgCl}}_{\\text{2}}\\left(s\\right)\\rightarrow{\\text{Hg}}_{\\text{2}}{\\text{Cl}}_{2}\\left(s\\right)\\Delta H=-41.2\\text{kJ}\\end{array}[\/latex]<\/li>\n<li>Calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for the process [latex]{\\text{Co}}_{3}{\\text{O}}_{4}\\left(s\\right)\\rightarrow 3\\text{Co}\\left(s\\right)+2{\\text{O}}_{2}\\left(g\\right)[\/latex] from the following information: [latex]\\begin{array}{l}\\\\ \\text{Co}\\left(s\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow\\text{CoO}\\left(s\\right)\\Delta{H}_{298}^{\\circ }=-237.9\\text{kJ}\\\\ \\text{3Co}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{Co}}_{3}{\\text{O}}_{4}\\left(s\\right)\\Delta{H}_{298}^{\\circ }=-177.5\\text{kJ}\\end{array}[\/latex]<\/li>\n<li>Calculate the enthalpy of combustion of propane, C<sub>3<\/sub>H<sub>8<\/sub>(<em>g<\/em>), for the formation of H<sub>2<\/sub>O(<em>g<\/em>) and CO<sub>2<\/sub>(<em>g<\/em>). The enthalpy of formation of propane is \u2212104 kJ\/mol.<\/li>\n<li>Calculate the enthalpy of combustion of butane, C<sub>4<\/sub>H<sub>10<\/sub>(<em>g<\/em>) for the formation of H<sub>2<\/sub>O(<em>g<\/em>) and CO<sub>2<\/sub>(<em>g<\/em>). The enthalpy of formation of butane is \u2212126 kJ\/mol.<\/li>\n<li>Both propane and butane are used as gaseous fuels. Which compound produces more heat per gram when burned?<\/li>\n<li>The white pigment TiO<sub>2<\/sub> is prepared by the reaction of titanium tetrachloride, TiCl<sub>4<\/sub>, with water vapor in the gas phase: [latex]{\\text{TiCl}}_{4}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow{\\text{TiO}}_{2}\\left(s\\right)+4\\text{HCl}\\left(g\\right)[\/latex]. How much heat is evolved in the production of exactly 1 mole of TiO<sub>2<\/sub>(<em>s<\/em>) under standard state conditions?<\/li>\n<li>Water gas, a mixture of H<sub>2<\/sub> and CO, is an important industrial fuel produced by the reaction of steam with red hot coke, essentially pure carbon: [latex]\\text{C}\\left(s\\right)+{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow\\text{CO}\\left(g\\right)+{\\text{H}}_{2}\\left(g\\right).[\/latex]\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Assuming that coke has the same enthalpy of formation as graphite, calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for this reaction.<\/li>\n<li>Methanol, a liquid fuel that could possibly replace gasoline, can be prepared from water gas and additional hydrogen at high temperature and pressure in the presence of a suitable catalyst: [latex]2{\\text{H}}_{2}\\left(g\\right)+\\text{CO}\\left(g\\right)\\rightarrow{\\text{CH}}_{3}\\text{OH}\\left(g\\right)[\/latex]. Under the conditions of the reaction, methanol forms as a gas. Calculate [latex]\\Delta{H}_{298}^{\\circ }[\/latex] for this reaction and for the condensation of gaseous methanol to liquid methanol.<\/li>\n<li>Calculate the heat of combustion of 1 mole of liquid methanol to H<sub>2<\/sub>O(<em>g<\/em>) and CO<sub>2<\/sub>(<em>g<\/em>).