{"id":3400,"date":"2015-05-06T03:51:01","date_gmt":"2015-05-06T03:51:01","guid":{"rendered":"https:\/\/courses.candelalearning.com\/oschemtemp\/?post_type=chapter&#038;p=3400"},"modified":"2016-10-12T20:02:20","modified_gmt":"2016-10-12T20:02:20","slug":"phase-diagrams-2","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/chapter\/phase-diagrams-2\/","title":{"raw":"Phase Diagrams","rendered":"Phase Diagrams"},"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>Explain the construction and use of a typical phase diagram<\/li>\r\n \t<li>Use phase diagrams to identify stable phases at given temperatures and pressures, and to describe phase transitions resulting from changes in these properties<\/li>\r\n \t<li>Describe the supercritical fluid phase of matter<\/li>\r\n<\/ul>\r\n<\/div>\r\nIn the previous module, the variation of a liquid\u2019s equilibrium vapor pressure with temperature was described. Considering the definition of boiling point, plots of vapor pressure versus temperature represent how the boiling point of the liquid varies with pressure. Also described was the use of heating and cooling curves to determine a substance\u2019s melting (or freezing) point. Making such measurements over a wide range of pressures yields data that may be presented graphically as a phase diagram. A <strong>phase diagram<\/strong>\u00a0combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature, and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). A typical phase diagram for a pure substance is shown in Figure 1.\r\n\r\n[caption id=\"attachment_4602\" align=\"aligncenter\" width=\"450\"]<img class=\"wp-image-4602\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214404\/CNX_Chem_10_04_PhaseDi.jpg\" alt=\"A graph is shown where the x-axis is labeled \u201cTemperature\u201d and the y-axis is labeled \u201cPressure.\u201d A line extends from the lower left bottom of the graph sharply upward to a point that is a third across the x-axis. A second line begins at the lower third of the first line at a point labeled \u201ctriple point\u201d and extends to the upper right corner of the graph where it is labeled \u201ccritical point.\u201d The two lines bisect the graph area to create three sections, labeled \u201csolid\u201d near the top left, \u201cliquid\u201d in the top middle and \u201cgas\u201d near the bottom right. A pair of horizontal arrows, one left-facing and labeled \u201cdeposition\u201d and one right-facing and labeled\u201d sublimation,\u201d are drawn on top of the bottom section of the first line. A second pair of horizontal arrows, one left-facing and labeled \u201cfreezing\u201d and one right-facing and labeled \u201cmelting\u201d, are drawn on top of the upper section of the first line. A third pair of horizontal arrows, one left-facing and labeled \u201ccondensation\u201d and one right-facing and labeled \u201dvaporization,\u201d are drawn on top of the middle section of the second line.\" width=\"450\" height=\"410\" \/> Figure 1. The physical state of a substance and its phase-transition temperatures are represented graphically in a phase diagram.[\/caption]\r\n\r\n&nbsp;\r\n\r\nTo illustrate the utility of these plots, consider the phase diagram for water shown in Figure 2.\r\n\r\n[caption id=\"attachment_4603\" align=\"aligncenter\" width=\"615\"]<img class=\"wp-image-4603\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214405\/CNX_Chem_10_04_H2OPhasDi2.jpg\" alt=\"A graph is shown where the x-axis is labeled \u201cTemperature in degrees Celsius\u201d and the y-axis is labeled \u201cPressure ( k P a ).\u201d A line extends from the origin of the graph which is labeled \u201cA\u201d sharply upward to a point in the bottom third of the diagram labeled \u201cB\u201d where it branches into a line that slants slightly backward until it hits the highest point on the y-axis labeled \u201cD\u201d and a second line that extends to the upper right corner of the graph labeled \u201cC\u201d. C is labeled \u201cCritical point, with a dotted line extending downward to the x-axis labeled 374 degrees Celsius, and another dotted line extending to the y-axis labeled 22,089 k P a. The two lines bisect the graph area to create three sections, labeled \u201cIce (solid)\u201d near the middle left, \u201cWater (liquid)\u201d in the top middle and \u201cWater vapor (gas)\u201d near the bottom middle. Point B is labeled \u201cTriple point\u201d and has a dotted line extending downward to the x-axis labeled 0.01, and another dotted line extending to the y-axis labeled 0.6. Halfway between points B and C a dotted line extends from the originally discussed line downward to the point 100 degrees Celsius on the x-axis, and another dotted line extends to the y-axis at 101 k P a. Another dotted line extends from this dotted line downward at 0 degrees Celsius.\" width=\"615\" height=\"399\" \/> Figure 2. The pressure and temperature axes on this phase diagram of water are not drawn to constant scale in order to illustrate several important properties.[\/caption]\r\n\r\nWe can use the phase diagram to identify the physical state of a sample of water under specified conditions of pressure and temperature. For example, a pressure of 50 kPa and a temperature of \u221210 \u00b0C correspond to the region of the diagram labeled \u201cice.\u201d Under these conditions, water exists only as a solid (ice). A pressure of 50 kPa and a temperature of 50 \u00b0C correspond to the \u201cwater\u201d region\u2014here, water exists only as a liquid. At 25 kPa and 200 \u00b0C, water exists only in the gaseous state. Note that on the H<sub>2<\/sub>O phase diagram, the pressure and temperature axes are not drawn to a constant scale in order to permit the illustration of several important features as described here.\r\n\r\nThe curve BC in Figure\u00a02 is the plot of vapor pressure versus temperature as described in the previous module of this chapter. This \u201cliquid-vapor\u201d curve separates the liquid and gaseous regions of the phase diagram and provides the boiling point for water at any pressure. For example, at 1 atm, the boiling point is 100 \u00b0C. Notice that the liquid-vapor curve terminates at a temperature of 374 \u00b0C and a pressure of 218 atm, indicating that water cannot exist as a liquid above this temperature, regardless of the pressure. The physical properties of water under these conditions are intermediate between those of its liquid and gaseous phases. This unique state of matter is called a supercritical fluid, a topic that will be described in the next section of this module.\r\n\r\n<figure id=\"CNX_Chem_10_04_FreezeDry\"><\/figure>\r\n\r\n[caption id=\"attachment_3388\" align=\"alignright\" width=\"350\"]<img class=\"wp-image-3388\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23213613\/CNX_Chem_10_04_FreezeDry.jpg\" alt=\"A photograph shows a packet of Freeze Dried Ice Cream, next to the contents of the package opened.\" width=\"350\" height=\"263\" \/> Figure 3 Freeze-dried foods, like this ice cream, are dehydrated by sublimation at pressures below the triple point for water. (credit: \u02balwao\u02ba\/Flickr)[\/caption]\r\n\r\nThe solid-vapor curve, labeled AB in Figure 2, indicates the temperatures and pressures at which ice and water vapor are in equilibrium. These temperature-pressure data pairs correspond to the sublimation, or deposition, points for water. If we could zoom in on the solid-gas line in Figure 2, we would see that ice has a vapor pressure of about 0.20 kPa at \u221210 \u00b0C. Thus, if we place a frozen sample in a vacuum with a pressure less than 0.20 kPa, ice will sublime. This is the basis for the \u201cfreeze-drying\u201d process often used to preserve foods, such as the ice cream shown in Figure 3.\r\n\r\nThe solid-liquid curve labeled BD shows the temperatures and pressures at which ice and liquid water are in equilibrium, representing the melting\/freezing points for water. Note that this curve exhibits a slight negative slope (greatly exaggerated for clarity), indicating that the melting point for water decreases slightly as pressure increases. Water is an unusual substance in this regard, as most substances exhibit an increase in melting point with increasing pressure. This behavior is partly responsible for the movement of glaciers, like the one shown in Figure 4. The bottom of a glacier experiences an immense pressure due to its weight that can melt some of the ice, forming a layer of liquid water on which the glacier may more easily slide.\r\n\r\n[caption id=\"attachment_4604\" align=\"aligncenter\" width=\"650\"]<img class=\"size-full wp-image-4604\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214407\/CNX_Chem_10_04_IceMelt.jpg\" alt=\"A photograph shows an aerial view of a land mass. The white mass of a glacier is shown near the top left quadrant of the photo and leads to two branching blue rivers. The open land is shown in brown.