<\/li>\n<\/ol>\n<\/li>\n<li>In the early days of automobiles, illumination at night was provided by burning acetylene, C<sub>2<\/sub>H<sub>2<\/sub>. Though no longer used as auto headlamps, acetylene is still used as a source of light by some cave explorers. The acetylene is (was) prepared in the lamp by the reaction of water with calcium carbide, CaC<sub>2<\/sub>: [latex]{\\text{CaC}}_{2}\\left(s\\right)+{\\text{H}}_{2}\\text{O}\\left(l\\right)\\rightarrow\\text{Ca}{\\left(\\text{OH}\\right)}_{2}\\left(s\\right)+{\\text{C}}_{2}{\\text{H}}_{2}\\left(g\\right).[\/latex] Calculate the standard enthalpy of the reaction. The [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of CaC<sub>2<\/sub> is \u221215.14 kcal\/mol.<\/li>\n<li>From the data in Table 1, determine which of the following fuels produces the greatest amount of heat per gram when burned under standard conditions: CO(<em>g<\/em>), CH<sub>4<\/sub>(<em>g<\/em>), or C<sub>2<\/sub>H<sub>2<\/sub>(<em>g<\/em>).<\/li>\n<li>The enthalpy of combustion of hard coal averages \u221235 kJ\/g, that of gasoline, 1.28 \u00d7 10<sup>5<\/sup> kJ\/gal. How many kilograms of hard coal provide the same amount of heat as is available from 1.0 gallon of gasoline? Assume that the density of gasoline is 0.692 g\/mL (the same as the density of isooctane).<\/li>\n<li>Ethanol, C<sub>2<\/sub>H<sub>5<\/sub>OH, is used as a fuel for motor vehicles, particularly in Brazil.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Write the balanced equation for the combustion of ethanol to CO<sub>2<\/sub>(<em>g<\/em>) and H<sub>2<\/sub>O(<em>g<\/em>), and, using the data in <a class=\"target-chapter\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, calculate the enthalpy of combustion of 1 mole of ethanol.<\/li>\n<li>The density of ethanol is 0.7893 g\/mL. Calculate the enthalpy of combustion of exactly 1 L of ethanol.<\/li>\n<li>Assuming that an automobile\u2019s mileage is directly proportional to the heat of combustion of the fuel, calculate how much farther an automobile could be expected to travel on 1 L of gasoline than on 1 L of ethanol. Assume that gasoline has the heat of combustion and the density of n\u2013octane, C<sub>8<\/sub>H<sub>18<\/sub> [latex]\\left(\\Delta{H}_{\\text{f}}^{\\circ }=-208.4\\text{kJ\/mol}\\right)[\/latex] density = 0.7025 g\/mL).<\/li>\n<\/ol>\n<\/li>\n<li>Among the substances that react with oxygen and that have been considered as potential rocket fuels are diborane [B<sub>2<\/sub>H<sub>6<\/sub>, produces B<sub>2<\/sub>O<sub>3<\/sub>(<em>s<\/em>) and H<sub>2<\/sub>O(<em>g<\/em>)], methane [CH<sub>4<\/sub>, produces CO<sub>2<\/sub>(<em>g<\/em>) and H<sub>2<\/sub>O(<em>g<\/em>)], and hydrazine [N<sub>2<\/sub>H<sub>4<\/sub>, produces N<sub>2<\/sub>(<em>g<\/em>) and H<sub>2<\/sub>O(<em>g<\/em>)]. On the basis of the heat released by 1.00 g of each substance in its reaction with oxygen, which of these compounds offers the best possibility as a rocket fuel? The [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of B<sub>2<\/sub>H<sub>6<\/sub>(<em>g<\/em>), CH<sub>4<\/sub>(<em>g<\/em>), and N<sub>2<\/sub>H<sub>4<\/sub>(<em>l<\/em>) may be found in <a class=\"target-chapter\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>.