\" width=\"650\" height=\"432\" \/> Figure 4. The immense pressures beneath glaciers result in partial melting to produce a layer of water that provides lubrication to assist glacial movement. This satellite photograph shows the advancing edge of the Perito Moreno glacier in Argentina. (credit: NASA)[\/caption]\r\n\r\nThe point of intersection of all three curves is labeled B in Figure 2. At the pressure and temperature represented by this point, all three phases of water coexist in equilibrium. This temperature-pressure data pair is called the <strong>triple point<\/strong>. At pressures lower than the triple point, water cannot exist as a liquid, regardless of the temperature.\r\n<div class=\"textbox examples\">\r\n<h3>Example 1:\u00a0<strong>Determining the State of Water<\/strong><\/h3>\r\nUsing the phase diagram for water given in Figure 10.30,\u00a0determine the state of water at the following temperatures and pressures:\r\n<ol>\r\n \t<li>\u221210 \u00b0C and 50 kPa<\/li>\r\n \t<li>25 \u00b0C and 90 kPa<\/li>\r\n \t<li>50 \u00b0C and 40 kPa<\/li>\r\n \t<li>80 \u00b0C and 5 kPa<\/li>\r\n \t<li>\u221210 \u00b0C and 0.3 kPa<\/li>\r\n \t<li>50 \u00b0C and 0.3 kPa<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"480813\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"480813\"]Using the phase diagram for water, we can determine that the state of water at each temperature and pressure given are as follows:\r\n<ol>\r\n \t<li>solid<\/li>\r\n \t<li>liquid<\/li>\r\n \t<li>liquid<\/li>\r\n \t<li>gas<\/li>\r\n \t<li>solid<\/li>\r\n \t<li>gas<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n<h4><strong>Check Your Learning<\/strong><\/h4>\r\nWhat phase changes can water undergo as the temperature changes if the pressure is held at 0.3 kPa? If the pressure is held at 50 kPa?\r\n[reveal-answer q=\"565714\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"565714\"]At 0.3 kPa: [latex]\\text{s}\\longrightarrow \\text{g}[\/latex] at \u221258 \u00b0C. At 50 kPa: [latex]\\text{s}\\longrightarrow \\text{l}[\/latex] at 0 \u00b0C, l \u27f6 g at 78 \u00b0C[\/hidden-answer]\r\n\r\n<\/div>\r\nConsider the phase diagram for carbon dioxide shown in Figure 5 as another example. The solid-liquid curve exhibits a positive slope, indicating that the melting point for CO<sub>2<\/sub> increases with pressure as it does for most substances (water being a notable exception as described previously). Notice that the triple point is well above 1 atm, indicating that carbon dioxide cannot exist as a liquid under ambient pressure conditions. Instead, cooling gaseous carbon dioxide at 1 atm results in its deposition into the solid state. Likewise, solid carbon dioxide does not melt at 1 atm pressure but instead sublimes to yield gaseous CO<sub>2<\/sub>. Finally, notice that the critical point for carbon dioxide is observed at a relatively modest temperature and pressure in comparison to water.\r\n\r\n[caption id=\"attachment_4605\" align=\"aligncenter\" width=\"650\"]<img class=\" wp-image-4605\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214409\/CNX_Chem_10_04_CO2phasdi.jpg\" alt=\"A graph is shown where the x-axis is labeled \u201cTemperature ( degree sign, C )\u201d and has values of negative 100 to 100 in increments of 25 and the y-axis is labeled \u201cPressure ( k P a )\u201d and has values of 10 to 1,000,000. A line extends from the lower left bottom of the graph upward to a point around\u201c27, 9000,\u201d where it ends. The space under this curve is labeled \u201cGas.\u201d A second line extends in a curve from point around \u201c-73, 100\u201d to \u201c27, 1,000,000.\u201d The area to the left of this line and above the first line is labeled \u201cSolid\u201d while the area to the right is labeled \u201cLiquid.\u201d A section on the graph under the second line and past the point \u201c28\u201d on the x-axis is labeled \u201cS C F.\u201d\" width=\"650\" height=\"396\" \/> Figure 5. The pressure and temperature axes on this phase diagram of carbon dioxide are not drawn to constant scale in order to illustrate several important properties.[\/caption]\r\n\r\n<figure id=\"CNX_Chem_10_04_CO2phasdi\"><\/figure>\r\n<div class=\"textbox examples\">\r\n<h3>Example 2:\u00a0<strong>Determining the State of Carbon Dioxide<\/strong><\/h3>\r\nUsing the phase diagram for carbon dioxide shown in\u00a0Figure 5, determine the state of CO<sub>2<\/sub> at the following temperatures and pressures:\r\n<ol>\r\n \t<li>\u221230 \u00b0C and 2000 kPa<\/li>\r\n \t<li>\u221260 \u00b0C and 1000 kPa<\/li>\r\n \t<li>\u221260 \u00b0C and 100 kPa<\/li>\r\n \t<li>20 \u00b0C and 1500 kPa<\/li>\r\n \t<li>0 \u00b0C and 100 kPa<\/li>\r\n \t<li>20 \u00b0C and 100 kPa<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"475095\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"475095\"]Using the phase diagram for carbon dioxide provided, we can determine that the state of CO<sub>2<\/sub> at each temperature and pressure given are as follows:\r\n<ol>\r\n \t<li>liquid<\/li>\r\n \t<li>solid<\/li>\r\n \t<li>gas<\/li>\r\n \t<li>liquid<\/li>\r\n \t<li>gas<\/li>\r\n \t<li>gas<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n<h4><strong>Check Your Learning<\/strong><\/h4>\r\nDetermine the phase changes carbon dioxide undergoes when its temperature is varied, thus holding its pressure constant at 1500 kPa? At 500 kPa? At what approximate temperatures do these phase changes occur?\r\n\r\n[reveal-answer q=\"185931\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"185931\"]at 1500 kPa: [latex]\\text{s}\\longrightarrow \\text{l}[\/latex] at \u221245 \u00b0C, [latex]\\text{l}\\longrightarrow \\text{g}[\/latex] at \u221210 \u00b0C;\u00a0at 500 kPa: [latex]\\text{s}\\longrightarrow \\text{g}[\/latex] at \u221258 \u00b0C[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Supercritical Fluids<\/h2>\r\nIf we place a sample of water in a sealed container at 25 \u00b0C, remove the air, and let the vaporization-condensation equilibrium establish itself, we are left with a mixture of liquid water and water vapor at a pressure of 0.03 atm. A distinct boundary between the more dense liquid and the less dense gas is clearly observed. As we increase the temperature, the pressure of the water vapor increases, as described by the liquid-gas curve in the phase diagram for water (Figure 2), and a two-phase equilibrium of liquid and gaseous phases remains. At a temperature of 374 \u00b0C, the vapor pressure has risen to 218 atm, and any further increase in temperature results in the disappearance of the boundary between liquid and vapor phases. All of the water in the container is now present in a single phase whose physical properties are intermediate between those of the gaseous and liquid states. This phase of matter is called a <strong>supercritical fluid<\/strong>, and the temperature and pressure above which this phase exists is the<strong> critical point<\/strong>. Above its critical temperature, a gas cannot be liquefied no matter how much pressure is applied. The pressure required to liquefy a gas at its critical temperature is called the critical pressure. The critical temperatures and critical pressures of some common substances are given in Table 1.\r\n<table id=\"fs-idm180459824\" class=\"medium unnumbered\" summary=\"none\" data-label=\"\">\r\n<thead>\r\n<tr valign=\"top\">\r\n<th colspan=\"3\">Table 1.<\/th>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<th>Substance<\/th>\r\n<th>Critical Temperature (K)<\/th>\r\n<th>Critical Pressure (atm)<\/th>\r\n<\/tr>\r\n<\/thead>\r\n<tbody>\r\n<tr valign=\"top\">\r\n<td>hydrogen<\/td>\r\n<td>33.2<\/td>\r\n<td>12.8<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>nitrogen<\/td>\r\n<td>126.0<\/td>\r\n<td>33.5<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>oxygen<\/td>\r\n<td>154.3<\/td>\r\n<td>49.7<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>carbon dioxide<\/td>\r\n<td>304.2<\/td>\r\n<td>73.0<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>ammonia<\/td>\r\n<td>405.5<\/td>\r\n<td>111.5<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>sulfur dioxide<\/td>\r\n<td>430.3<\/td>\r\n<td>77.7<\/td>\r\n<\/tr>\r\n<tr valign=\"top\">\r\n<td>water<\/td>\r\n<td>647.1<\/td>\r\n<td>217.7<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n[caption id=\"attachment_4606\" align=\"aligncenter\" width=\"1024\"]<img class=\"size-large wp-image-4606\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214410\/CNX_Chem_10_04_CritFluid-1024x241.jpg\" alt=\"Four photographs are shown where each shows a circular container with a green and red float in each. In the left diagram, the container is half filled with a colorless liquid and the floats sit on the surface of the liquid. In the second photo, the green float is near the top and the red float lies near the bottom of the container. In the third photo, the fluid is darker and the green float sits halfway up the container while the red is sitting at the bottom. In the right photo, the liquid is colorless again and the two floats sit on the surface.\" width=\"1024\" height=\"241\" \/> Figure 6. (a) A sealed container of liquid carbon dioxide slightly below its critical point is heated, resulting in (b) the formation of the supercritical fluid phase. Cooling the supercritical fluid lowers its temperature and pressure below the critical point, resulting in the reestablishment of separate liquid and gaseous phases (c and d). Colored floats illustrate differences in density between the liquid, gaseous, and supercritical fluid states. (credit: modification of work by \u201cmrmrobin\u201d\/YouTube)[\/caption]\r\n\r\n<div class=\"textbox\">\r\n\r\nObserve the liquid-to-supercritical fluid transition for carbon dioxide in this video.\r\n\r\nhttps:\/\/youtu.be\/P9EftqFYaHg\r\n\r\n<\/div>\r\nLike a gas, a supercritical fluid will expand and fill a container, but its density is much greater than typical gas densities, typically being close to those for liquids. Similar to liquids, these fluids are capable of dissolving nonvolatile solutes. They exhibit essentially no surface tension and very low viscosities, however, so they can more effectively penetrate very small openings in a solid mixture and remove soluble components. These properties make supercritical fluids extremely useful solvents for a wide range of applications. For example, supercritical carbon dioxide has become a very popular solvent in the food industry, being used to decaffeinate coffee, remove fats from potato chips, and extract flavor and fragrance compounds from citrus oils. It is nontoxic, relatively inexpensive, and not considered to be a pollutant. After use, the CO<sub>2<\/sub> can be easily recovered by reducing the pressure and collecting the resulting gas.\r\n<div class=\"textbox examples\">\r\n<h3>Example 3:\u00a0<strong>The Critical Temperature of Carbon Dioxide<\/strong><\/h3>\r\nIf we shake a carbon dioxide fire extinguisher on a cool day (18 \u00b0C), we can hear liquid CO<sub>2<\/sub> sloshing around inside the cylinder. However, the same cylinder appears to contain no liquid on a hot summer day (35 \u00b0C). Explain these observations.\r\n[reveal-answer q=\"589074\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"589074\"]\r\n\r\nOn the cool day, the temperature of the CO<sub>2<\/sub> is below the critical temperature of CO<sub>2<\/sub>, 304 K or 31 \u00b0C (Table 10.3), so liquid CO<sub>2<\/sub> is present in the cylinder. On the hot day, the temperature of the CO<sub>2<\/sub> is greater than its critical temperature of 31 \u00b0C. Above this temperature no amount of pressure can liquefy CO<sub>2<\/sub> so no liquid CO<sub>2<\/sub> exists in the fire extinguisher.\r\n\r\n[\/hidden-answer]\r\n<h4><strong>Check Your Learning<\/strong><\/h4>\r\nAmmonia can be liquefied by compression at room temperature; oxygen cannot be liquefied under these conditions. Why do the two gases exhibit different behavior?\r\n\r\n[reveal-answer q=\"857707\"]Show Answer[\/reveal-answer]\r\n[hidden-answer a=\"857707\"]The critical temperature of ammonia is 405.5 K, which is higher than room temperature. The critical temperature of oxygen is below room temperature; thus oxygen cannot be liquefied at room temperature.[\/hidden-answer]\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\">\r\n<h3>Decaffeinating Coffee Using Supercritical CO<sub>2<\/sub><\/h3>\r\nCoffee is the world\u2019s second most widely traded commodity, following only petroleum. Across the globe, people love coffee\u2019s aroma and taste. Many of us also depend on one component of coffee\u2014caffeine\u2014to help us get going in the morning or stay alert in the afternoon. But late in the day, coffee\u2019s stimulant effect can keep you from sleeping, so you may choose to drink decaffeinated coffee in the evening.\r\n\r\nSince the early 1900s, many methods have been used to decaffeinate coffee. All have advantages and disadvantages, and all depend on the physical and chemical properties of caffeine. Because caffeine is a somewhat polar molecule, it dissolves well in water, a polar liquid. However, since many of the other 400-plus compounds that contribute to coffee\u2019s taste and aroma also dissolve in H<sub>2<\/sub>O, hot water decaffeination processes can also remove some of these compounds, adversely affecting the smell and taste of the decaffeinated coffee. Dichloromethane (CH<sub>2<\/sub>Cl<sub>2<\/sub>) and ethyl acetate (CH<sub>3<\/sub>CO<sub>2<\/sub>C<sub>2<\/sub>H<sub>5<\/sub>) have similar polarity to caffeine, and are therefore very effective solvents for caffeine extraction, but both also remove some flavor and aroma components, and their use requires long extraction and cleanup times. Because both of these solvents are toxic, health concerns have been raised regarding the effect of residual solvent remaining in the decaffeinated coffee.\r\n\r\nSupercritical fluid extraction using carbon dioxide is now being widely used as a more effective and environmentally friendly decaffeination method (Figure 7). At temperatures above 304.2 K and pressures above 7376 kPa, CO<sub>2<\/sub> is a supercritical fluid, with properties of both gas and liquid. Like a gas, it penetrates deep into the coffee beans; like a liquid, it effectively dissolves certain substances. Supercritical carbon dioxide extraction of steamed coffee beans removes 97\u221299% of the caffeine, leaving coffee\u2019s flavor and aroma compounds intact. Because CO<sub>2<\/sub> is a gas under standard conditions, its removal from the extracted coffee beans is easily accomplished, as is the recovery of the caffeine from the extract. The caffeine recovered from coffee beans via this process is a valuable product that can be used subsequently as an additive to other foods or drugs.\r\n\r\n[caption id=\"attachment_4607\" align=\"aligncenter\" width=\"700\"]<img class=\" wp-image-4607\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214412\/CNX_Chem_10_04_SupCritCof-1024x692.jpg\" alt=\"Two images are shown and labeled \u201ca\u201d and \u201cb.\u201d Image a shows a molecule composed of a five member ring composed of two blue spheres and three black spheres. One of the blue spheres is bonded to a black sphere bonded to three white spheres and one of the black spheres is bonded to a white sphere. The other two black spheres are double bonded together and make up one side of a six-membered ring that is also composed of two more black spheres and two blue spheres, both of which are bonded to a black sphere bonded to three white spheres. The black spheres are each double bonded to red spheres. Image b shows a diagram of two vertical tubes that lie next to one another. The left-hand tube is labeled \u201cExtraction vessel.\u201d A small tube labeled \u201cSoaked beans\u201d leads into the top of the tube and a label at the bottom of the tube reads \u201cDecaffeinated beans.\u201d The right tube is labeled \u201cAbsorption vessel.\u201d A tube near the top of this tube is labeled \u201cWater\u201d and another tube leads from the right tube to the left. This tube is labeled with a left-facing arrow and the phrase \u201csupercritical carbon dioxide.\u201d There is a tube leading away from the bottom which is labeled, \u201cCaffeine and water.\u201d There is another tube that leads from the extraction vessel to the absorption vessel which is labeled, \u201csupercritical C O subscript 2 plus caffeine.\u201d\" width=\"700\" height=\"473\" \/> Figure 7. (a) Caffeine molecules have both polar and nonpolar regions, making it soluble in solvents of varying polarities. (b) The schematic shows a typical decaffeination process involving supercritical carbon dioxide.[\/caption]\r\n\r\n<\/div>\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Concepts and Summary<\/h3>\r\nThe temperature and pressure conditions at which a substance exists in solid, liquid, and gaseous states are summarized in a phase diagram for that substance. Phase diagrams are combined plots of three pressure-temperature equilibrium curves: solid-liquid, liquid-gas, and solid-gas. These curves represent the relationships between phase-transition temperatures and pressures. The point of intersection of all three curves represents the substance\u2019s triple point\u2014the temperature and pressure at which all three phases are in equilibrium. At pressures below the triple point, a substance cannot exist in the liquid state, regardless of its temperature. The terminus of the liquid-gas curve represents the substance\u2019s critical point, the pressure and temperature above which a liquid phase cannot exist.