<\/li>\n<li>How much heat is produced when 1.25 g of chromium metal reacts with oxygen gas under standard conditions?<\/li>\n<li>Ethylene, C<sub>2<\/sub>H<sub>2<\/sub>, a byproduct from the fractional distillation of petroleum, is fourth among the 50 chemical compounds produced commercially in the largest quantities. About 80% of synthetic ethanol is manufactured from ethylene by its reaction with water in the presence of a suitable catalyst. [latex]{\\text{C}}_{2}{\\text{H}}_{4}\\left(g\\right)+{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)[\/latex] Using the data in the table in <a class=\"target-chapter\" href=\".\/chapter\/standard-thermodynamic-properties-for-selected-substances-2\/\" target=\"_blank\">Standard Thermodynamic Properties for Selected Substances<\/a>, calculate \u0394<em>H<\/em>\u00b0 for the reaction.<\/li>\n<li>The oxidation of the sugar glucose, C<sub>6<\/sub>H<sub>12<\/sub>O<sub>6<\/sub>, is described by the following equation: [latex]{\\text{C}}_{6}{\\text{H}}_{12}{\\text{O}}_{6}\\left(s\\right)+6{\\text{O}}_{2}\\left(g\\right)\\rightarrow 6{\\text{CO}}_{2}\\left(g\\right)+6{\\text{H}}_{2}\\text{O}\\left(l\\right)\\Delta\\text{H}=-2816\\text{kJ}[\/latex] The metabolism of glucose gives the same products, although the glucose reacts with oxygen in a series of steps in the body.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>How much heat in kilojoules can be produced by the metabolism of 1.0 g of glucose?<\/li>\n<li>How many Calories can be produced by the metabolism of 1.0 g of glucose?<\/li>\n<\/ol>\n<\/li>\n<li>Propane, C<sub>3<\/sub>H<sub>8<\/sub>, is a hydrocarbon that is commonly used as a fuel.\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Write a balanced equation for the complete combustion of propane gas.<\/li>\n<li>Calculate the volume of air at 25 \u00b0C and 1.00 atmosphere that is needed to completely combust 25.0 grams of propane. Assume that air is 21.0 percent O<sub>2<\/sub> by volume. (Hint: we will see how to do this calculation in a later chapter on gases\u2014for now use the information that 1.00 L of air at 25 \u00b0C and 1.00 atm contains 0.275 g of O<sub>2<\/sub> per liter.)<\/li>\n<li>The heat of combustion of propane is -2,219.2 kJ\/mol. Calculate the heat of formation, [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of propane given that [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of H<sub>2<\/sub>O(<em>l<\/em>) = \u2212285.8 kJ\/mol and [latex]\\Delta{H}_{\\text{f}}^{\\circ }[\/latex] of CO<sub>2<\/sub>(<em>g<\/em>) = \u2212393.5 kJ\/mol.<\/li>\n<li>Assuming that all of the heat released in burning 25.0 grams of propane is transferred to 4.00 kilograms of water, calculate the increase in temperature of the water.<\/li>\n<\/ol>\n<\/li>\n<li>During a recent winter month in Sheboygan, Wisconsin, it was necessary to obtain 3500 kWh of heat provided by a natural gas furnace with 89% efficiency to keep a small house warm (the efficiency of a gas furnace is the percent of the heat produced by combustion that is transferred into the house).