\r\n\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Exercises<\/h3>\r\n<ol>\r\n \t<li>From the phase diagram for water (Figure 2), determine the state of water at:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>35 \u00b0C and 85 kPa<\/li>\r\n \t<li>\u221215 \u00b0C and 40 kPa<\/li>\r\n \t<li>\u221215 \u00b0C and 0.1 kPa<\/li>\r\n \t<li>75 \u00b0C and 3 kPa<\/li>\r\n \t<li>40 \u00b0C and 0.1 kPa<\/li>\r\n \t<li>60 \u00b0C and 50 kPa<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>What phase changes will take place when water is subjected to varying pressure at a constant temperature of 0.005 \u00b0C? At 40 \u00b0C? At \u221240 \u00b0C?<\/li>\r\n \t<li>Pressure cookers allow food to cook faster because the higher pressure inside the pressure cooker increases the boiling temperature of water. A particular pressure cooker has a safety valve that is set to vent steam if the pressure exceeds 3.4 atm. What is the approximate maximum temperature that can be reached inside this pressure cooker? Explain your reasoning.<\/li>\r\n \t<li>From the phase diagram for carbon dioxide in Figure 5, determine the state of CO<sub>2<\/sub> at:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>20 \u00b0C and 1000 kPa<\/li>\r\n \t<li>10 \u00b0C and 2000 kPa<\/li>\r\n \t<li>10 \u00b0C and 100 kPa<\/li>\r\n \t<li>\u221240 \u00b0C and 500 kPa<\/li>\r\n \t<li>\u221280 \u00b0C and 1500 kPa<\/li>\r\n \t<li>\u221280 \u00b0C and 10 kPa<\/li>\r\n<\/ol>\r\n<\/li>\r\n \t<li>Determine the phase changes that carbon dioxide undergoes as the pressure changes if the temperature is held at \u221250 \u00b0C? If the temperature is held at \u221240 \u00b0C? At 20 \u00b0C? (See the phase diagram in Figure 5).<\/li>\r\n \t<li>Consider a cylinder containing a mixture of liquid carbon dioxide in equilibrium with gaseous carbon dioxide at an initial pressure of 65 atm and a temperature of 20 \u00b0C. Sketch a plot depicting the change in the cylinder pressure with time as gaseous carbon dioxide is released at constant temperature.<\/li>\r\n \t<li>Dry ice, CO<sub>2<\/sub>(<em>s<\/em>), does not melt at atmospheric pressure. It sublimes at a temperature of \u221278 \u00b0C. What is the lowest pressure at which CO<sub>2<\/sub>(<em>s<\/em>) will melt to give CO<sub>2<\/sub>(<em>l<\/em>)? At approximately what temperature will this occur? (See Figure 5\u00a0for the phase diagram.)<\/li>\r\n \t<li>If a severe storm results in the loss of electricity, it may be necessary to use a clothesline to dry laundry. In many parts of the country in the dead of winter, the clothes will quickly freeze when they are hung on the line. If it does not snow, will they dry anyway? Explain your answer.<\/li>\r\n \t<li>Is it possible to liquefy nitrogen at room temperature (about 25 \u00b0C)? Is it possible to liquefy sulfur dioxide at room temperature? Explain your answers.<\/li>\r\n \t<li>Elemental carbon has one gas phase, one liquid phase, and three different solid phases, as shown in the phase diagram:\r\n<img class=\"alignnone wp-image-5211\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214547\/CNX_Chem_10_04_CPhaseDi_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right.\" width=\"400\" height=\"451\" \/>\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>On the phase diagram, label the gas and liquid regions.<\/li>\r\n \t<li>Graphite is the most stable phase of carbon at normal conditions. On the phase diagram, label the graphite phase.<\/li>\r\n \t<li>If graphite at normal conditions is heated to 2500 K while the pressure is increased to 10<sup>5<\/sup> atm, it is converted into diamond. Label the diamond phase.<\/li>\r\n \t<li>Circle each triple point on the phase diagram.<\/li>\r\n \t<li>In what phase does carbon exist at 4000 K and 10<sup>5<\/sup> atm?<\/li>\r\n \t<li>If the temperature of a sample of carbon increases from 4000 K to 5000 K at a constant pressure of 10<sup>2<\/sup> atm, which phase transition occurs, if any?<\/li>\r\n<\/ol>\r\n<\/li>\r\n<\/ol>\r\n[reveal-answer q=\"799811\"]Show Selected Answers[\/reveal-answer]\r\n[hidden-answer a=\"799811\"]\r\n\r\n2.\u00a0At low pressures and 0.005 \u00b0C, the water is a gas. As the pressure increases to 4.6 torr, the water becomes a solid; as the pressure increases still more, it becomes a liquid. At 40 \u00b0C, water at low pressure is a vapor; at pressures higher than about 75 torr, it converts into a liquid. At \u221240 \u00b0C, water goes from a gas to a solid as the pressure increases above very low values.\r\n\r\n4. Using the phase diagram for carbon dioxide provided, we can determine that the state of CO<sub>2<\/sub> at each temperature and pressure given are as follows:\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li>liquid<\/li>\r\n \t<li>solid<\/li>\r\n \t<li>gas<\/li>\r\n \t<li>gas<\/li>\r\n \t<li>gas<\/li>\r\n \t<li>gas<\/li>\r\n<\/ol>\r\n6. The plot will look something like this:\r\n\r\n<img class=\"alignnone wp-image-5210\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214545\/CNX_Chem_10_04_Ex06answer_img.jpg\" alt=\"An x-axis is labeled at the left as \u201cFull\u201d and at the right as \u201cEmpty.\u201d A y-axis is labeled at the top as \u201cP.\u201d Beneath the x-axis is the label \u201cAmount released.\u201d A horizontal line that then slopes downward is drawn about halfway up the vertical line and labeled on the left as \u201c65 a t m.\u201d About two-thirds of the way across the x-axis, it slopes downward in a straight line to meet the \u201cempty\u201d label on the bottom right of the axis.\" width=\"500\" height=\"275\" \/>\r\n\r\n8.\u00a0Yes, ice will sublime, although it may take it several days. Ice has a small vapor pressure, and some ice molecules form gas and escape from the ice crystals. As time passes, more and more solid converts to gas until eventually the clothes are dry.\r\n\r\n10. Answers\r\n<ol style=\"list-style-type: lower-alpha;\">\r\n \t<li><img class=\"alignnone wp-image-5212\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214548\/CNX_Chem_10_04_Exercise10a_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right. The two quadrants to the right are labeled, \u201cWater ( liquid )\u201d and \u201cWater vapor ( gas ).\u201d\" width=\"400\" height=\"451\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-5213\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214549\/CNX_Chem_10_04_Exercise10b_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right. The quadrant to the left is labeled, \u201cGraphite.\u201d\" width=\"400\" height=\"451\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-5214\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214550\/CNX_Chem_10_04_Exercise10c_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right. The top quadrant is labeled, \u201cDiamond.\u201d\" width=\"400\" height=\"451\" \/><\/li>\r\n \t<li><img class=\"alignnone wp-image-5215\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214552\/CNX_Chem_10_04_Exercise10d_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right. The four quadrants are labeled, \u201cDiamond\u201d at the top, \u201cGraphite\u201d, to the left, \u201cwater ( liquid )\u201d to the top right, and \u201cwater vapor ( gas ),\u201d to the bottom right. There is a red circle where the liquid, gas, and graphite lines intersect.\" width=\"400\" height=\"451\" \/><\/li>\r\n \t<li>liquid phase<\/li>\r\n \t<li>sublimation<\/li>\r\n<\/ol>\r\n[\/hidden-answer]\r\n\r\n<\/div>\r\n<h2>Glossary<\/h2>\r\n<strong>critical point: <\/strong>temperature and pressure above which a gas cannot be condensed into a liquid\r\n\r\n<strong>phase diagram: <\/strong>pressure-temperature graph summarizing conditions under which the phases of a substance can exist\r\n\r\n<strong>supercritical fluid: <\/strong>substance at a temperature and pressure higher than its critical point; exhibits properties intermediate between those of gaseous and liquid states\r\n\r\n<strong>triple point: <\/strong>temperature and pressure at which the vapor, liquid, and solid phases of a substance are in equilibrium","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>Explain the construction and use of a typical phase diagram<\/li>\n<li>Use phase diagrams to identify stable phases at given temperatures and pressures, and to describe phase transitions resulting from changes in these properties<\/li>\n<li>Describe the supercritical fluid phase of matter<\/li>\n<\/ul>\n<\/div>\n<p>In the previous module, the variation of a liquid\u2019s equilibrium vapor pressure with temperature was described. Considering the definition of boiling point, plots of vapor pressure versus temperature represent how the boiling point of the liquid varies with pressure. Also described was the use of heating and cooling curves to determine a substance\u2019s melting (or freezing) point. Making such measurements over a wide range of pressures yields data that may be presented graphically as a phase diagram. A <strong>phase diagram<\/strong>\u00a0combines plots of pressure versus temperature for the liquid-gas, solid-liquid, and solid-gas phase-transition equilibria of a substance. These diagrams indicate the physical states that exist under specific conditions of pressure and temperature, and also provide the pressure dependence of the phase-transition temperatures (melting points, sublimation points, boiling points). A typical phase diagram for a pure substance is shown in Figure 1.<\/p>\n<div id=\"attachment_4602\" style=\"width: 460px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4602\" class=\"wp-image-4602\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214404\/CNX_Chem_10_04_PhaseDi.jpg\" alt=\"A graph is shown where the x-axis is labeled \u201cTemperature\u201d and the y-axis is labeled \u201cPressure.\u201d A line extends from the lower left bottom of the graph sharply upward to a point that is a third across the x-axis. A second line begins at the lower third of the first line at a point labeled \u201ctriple point\u201d and extends to the upper right corner of the graph where it is labeled \u201ccritical point.\u201d The two lines bisect the graph area to create three sections, labeled \u201csolid\u201d near the top left, \u201cliquid\u201d in the top middle and \u201cgas\u201d near the bottom right. A pair of horizontal arrows, one left-facing and labeled \u201cdeposition\u201d and one right-facing and labeled\u201d sublimation,\u201d are drawn on top of the bottom section of the first line. A second pair of horizontal arrows, one left-facing and labeled \u201cfreezing\u201d and one right-facing and labeled \u201cmelting\u201d, are drawn on top of the upper section of the first line. A third pair of horizontal arrows, one left-facing and labeled \u201ccondensation\u201d and one right-facing and labeled \u201dvaporization,\u201d are drawn on top of the middle section of the second line.\" width=\"450\" height=\"410\" \/><\/p>\n<p id=\"caption-attachment-4602\" class=\"wp-caption-text\">Figure 1. The physical state of a substance and its phase-transition temperatures are represented graphically in a phase diagram.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<p>To illustrate the utility of these plots, consider the phase diagram for water shown in Figure 2.<\/p>\n<div id=\"attachment_4603\" style=\"width: 625px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4603\" class=\"wp-image-4603\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214405\/CNX_Chem_10_04_H2OPhasDi2.jpg\" alt=\"A graph is shown where the x-axis is labeled \u201cTemperature in degrees Celsius\u201d and the y-axis is labeled \u201cPressure ( k P a ).\u201d A line extends from the origin of the graph which is labeled \u201cA\u201d sharply upward to a point in the bottom third of the diagram labeled \u201cB\u201d where it branches into a line that slants slightly backward until it hits the highest point on the y-axis labeled \u201cD\u201d and a second line that extends to the upper right corner of the graph labeled \u201cC\u201d. C is labeled \u201cCritical point, with a dotted line extending downward to the x-axis labeled 374 degrees Celsius, and another dotted line extending to the y-axis labeled 22,089 k P a. The two lines bisect the graph area to create three sections, labeled \u201cIce (solid)\u201d near the middle left, \u201cWater (liquid)\u201d in the top middle and \u201cWater vapor (gas)\u201d near the bottom middle. Point B is labeled \u201cTriple point\u201d and has a dotted line extending downward to the x-axis labeled 0.01, and another dotted line extending to the y-axis labeled 0.6. Halfway between points B and C a dotted line extends from the originally discussed line downward to the point 100 degrees Celsius on the x-axis, and another dotted line extends to the y-axis at 101 k P a. Another dotted line extends from this dotted line downward at 0 degrees Celsius.\" width=\"615\" height=\"399\" \/><\/p>\n<p id=\"caption-attachment-4603\" class=\"wp-caption-text\">Figure 2. The pressure and temperature axes on this phase diagram of water are not drawn to constant scale in order to illustrate several important properties.<\/p>\n<\/div>\n<p>We can use the phase diagram to identify the physical state of a sample of water under specified conditions of pressure and temperature. For example, a pressure of 50 kPa and a temperature of \u221210 \u00b0C correspond to the region of the diagram labeled \u201cice.\u201d Under these conditions, water exists only as a solid (ice). A pressure of 50 kPa and a temperature of 50 \u00b0C correspond to the \u201cwater\u201d region\u2014here, water exists only as a liquid. At 25 kPa and 200 \u00b0C, water exists only in the gaseous state. Note that on the H<sub>2<\/sub>O phase diagram, the pressure and temperature axes are not drawn to a constant scale in order to permit the illustration of several important features as described here.<\/p>\n<p>The curve BC in Figure\u00a02 is the plot of vapor pressure versus temperature as described in the previous module of this chapter. This \u201cliquid-vapor\u201d curve separates the liquid and gaseous regions of the phase diagram and provides the boiling point for water at any pressure. For example, at 1 atm, the boiling point is 100 \u00b0C. Notice that the liquid-vapor curve terminates at a temperature of 374 \u00b0C and a pressure of 218 atm, indicating that water cannot exist as a liquid above this temperature, regardless of the pressure. The physical properties of water under these conditions are intermediate between those of its liquid and gaseous phases. This unique state of matter is called a supercritical fluid, a topic that will be described in the next section of this module.<\/p>\n<figure id=\"CNX_Chem_10_04_FreezeDry\"><\/figure>\n<div id=\"attachment_3388\" style=\"width: 360px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-3388\" class=\"wp-image-3388\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/05\/23213613\/CNX_Chem_10_04_FreezeDry.jpg\" alt=\"A photograph shows a packet of Freeze Dried Ice Cream, next to the contents of the package opened.\" width=\"350\" height=\"263\" \/><\/p>\n<p id=\"caption-attachment-3388\" class=\"wp-caption-text\">Figure 3 Freeze-dried foods, like this ice cream, are dehydrated by sublimation at pressures below the triple point for water. (credit: \u02balwao\u02ba\/Flickr)<\/p>\n<\/div>\n<p>The solid-vapor curve, labeled AB in Figure 2, indicates the temperatures and pressures at which ice and water vapor are in equilibrium. These temperature-pressure data pairs correspond to the sublimation, or deposition, points for water. If we could zoom in on the solid-gas line in Figure 2, we would see that ice has a vapor pressure of about 0.20 kPa at \u221210 \u00b0C. Thus, if we place a frozen sample in a vacuum with a pressure less than 0.20 kPa, ice will sublime. This is the basis for the \u201cfreeze-drying\u201d process often used to preserve foods, such as the ice cream shown in Figure 3.<\/p>\n<p>The solid-liquid curve labeled BD shows the temperatures and pressures at which ice and liquid water are in equilibrium, representing the melting\/freezing points for water. Note that this curve exhibits a slight negative slope (greatly exaggerated for clarity), indicating that the melting point for water decreases slightly as pressure increases. Water is an unusual substance in this regard, as most substances exhibit an increase in melting point with increasing pressure. This behavior is partly responsible for the movement of glaciers, like the one shown in Figure 4. The bottom of a glacier experiences an immense pressure due to its weight that can melt some of the ice, forming a layer of liquid water on which the glacier may more easily slide.<\/p>\n<div id=\"attachment_4604\" style=\"width: 660px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4604\" class=\"size-full wp-image-4604\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214407\/CNX_Chem_10_04_IceMelt.jpg\" alt=\"A photograph shows an aerial view of a land mass. The white mass of a glacier is shown near the top left quadrant of the photo and leads to two branching blue rivers. The open land is shown in brown.\" width=\"650\" height=\"432\" \/><\/p>\n<p id=\"caption-attachment-4604\" class=\"wp-caption-text\">Figure 4. The immense pressures beneath glaciers result in partial melting to produce a layer of water that provides lubrication to assist glacial movement. This satellite photograph shows the advancing edge of the Perito Moreno glacier in Argentina. (credit: NASA)<\/p>\n<\/div>\n<p>The point of intersection of all three curves is labeled B in Figure 2. At the pressure and temperature represented by this point, all three phases of water coexist in equilibrium. This temperature-pressure data pair is called the <strong>triple point<\/strong>. At pressures lower than the triple point, water cannot exist as a liquid, regardless of the temperature.