\n<ol style=\"list-style-type: lower-alpha;\">\n<li>Assume that natural gas is pure methane and determine the volume of natural gas in cubic feet that was required to heat the house. The average temperature of the natural gas was 56 \u00b0F; at this temperature and a pressure of 1 atm, natural gas has a density of 0.681 g\/L.<\/li>\n<li>How many gallons of LPG (liquefied petroleum gas) would be required to replace the natural gas used? Assume the LPG is liquid propane [C<sub>3<\/sub>H<sub>8<\/sub>: density, 0.5318 g\/mL; enthalpy of combustion, 2219 kJ\/mol for the formation of CO<sub>2<\/sub>(<em>g<\/em>) and H<sub>2<\/sub>O(<em>l<\/em>)] and the furnace used to burn the LPG has the same efficiency as the gas furnace.<\/li>\n<li>What mass of carbon dioxide is produced by combustion of the methane used to heat the house?<\/li>\n<li>What mass of water is produced by combustion of the methane used to heat the house?<\/li>\n<li>What volume of air is required to provide the oxygen for the combustion of the methane used to heat the house? Air contains 23% oxygen by mass. The average density of air during the month was 1.22 g\/L.<\/li>\n<li>How many kilowatt\u2013hours (1 kWh = 3.6 \u00d7 10<sup>6<\/sup> J) of electricity would be required to provide the heat necessary to heat the house? Note electricity is 100% efficient in producing heat inside a house.<\/li>\n<li>Although electricity is 100% efficient in producing heat inside a house, production and distribution of electricity is not 100% efficient. The efficiency of production and distribution of electricity produced in a coal-fired power plant is about 40%. A certain type of coal provides 2.26 kWh per pound upon combustion. What mass of this coal in kilograms will be required to produce the electrical energy necessary to heat the house if the efficiency of generation and distribution is 40%?<\/li>\n<\/ol>\n<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q659342\">Show Selected Answers<\/span><\/p>\n<div id=\"q659342\" class=\"hidden-answer\" style=\"display: none\">\n<p>2. Reverse the direction of both equations and add the new equations and enthalpies.<\/p>\n<p>[latex]\\begin{array}{lll}{\\text{HgCl}}_{2}\\rightarrow\\text{Hg}\\left(l\\right)+{\\text{Cl}}_{2}\\left(l\\right)\\hfill & \\hfill & \\Delta H=224\\text{kJ}\\hfill \\\\ \\frac{{\\text{Hg}}_{\\text{2}}{\\text{Cl}}_{2}\\left(s\\right)\\rightarrow\\text{Hg}\\left(l\\right)+{\\text{HgCl}}_{2}\\left(s\\right)}{{\\text{Hg}}_{\\text{2}}{\\text{Cl}}_{2}\\left(s\\right)\\rightarrow 2\\text{Hg}\\left(l\\right)+{\\text{Cl}}_{2}\\left(g\\right)}\\hfill & \\hfill & \\frac{\\Delta H=41.2\\text{kJ}}{\\Delta H=265\\text{kJ}}\\hfill \\end{array}[\/latex]<\/p>\n<p>5. The enthalpy\u00a0can be found through the following steps:<\/p>\n<p>[latex]\\begin{array}{llll}\\text{Step}1:\\hfill & 4\\left[\\text{C}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)\\right]\\hfill & \\hfill & \\Delta H^{\\circ }=4\\left(-394\\text{kJ}{\\text{mol}}^{-1}\\right)\\hfill \\\\ \\text{Step}2:\\hfill & 5\\left[{\\text{H}}_{\\text{2}}\\left(g\\right)+\\frac{1}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{H}}_{\\text{2}}\\text{O}\\left(g\\right)\\right]\\hfill & \\hfill & \\Delta H^{\\circ }=5\\left(-242\\text{kJ}{\\text{mol}}^{-1}\\right)\\hfill \\\\ \\text{Step}\\text{3:}\\hfill & \\underline{{\\text{C}}_{\\text{4}}{\\text{H}}_{10}\\rightarrow 4\\text{C}\\left(s\\right)+5{\\text{H}}_{2}\\left(g\\right)}\\hfill & \\hfill & \\underline{\\Delta H^{\\circ }=+126\\text{kJ}{\\text{mol}}^{-1}}\\hfill \\\\ \\text{Sum:}\\hfill & {\\text{C}}_{\\text{4}}{\\text{H}}_{10}+\\frac{13}{2}{\\text{O}}_{2}\\left(g\\right)\\rightarrow 4{\\text{CO}}_{2}\\left(g\\right)+5{\\text{H}}_{2}\\text{O}\\left(l\\right)\\hfill & \\hfill & \\Delta{H}_{298}^{\\circ }=-2660\\text{kJ}{\\text{mol}}^{-1}\\hfill \\end{array}[\/latex]<\/p>\n<p>7.\u00a0The heat\u00a0can be found through the following steps:<\/p>\n<p>[latex]\\begin{array}{lllllll}{\\text{TiCl}}_{4}\\left(g\\right)\\rightarrow\\text{Ti}\\left(s\\right)+2{\\text{Cl}}_{2}\\left(g\\right)\\hfill & & & & & & \\Delta{H}_{1}^{\\circ }=-\\left(-763.2\\text{kJ}\\right)\\hfill \\\\ 2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow 2{\\text{H}}_{2}\\left(g\\right)+{\\text{O}}_{2}\\left(s\\right)\\hfill & & & & & & \\Delta{H}_{2}^{\\circ }=-2\\text{(}-241.82\\text{kJ)}=483.6\\text{kJ}\\hfill \\\\ \\text{Ti}\\left(s\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{TiO}}_{2}\\left(s\\right)\\hfill & & & & & & \\Delta{H}_{3}^{\\circ }=-944.7\\text{kJ}\\hfill \\\\ \\underline{2{\\text{H}}_{2}\\left(g\\right)\\rightarrow 2{\\text{Cl}}_{2}\\left(g\\right)+4\\text{HCl}\\left(s\\right)}\\hfill & & & & & & \\underline{\\Delta{H}_{4}^{\\circ }=4\\text{(}-92.3\\text{kJ)}=-369.2\\text{kJ}}\\hfill \\\\ {\\text{TiCl}}_{4}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\rightarrow{\\text{TiO}}_{2}\\left(s\\right)+4\\text{HCl}\\left(g\\right)\\hfill & & & & & & \\Delta{H}_{298}^{\\circ }=-67.1\\text{kJ}\\hfill \\end{array}[\/latex]<br \/>\nThus, 67.1 kJ of heat is evolved.<\/p>\n<p>9. Convert \u221215.14 kcal to kJ:\u00a0\u221215.14 kcal \u00d7 4.184 kJ\/kcal = 63.35 kJ\/mol<\/p>\n<p>[latex]\\begin{array}{ll}\\hfill \\Delta{H}_{\\text{reaction}}^{\\circ }& =\\Delta{H}_{\\text{products}}^{\\circ }-\\Delta{H}_{\\text{reactants}}^{\\circ }\\hfill \\\\ & =\\Delta{H}_{\\text{Ca}{\\left(\\text{OH}\\right)}_{2}\\left(s\\right)}^{\\circ }+\\Delta{H}_{{\\text{C}}_{2}{\\text{H}}_{2}\\left(g\\right)}^{\\circ }-\\Delta{H}_{{\\text{CaC}}_{2}\\left(s\\right)}^{\\circ }-2\\Delta{H}_{{\\text{H}}_{2}{\\text{O}}_{2}\\left(l\\right)}^{\\circ }\\hfill \\\\ & =-985.2+227.4-63.35-2\\left(-285.83\\right)=-249.5\\text{kJ}\\hfill \\end{array}[\/latex]<\/p>\n<p>11. the amount of heat produced by burning of 1.0 gallon of gasoline is:<br \/>\n<em>q<\/em> = 1.0 gallon \u00d7 (\u20131.28 \u00d7 10<sup>5<\/sup> kJ\/gal) = -1.28 \u00d7 10<sup>5<\/sup> kJ<br \/>\nMass \u00d7 (-35 kJ\/g) = -1.28 \u00d7 10<sup>5<\/sup> kJ<br \/>\nMass = 3657 g or 3.7 kg<\/p>\n<p>13. Write the balanced equation for each reaction.