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 1:\u00a0<strong>Determining the State of Water<\/strong><\/h3>\n<p>Using the phase diagram for water given in Figure 10.30,\u00a0determine the state of water at the following temperatures and pressures:<\/p>\n<ol>\n<li>\u221210 \u00b0C and 50 kPa<\/li>\n<li>25 \u00b0C and 90 kPa<\/li>\n<li>50 \u00b0C and 40 kPa<\/li>\n<li>80 \u00b0C and 5 kPa<\/li>\n<li>\u221210 \u00b0C and 0.3 kPa<\/li>\n<li>50 \u00b0C and 0.3 kPa<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q480813\">Show Answer<\/span><\/p>\n<div id=\"q480813\" class=\"hidden-answer\" style=\"display: none\">Using the phase diagram for water, we can determine that the state of water at each temperature and pressure given are as follows:<\/p>\n<ol>\n<li>solid<\/li>\n<li>liquid<\/li>\n<li>liquid<\/li>\n<li>gas<\/li>\n<li>solid<\/li>\n<li>gas<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h4><strong>Check Your Learning<\/strong><\/h4>\n<p>What phase changes can water undergo as the temperature changes if the pressure is held at 0.3 kPa? If the pressure is held at 50 kPa?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q565714\">Show Answer<\/span><\/p>\n<div id=\"q565714\" class=\"hidden-answer\" style=\"display: none\">At 0.3 kPa: [latex]\\text{s}\\longrightarrow \\text{g}[\/latex] at \u221258 \u00b0C. At 50 kPa: [latex]\\text{s}\\longrightarrow \\text{l}[\/latex] at 0 \u00b0C, l \u27f6 g at 78 \u00b0C<\/div>\n<\/div>\n<\/div>\n<p>Consider the phase diagram for carbon dioxide shown in Figure 5 as another example. The solid-liquid curve exhibits a positive slope, indicating that the melting point for CO<sub>2<\/sub> increases with pressure as it does for most substances (water being a notable exception as described previously). Notice that the triple point is well above 1 atm, indicating that carbon dioxide cannot exist as a liquid under ambient pressure conditions. Instead, cooling gaseous carbon dioxide at 1 atm results in its deposition into the solid state. Likewise, solid carbon dioxide does not melt at 1 atm pressure but instead sublimes to yield gaseous CO<sub>2<\/sub>. Finally, notice that the critical point for carbon dioxide is observed at a relatively modest temperature and pressure in comparison to water.<\/p>\n<div id=\"attachment_4605\" style=\"width: 660px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4605\" class=\"wp-image-4605\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214409\/CNX_Chem_10_04_CO2phasdi.jpg\" alt=\"A graph is shown where the x-axis is labeled \u201cTemperature ( degree sign, C )\u201d and has values of negative 100 to 100 in increments of 25 and the y-axis is labeled \u201cPressure ( k P a )\u201d and has values of 10 to 1,000,000. A line extends from the lower left bottom of the graph upward to a point around\u201c27, 9000,\u201d where it ends. The space under this curve is labeled \u201cGas.\u201d A second line extends in a curve from point around \u201c-73, 100\u201d to \u201c27, 1,000,000.\u201d The area to the left of this line and above the first line is labeled \u201cSolid\u201d while the area to the right is labeled \u201cLiquid.\u201d A section on the graph under the second line and past the point \u201c28\u201d on the x-axis is labeled \u201cS C F.\u201d\" width=\"650\" height=\"396\" \/><\/p>\n<p id=\"caption-attachment-4605\" class=\"wp-caption-text\">Figure 5. The pressure and temperature axes on this phase diagram of carbon dioxide are not drawn to constant scale in order to illustrate several important properties.<\/p>\n<\/div>\n<figure id=\"CNX_Chem_10_04_CO2phasdi\"><\/figure>\n<div class=\"textbox examples\">\n<h3>Example 2:\u00a0<strong>Determining the State of Carbon Dioxide<\/strong><\/h3>\n<p>Using the phase diagram for carbon dioxide shown in\u00a0Figure 5, determine the state of CO<sub>2<\/sub> at the following temperatures and pressures:<\/p>\n<ol>\n<li>\u221230 \u00b0C and 2000 kPa<\/li>\n<li>\u221260 \u00b0C and 1000 kPa<\/li>\n<li>\u221260 \u00b0C and 100 kPa<\/li>\n<li>20 \u00b0C and 1500 kPa<\/li>\n<li>0 \u00b0C and 100 kPa<\/li>\n<li>20 \u00b0C and 100 kPa<\/li>\n<\/ol>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q475095\">Show Answer<\/span><\/p>\n<div id=\"q475095\" class=\"hidden-answer\" style=\"display: none\">Using the phase diagram for carbon dioxide provided, we can determine that the state of CO<sub>2<\/sub> at each temperature and pressure given are as follows:<\/p>\n<ol>\n<li>liquid<\/li>\n<li>solid<\/li>\n<li>gas<\/li>\n<li>liquid<\/li>\n<li>gas<\/li>\n<li>gas<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<h4><strong>Check Your Learning<\/strong><\/h4>\n<p>Determine the phase changes carbon dioxide undergoes when its temperature is varied, thus holding its pressure constant at 1500 kPa? At 500 kPa? At what approximate temperatures do these phase changes occur?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q185931\">Show Answer<\/span><\/p>\n<div id=\"q185931\" class=\"hidden-answer\" style=\"display: none\">at 1500 kPa: [latex]\\text{s}\\longrightarrow \\text{l}[\/latex] at \u221245 \u00b0C, [latex]\\text{l}\\longrightarrow \\text{g}[\/latex] at \u221210 \u00b0C;\u00a0at 500 kPa: [latex]\\text{s}\\longrightarrow \\text{g}[\/latex] at \u221258 \u00b0C<\/div>\n<\/div>\n<\/div>\n<h2>Supercritical Fluids<\/h2>\n<p>If we place a sample of water in a sealed container at 25 \u00b0C, remove the air, and let the vaporization-condensation equilibrium establish itself, we are left with a mixture of liquid water and water vapor at a pressure of 0.03 atm. A distinct boundary between the more dense liquid and the less dense gas is clearly observed. As we increase the temperature, the pressure of the water vapor increases, as described by the liquid-gas curve in the phase diagram for water (Figure 2), and a two-phase equilibrium of liquid and gaseous phases remains. At a temperature of 374 \u00b0C, the vapor pressure has risen to 218 atm, and any further increase in temperature results in the disappearance of the boundary between liquid and vapor phases. All of the water in the container is now present in a single phase whose physical properties are intermediate between those of the gaseous and liquid states. This phase of matter is called a <strong>supercritical fluid<\/strong>, and the temperature and pressure above which this phase exists is the<strong> critical point<\/strong>. Above its critical temperature, a gas cannot be liquefied no matter how much pressure is applied. The pressure required to liquefy a gas at its critical temperature is called the critical pressure. The critical temperatures and critical pressures of some common substances are given in Table 1.<\/p>\n<table id=\"fs-idm180459824\" class=\"medium unnumbered\" summary=\"none\" data-label=\"\">\n<thead>\n<tr valign=\"top\">\n<th colspan=\"3\">Table 1.<\/th>\n<\/tr>\n<tr valign=\"top\">\n<th>Substance<\/th>\n<th>Critical Temperature (K)<\/th>\n<th>Critical Pressure (atm)<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr valign=\"top\">\n<td>hydrogen<\/td>\n<td>33.2<\/td>\n<td>12.8<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>nitrogen<\/td>\n<td>126.0<\/td>\n<td>33.5<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>oxygen<\/td>\n<td>154.3<\/td>\n<td>49.7<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>carbon dioxide<\/td>\n<td>304.2<\/td>\n<td>73.0<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>ammonia<\/td>\n<td>405.5<\/td>\n<td>111.5<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>sulfur dioxide<\/td>\n<td>430.3<\/td>\n<td>77.7<\/td>\n<\/tr>\n<tr valign=\"top\">\n<td>water<\/td>\n<td>647.1<\/td>\n<td>217.7<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<div id=\"attachment_4606\" style=\"width: 1034px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4606\" class=\"size-large wp-image-4606\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214410\/CNX_Chem_10_04_CritFluid-1024x241.jpg\" alt=\"Four photographs are shown where each shows a circular container with a green and red float in each. In the left diagram, the container is half filled with a colorless liquid and the floats sit on the surface of the liquid. In the second photo, the green float is near the top and the red float lies near the bottom of the container. In the third photo, the fluid is darker and the green float sits halfway up the container while the red is sitting at the bottom. In the right photo, the liquid is colorless again and the two floats sit on the surface.\" width=\"1024\" height=\"241\" \/><\/p>\n<p id=\"caption-attachment-4606\" class=\"wp-caption-text\">Figure 6. (a) A sealed container of liquid carbon dioxide slightly below its critical point is heated, resulting in (b) the formation of the supercritical fluid phase. Cooling the supercritical fluid lowers its temperature and pressure below the critical point, resulting in the reestablishment of separate liquid and gaseous phases (c and d). Colored floats illustrate differences in density between the liquid, gaseous, and supercritical fluid states. (credit: modification of work by \u201cmrmrobin\u201d\/YouTube)<\/p>\n<\/div>\n<div class=\"textbox\">\n<p>Observe the liquid-to-supercritical fluid transition for carbon dioxide in this video.<\/p>\n<p><iframe loading=\"lazy\" id=\"oembed-1\" title=\"Supercritical CO2\" width=\"500\" height=\"281\" src=\"https:\/\/www.youtube.com\/embed\/P9EftqFYaHg?feature=oembed&#38;rel=0\" frameborder=\"0\" allowfullscreen=\"allowfullscreen\"><\/iframe><\/p>\n<\/div>\n<p>Like a gas, a supercritical fluid will expand and fill a container, but its density is much greater than typical gas densities, typically being close to those for liquids. Similar to liquids, these fluids are capable of dissolving nonvolatile solutes. They exhibit essentially no surface tension and very low viscosities, however, so they can more effectively penetrate very small openings in a solid mixture and remove soluble components. These properties make supercritical fluids extremely useful solvents for a wide range of applications. For example, supercritical carbon dioxide has become a very popular solvent in the food industry, being used to decaffeinate coffee, remove fats from potato chips, and extract flavor and fragrance compounds from citrus oils. It is nontoxic, relatively inexpensive, and not considered to be a pollutant. After use, the CO<sub>2<\/sub> can be easily recovered by reducing the pressure and collecting the resulting gas.<\/p>\n<div class=\"textbox examples\">\n<h3>Example 3:\u00a0<strong>The Critical Temperature of Carbon Dioxide<\/strong><\/h3>\n<p>If we shake a carbon dioxide fire extinguisher on a cool day (18 \u00b0C), we can hear liquid CO<sub>2<\/sub> sloshing around inside the cylinder. However, the same cylinder appears to contain no liquid on a hot summer day (35 \u00b0C). Explain these observations.<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q589074\">Show Answer<\/span><\/p>\n<div id=\"q589074\" class=\"hidden-answer\" style=\"display: none\">\n<p>On the cool day, the temperature of the CO<sub>2<\/sub> is below the critical temperature of CO<sub>2<\/sub>, 304 K or 31 \u00b0C (Table 10.3), so liquid CO<sub>2<\/sub> is present in the cylinder. On the hot day, the temperature of the CO<sub>2<\/sub> is greater than its critical temperature of 31 \u00b0C. Above this temperature no amount of pressure can liquefy CO<sub>2<\/sub> so no liquid CO<sub>2<\/sub> exists in the fire extinguisher.<\/p>\n<\/div>\n<\/div>\n<h4><strong>Check Your Learning<\/strong><\/h4>\n<p>Ammonia can be liquefied by compression at room temperature; oxygen cannot be liquefied under these conditions. Why do the two gases exhibit different behavior?<\/p>\n<div class=\"qa-wrapper\" style=\"display: block\"><span class=\"show-answer collapsed\" style=\"cursor: pointer\" data-target=\"q857707\">Show Answer<\/span><\/p>\n<div id=\"q857707\" class=\"hidden-answer\" style=\"display: none\">The critical temperature of ammonia is 405.5 K, which is higher than room temperature. The critical temperature of oxygen is below room temperature; thus oxygen cannot be liquefied at room temperature.<\/div>\n<\/div>\n<\/div>\n<div class=\"textbox shaded\">\n<h3>Decaffeinating Coffee Using Supercritical CO<sub>2<\/sub><\/h3>\n<p>Coffee is the world\u2019s second most widely traded commodity, following only petroleum. Across the globe, people love coffee\u2019s aroma and taste. Many of us also depend on one component of coffee\u2014caffeine\u2014to help us get going in the morning or stay alert in the afternoon. But late in the day, coffee\u2019s stimulant effect can keep you from sleeping, so you may choose to drink decaffeinated coffee in the evening.<\/p>\n<p>Since the early 1900s, many methods have been used to decaffeinate coffee. All have advantages and disadvantages, and all depend on the physical and chemical properties of caffeine. Because caffeine is a somewhat polar molecule, it dissolves well in water, a polar liquid. However, since many of the other 400-plus compounds that contribute to coffee\u2019s taste and aroma also dissolve in H<sub>2<\/sub>O, hot water decaffeination processes can also remove some of these compounds, adversely affecting the smell and taste of the decaffeinated coffee. Dichloromethane (CH<sub>2<\/sub>Cl<sub>2<\/sub>) and ethyl acetate (CH<sub>3<\/sub>CO<sub>2<\/sub>C<sub>2<\/sub>H<sub>5<\/sub>) have similar polarity to caffeine, and are therefore very effective solvents for caffeine extraction, but both also remove some flavor and aroma components, and their use requires long extraction and cleanup times. Because both of these solvents are toxic, health concerns have been raised regarding the effect of residual solvent remaining in the decaffeinated coffee.<\/p>\n<p>Supercritical fluid extraction using carbon dioxide is now being widely used as a more effective and environmentally friendly decaffeination method (Figure 7). At temperatures above 304.2 K and pressures above 7376 kPa, CO<sub>2<\/sub> is a supercritical fluid, with properties of both gas and liquid. Like a gas, it penetrates deep into the coffee beans; like a liquid, it effectively dissolves certain substances. Supercritical carbon dioxide extraction of steamed coffee beans removes 97\u221299% of the caffeine, leaving coffee\u2019s flavor and aroma compounds intact. Because CO<sub>2<\/sub> is a gas under standard conditions, its removal from the extracted coffee beans is easily accomplished, as is the recovery of the caffeine from the extract. The caffeine recovered from coffee beans via this process is a valuable product that can be used subsequently as an additive to other foods or drugs.<\/p>\n<div id=\"attachment_4607\" style=\"width: 710px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4607\" class=\"wp-image-4607\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/06\/23214412\/CNX_Chem_10_04_SupCritCof-1024x692.jpg\" alt=\"Two images are shown and labeled \u201ca\u201d and \u201cb.\u201d Image a shows a molecule composed of a five member ring composed of two blue spheres and three black spheres. One of the blue spheres is bonded to a black sphere bonded to three white spheres and one of the black spheres is bonded to a white sphere. The other two black spheres are double bonded together and make up one side of a six-membered ring that is also composed of two more black spheres and two blue spheres, both of which are bonded to a black sphere bonded to three white spheres. The black spheres are each double bonded to red spheres. Image b shows a diagram of two vertical tubes that lie next to one another. The left-hand tube is labeled \u201cExtraction vessel.\u201d A small tube labeled \u201cSoaked beans\u201d leads into the top of the tube and a label at the bottom of the tube reads \u201cDecaffeinated beans.\u201d The right tube is labeled \u201cAbsorption vessel.\u201d A tube near the top of this tube is labeled \u201cWater\u201d and another tube leads from the right tube to the left. This tube is labeled with a left-facing arrow and the phrase \u201csupercritical carbon dioxide.\u201d There is a tube leading away from the bottom which is labeled, \u201cCaffeine and water.\u201d There is another tube that leads from the extraction vessel to the absorption vessel which is labeled, \u201csupercritical C O subscript 2 plus caffeine.\u201d\" width=\"700\" height=\"473\" \/><\/p>\n<p id=\"caption-attachment-4607\" class=\"wp-caption-text\">Figure 7. (a) Caffeine molecules have both polar and nonpolar regions, making it soluble in solvents of varying polarities. (b) The schematic shows a typical decaffeination process involving supercritical carbon dioxide.<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox key-takeaways\">\n<h3>Key Concepts and Summary<\/h3>\n<p>The temperature and pressure conditions at which a substance exists in solid, liquid, and gaseous states are summarized in a phase diagram for that substance. Phase diagrams are combined plots of three pressure-temperature equilibrium curves: solid-liquid, liquid-gas, and solid-gas. These curves represent the relationships between phase-transition temperatures and pressures. The point of intersection of all three curves represents the substance\u2019s triple point\u2014the temperature and pressure at which all three phases are in equilibrium. At pressures below the triple point, a substance cannot exist in the liquid state, regardless of its temperature. The terminus of the liquid-gas curve represents the substance\u2019s critical point, the pressure and temperature above which a liquid phase cannot exist.