<br \/>\n[latex]\\begin{array}{l}{\\text{B}}_{2}{\\text{H}}_{6}\\left(g\\right)+3{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{B}}_{2}{\\text{O}}_{3}\\left(s\\right)+3{\\text{H}}_{2}\\text{O}\\left(g\\right)\\\\ {\\text{CH}}_{4}\\left(g\\right)+2{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{CO}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\\\ {\\text{N}}_{2}{\\text{H}}_{4}\\left(l\\right)+{\\text{O}}_{2}\\left(g\\right)\\rightarrow{\\text{N}}_{2}\\left(g\\right)+2{\\text{H}}_{2}\\text{O}\\left(g\\right)\\end{array}[\/latex]<\/p>\n<p>Calculate the heat released per mole; then, calculate the heat per gram.<\/p>\n<p>[latex]\\begin{array}{l}\\Delta{H}_{\\text{rxn}}^{\\circ }=\\Delta{H}_{\\text{P}}^{\\circ }-\\Delta{H}_{\\text{R}}^{\\circ }\\\\ \\Delta{H}_{\\text{comb}}^{\\circ }=-1273.5+3\\left(-241.82\\right)+36.4=-1962.6\\text{kJ}{\\text{mol}}^{-1}\\\\ \\Delta{H}_{\\text{comb}}^{\\circ }=-393.51+2\\left(-241.82\\right)-\\left(-74.6\\right)=-802.6\\text{kJ}{\\text{mol}}^{-1}\\\\ \\Delta{H}_{\\text{comb}}^{\\circ }=2\\left(-241.82\\right)-\\left(50.63\\right)=-534.27\\text{kJ}{\\text{mol}}^{-1}\\end{array}[\/latex]<\/p>\n<p>Calculate the heat per mole released per gram.<\/p>\n<p>For B<sub>2<\/sub>H<sub>6<\/sub>: [latex]\\frac{-1912.26\\text{kJ}}{27.610\\text{g}}=-69.26\\text{kJ}{\\text{g}}^{-1}-\\frac{1962.6}{27.67}=-70.93[\/latex]<\/p>\n<p>For CH<sub>4<\/sub>: [latex]\\frac{-802.34\\text{kJ}}{16.043\\text{g}}=-50.012\\text{kJ}{\\text{g}}^{-1}-\\frac{802.6}{16.043}=-50.03[\/latex]<\/p>\n<p>For N<sub>2<\/sub>H<sub>4<\/sub>: [latex]\\frac{-534.27\\text{kJ}}{32.0452\\text{g}}=16.67[\/latex]<\/p>\n<p>On the assumption that the best rocket fuel is the one that gives off the most heat, B<sub>2<\/sub>H<sub>6<\/sub> is the prime candidate. Other things must be considered, however. For example, the moles of gaseous product formed are related to the specific impulse of the fuel, toxicity of products, cost, and ability to contain original fuel (stability and corrosiveness).<\/p>\n<p>15. [latex]\\begin{array}{cc}\\hfill \\Delta{H}_{\\text{rxn}}^{\\circ }& =\\Delta{H}_{{\\text{C}}_{2}{\\text{H}}_{5}\\text{OH}\\left(l\\right)}^{\\circ }-\\Delta{H}_{{\\text{H}}_{2}\\text{O}\\left(g\\right)}^{\\circ }-\\Delta{H}_{{\\text{C}}_{2}{\\text{H}}_{4}\\left(g\\right)}^{\\circ }\\hfill \\\\ & =-277.7-\\left(-241.82\\right)-\\left(52.4\\right)\\hfill \\\\ & =-88.2\\text{kJ}\\hfill \\end{array}[\/latex]<\/p>\n<p>17. The answers are as follows:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>(a) [latex]{\\text{C}}_{3}{\\text{H}}_{8}\\left(g\\right)+5{\\text{O}}_{2}\\left(g\\right)\\rightarrow 3{\\text{CO}}_{2}\\left(g\\right)+4{\\text{H}}_{2}\\text{O}\\left(l\\right);[\/latex]<\/li>\n<li>(b) Determine the number of moles of O<sub>2<\/sub> required and from that the number of grams. Then use the density to find the volume.<br \/>\n[latex]\\begin{array}{lll}\\\\ \\hfill \\text{Mass}{\\text{O}}_{2}& =& 25.0\\cancel{\\text{g}{\\text{C}}_{3}{\\text{H}}_{8}}\\times \\frac{1\\cancel{\\text{mol}{\\text{C}}_{3}{\\text{H}}_{8}}}{44.097\\cancel{\\text{g}}}\\times \\frac{5\\cancel{\\text{mol}{\\text{O}}_{2}}}{1\\cancel{\\text{mol}{\\text{C}}_{3}{\\text{H}}_{8}\\left(g\\right)}}\\times \\frac{31.999\\text{g}}{1\\cancel{\\text{mol}{\\text{O}}_{2}}}\\\\ & =& 90.7\\text{g}\\\\ \\text{Volume}{\\text{O}}_{2}& =& \\frac{90.7\\cancel{\\text{g}}}{0.275\\cancel{\\text{g}}{\\text{L}}^{-1}}=330\\text{L}\\end{array}[\/latex]<\/li>\n<li>(c) [latex]\\begin{array}{ccc}\\hfill \\Delta{H}_{\\text{comb}}^{\\circ }\\left({\\text{C}}_{3}{\\text{H}}_{6}\\left(g\\right)\\right)& =& -2219.2\\text{kJ}{\\text{mol}}^{-1}=3\\Delta{H}_{\\text{f}}^{\\circ }\\text{(}{\\text{CO}}_{2}\\left(g\\right)\\text{)}+4\\Delta{H}_{\\text{f}}^{\\circ }\\text{(}{\\text{H}}_{2}\\text{O}\\left(l\\right)\\text{)}-\\Delta{H}_{\\text{f}}^{\\circ }\\text{(}{\\text{C}}_{3}{\\text{H}}_{6}\\left(g\\right)\\text{)}\\hfill \\\\ \\hfill \\Delta{H}_{\\text{f}}^{\\circ }\\left({\\text{C}}_{3}{\\text{H}}_{6}\\left(g\\right)\\right)& =& \\left[2220.1+3\\left(-393.5\\right)+4\\left(-285.8\\right)\\right]\\text{kJ}{\\text{mol}}^{-1}\\hfill \\\\ & =& -104.5\\text{kJ}{\\text{mol}}^{-1}\\hfill \\end{array}[\/latex]<\/li>\n<li>(d) [latex]\\frac{25.0\\cancel{\\text{g}}}{44.097\\cancel{\\text{g}}{\\text{mol}}^{-1}}\\times 2219.2\\text{kJ}{\\text{mol}}^{-1}=1258\\text{kJ}=1.26\\times {10}^{6}\\text{J}[\/latex]<br \/>\nHeat = 1.26 \u00d7 10<sup>6<\/sup> J = 4.18 J g<sup>-1<\/sup> \u00b0C<sup>-1<\/sup> \u00d7 4.00 \u00d7 10<sup>3<\/sup> \u00d7 \u0394<em>T<br \/>\n<\/em>\u0394<em>T<\/em> = 75.4 \u00b0C<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<h2>Glossary<\/h2>\n<p><strong>chemical thermodynamics: <\/strong>area of science that deals with the relationships between heat, work, and all forms of energy associated with chemical and physical processes<\/p>\n<p><strong>enthalpy (<em>H<\/em>): <\/strong>sum of a system\u2019s internal energy and the mathematical product of its pressure and volume<\/p>\n<p><strong>enthalpy change (\u0394<em>H<\/em>): <\/strong>heat released or absorbed by a system under constant pressure during a chemical or physical process<\/p>\n<p><strong>expansion work (pressure-volume work): <\/strong>work done as a system expands or contracts against external pressure<\/p>\n<p><strong>first law of thermodynamics: <\/strong>internal energy of a system changes due to heat flow in or out of the system or work done on or by the system<\/p>\n<p><strong>Hess\u2019s law: <\/strong>if a process can be represented as the sum of several steps, the enthalpy change of the process equals the sum of the enthalpy changes of the steps<\/p>\n<p><strong>hydrocarbon: <\/strong>compound composed only of hydrogen and carbon; the major component of fossil fuels<\/p>\n<p><strong>internal energy (<em>U<\/em>): <\/strong>total of all possible kinds of energy present in a substance or substances<\/p>\n<p><strong>standard enthalpy of combustion [latex]\\text{(}\\Delta{H}_{\\text{c}}^{\\circ }\\text{)}[\/latex]: <\/strong>heat released when one mole of a compound undergoes complete combustion under standard conditions<\/p>\n<p><strong>standard enthalpy of formation [latex]\\text{(}\\Delta{H}_{\\text{f}}^{\\circ }\\text{)}[\/latex]: <\/strong>enthalpy change of a chemical reaction in which 1 mole of a pure substance is formed from its elements in their most stable states under standard state conditions<\/p>\n<p><strong>standard state: <\/strong>set of physical conditions as accepted as common reference conditions for reporting thermodynamic properties; 1 bar of pressure, and solutions at 1 molar concentrations, usually at a temperature of 298.15 K<\/p>\n<p><strong>state function: <\/strong>property depending only on the state of a system, and not the path taken to reach that state<\/p>\n\n\t\t\t <section class=\"citations-section\" role=\"contentinfo\">\n\t\t\t <h3>Candela Citations<\/h3>\n\t\t\t\t\t <div>\n\t\t\t\t\t\t <div id=\"citation-list-1731\">\n\t\t\t\t\t\t\t <div class=\"licensing\"><div class=\"license-attribution-dropdown-subheading\">CC licensed content, Shared previously<\/div><ul class=\"citation-list\"><li>Chemistry. <strong>Provided by<\/strong>: OpenStax College. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/openstaxcollege.org\">http:\/\/openstaxcollege.org<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by\/4.0\/\">CC BY: Attribution<\/a><\/em>. <strong>License Terms<\/strong>: Download for free at https:\/\/openstaxcollege.org\/textbooks\/chemistry\/get<\/li><\/ul><div class=\"license-attribution-dropdown-subheading\">All rights reserved content<\/div><ul class=\"citation-list\"><li>Algae for Fuel - a QUEST Nebraska Feature. <strong>Authored by<\/strong>: NETNebraska. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/q9X7UNLRbds\">https:\/\/youtu.be\/q9X7UNLRbds<\/a>. <strong>License<\/strong>: <em>All Rights Reserved<\/em>. <strong>License Terms<\/strong>: Standard YouTube License<\/li><\/ul><\/div>\n\t\t\t\t\t\t <\/div>\n\t\t\t\t\t <\/div>\n\t\t\t <\/section>","protected":false},"author":17,"menu_order":8,"template":"","meta":{"_candela_citation":"[{\"type\":\"copyrighted_video\",\"description\":\"Algae for Fuel - a QUEST Nebraska Feature\",\"author\":\"NETNebraska\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/q9X7UNLRbds\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"},{\"type\":\"cc\",\"description\":\"Chemistry\",\"author\":\"\",\"organization\":\"OpenStax College\",\"url\":\"http:\/\/openstaxcollege.org\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Download for free at https:\/\/openstaxcollege.org\/textbooks\/chemistry\/get\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1731","chapter","type-chapter","status-publish","hentry"],"part":3023,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/1731","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/users\/17"}],"version-history":[{"count":27,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/1731\/revisions"}],"predecessor-version":[{"id":6058,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/1731\/revisions\/6058"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/parts\/3023"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/1731\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/media?parent=1731"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapter-type?post=1731"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/contributor?post=1731"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/license?post=1731"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}