<\/p>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Exercises<\/h3>\n<ol>\n<li>From the phase diagram for water (Figure 2), determine the state of water at:\n<ol style=\"list-style-type: lower-alpha;\">\n<li>35 \u00b0C and 85 kPa<\/li>\n<li>\u221215 \u00b0C and 40 kPa<\/li>\n<li>\u221215 \u00b0C and 0.1 kPa<\/li>\n<li>75 \u00b0C and 3 kPa<\/li>\n<li>40 \u00b0C and 0.1 kPa<\/li>\n<li>60 \u00b0C and 50 kPa<\/li>\n<\/ol>\n<\/li>\n<li>What phase changes will take place when water is subjected to varying pressure at a constant temperature of 0.005 \u00b0C? At 40 \u00b0C? At \u221240 \u00b0C?<\/li>\n<li>Pressure cookers allow food to cook faster because the higher pressure inside the pressure cooker increases the boiling temperature of water. A particular pressure cooker has a safety valve that is set to vent steam if the pressure exceeds 3.4 atm. What is the approximate maximum temperature that can be reached inside this pressure cooker? Explain your reasoning.<\/li>\n<li>From the phase diagram for carbon dioxide in Figure 5, determine the state of CO<sub>2<\/sub> at:\n<ol style=\"list-style-type: lower-alpha;\">\n<li>20 \u00b0C and 1000 kPa<\/li>\n<li>10 \u00b0C and 2000 kPa<\/li>\n<li>10 \u00b0C and 100 kPa<\/li>\n<li>\u221240 \u00b0C and 500 kPa<\/li>\n<li>\u221280 \u00b0C and 1500 kPa<\/li>\n<li>\u221280 \u00b0C and 10 kPa<\/li>\n<\/ol>\n<\/li>\n<li>Determine the phase changes that carbon dioxide undergoes as the pressure changes if the temperature is held at \u221250 \u00b0C? If the temperature is held at \u221240 \u00b0C? At 20 \u00b0C? (See the phase diagram in Figure 5).<\/li>\n<li>Consider a cylinder containing a mixture of liquid carbon dioxide in equilibrium with gaseous carbon dioxide at an initial pressure of 65 atm and a temperature of 20 \u00b0C. Sketch a plot depicting the change in the cylinder pressure with time as gaseous carbon dioxide is released at constant temperature.<\/li>\n<li>Dry ice, CO<sub>2<\/sub>(<em>s<\/em>), does not melt at atmospheric pressure. It sublimes at a temperature of \u221278 \u00b0C. What is the lowest pressure at which CO<sub>2<\/sub>(<em>s<\/em>) will melt to give CO<sub>2<\/sub>(<em>l<\/em>)? At approximately what temperature will this occur? (See Figure 5\u00a0for the phase diagram.)<\/li>\n<li>If a severe storm results in the loss of electricity, it may be necessary to use a clothesline to dry laundry. In many parts of the country in the dead of winter, the clothes will quickly freeze when they are hung on the line. If it does not snow, will they dry anyway? Explain your answer.<\/li>\n<li>Is it possible to liquefy nitrogen at room temperature (about 25 \u00b0C)? Is it possible to liquefy sulfur dioxide at room temperature? Explain your answers.<\/li>\n<li>Elemental carbon has one gas phase, one liquid phase, and three different solid phases, as shown in the phase diagram:<br \/>\n<img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5211\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214547\/CNX_Chem_10_04_CPhaseDi_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right.\" width=\"400\" height=\"451\" \/><\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>On the phase diagram, label the gas and liquid regions.<\/li>\n<li>Graphite is the most stable phase of carbon at normal conditions. On the phase diagram, label the graphite phase.<\/li>\n<li>If graphite at normal conditions is heated to 2500 K while the pressure is increased to 10<sup>5<\/sup> atm, it is converted into diamond. Label the diamond phase.<\/li>\n<li>Circle each triple point on the phase diagram.<\/li>\n<li>In what phase does carbon exist at 4000 K and 10<sup>5<\/sup> atm?<\/li>\n<li>If the temperature of a sample of carbon increases from 4000 K to 5000 K at a constant pressure of 10<sup>2<\/sup> atm, which phase transition occurs, if any?<\/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=\"q799811\">Show Selected Answers<\/span><\/p>\n<div id=\"q799811\" class=\"hidden-answer\" style=\"display: none\">\n<p>2.\u00a0At low pressures and 0.005 \u00b0C, the water is a gas. As the pressure increases to 4.6 torr, the water becomes a solid; as the pressure increases still more, it becomes a liquid. At 40 \u00b0C, water at low pressure is a vapor; at pressures higher than about 75 torr, it converts into a liquid. At \u221240 \u00b0C, water goes from a gas to a solid as the pressure increases above very low values.<\/p>\n<p>4. Using the phase diagram for carbon dioxide provided, we can determine that the state of CO<sub>2<\/sub> at each temperature and pressure given are as follows:<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li>liquid<\/li>\n<li>solid<\/li>\n<li>gas<\/li>\n<li>gas<\/li>\n<li>gas<\/li>\n<li>gas<\/li>\n<\/ol>\n<p>6. The plot will look something like this:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5210\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214545\/CNX_Chem_10_04_Ex06answer_img.jpg\" alt=\"An x-axis is labeled at the left as \u201cFull\u201d and at the right as \u201cEmpty.\u201d A y-axis is labeled at the top as \u201cP.\u201d Beneath the x-axis is the label \u201cAmount released.\u201d A horizontal line that then slopes downward is drawn about halfway up the vertical line and labeled on the left as \u201c65 a t m.\u201d About two-thirds of the way across the x-axis, it slopes downward in a straight line to meet the \u201cempty\u201d label on the bottom right of the axis.\" width=\"500\" height=\"275\" \/><\/p>\n<p>8.\u00a0Yes, ice will sublime, although it may take it several days. Ice has a small vapor pressure, and some ice molecules form gas and escape from the ice crystals. As time passes, more and more solid converts to gas until eventually the clothes are dry.<\/p>\n<p>10. Answers<\/p>\n<ol style=\"list-style-type: lower-alpha;\">\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5212\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214548\/CNX_Chem_10_04_Exercise10a_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right. The two quadrants to the right are labeled, \u201cWater ( liquid )\u201d and \u201cWater vapor ( gas ).\u201d\" width=\"400\" height=\"451\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5213\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214549\/CNX_Chem_10_04_Exercise10b_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right. The quadrant to the left is labeled, \u201cGraphite.\u201d\" width=\"400\" height=\"451\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5214\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214550\/CNX_Chem_10_04_Exercise10c_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right. The top quadrant is labeled, \u201cDiamond.\u201d\" width=\"400\" height=\"451\" \/><\/li>\n<li><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-5215\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214552\/CNX_Chem_10_04_Exercise10d_img.jpg\" alt=\"This figure shows an x-axis that is labeled, \u201cTemperature ( K ),\u201d and a y-axis labeled, \u201cPressure ( P a ).\u201d The x-axis is marked off in increments of 2000 starting from 0. The y-axis is marked off at 0, 10 to the 7, ten to the 9, and ten to the 11. There is a slightly negatively sloped line that passes through the x-axis at about 3800. From this line there is a line that curves up and then down to the left to pass through the y-axis at ten to the 9. There is another line that goes up and to the right. The four quadrants are labeled, \u201cDiamond\u201d at the top, \u201cGraphite\u201d, to the left, \u201cwater ( liquid )\u201d to the top right, and \u201cwater vapor ( gas ),\u201d to the bottom right. There is a red circle where the liquid, gas, and graphite lines intersect.\" width=\"400\" height=\"451\" \/><\/li>\n<li>liquid phase<\/li>\n<li>sublimation<\/li>\n<\/ol>\n<\/div>\n<\/div>\n<\/div>\n<h2>Glossary<\/h2>\n<p><strong>critical point: <\/strong>temperature and pressure above which a gas cannot be condensed into a liquid<\/p>\n<p><strong>phase diagram: <\/strong>pressure-temperature graph summarizing conditions under which the phases of a substance can exist<\/p>\n<p><strong>supercritical fluid: <\/strong>substance at a temperature and pressure higher than its critical point; exhibits properties intermediate between those of gaseous and liquid states<\/p>\n<p><strong>triple point: <\/strong>temperature and pressure at which the vapor, liquid, and solid phases of a substance are in equilibrium<\/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-3400\">\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>Supercritical CO2. <strong>Authored by<\/strong>: mrmrobin. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/youtu.be\/P9EftqFYaHg\">https:\/\/youtu.be\/P9EftqFYaHg<\/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":5,"template":"","meta":{"_candela_citation":"[{\"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\"},{\"type\":\"copyrighted_video\",\"description\":\"Supercritical CO2\",\"author\":\"mrmrobin\",\"organization\":\"\",\"url\":\"https:\/\/youtu.be\/P9EftqFYaHg\",\"project\":\"\",\"license\":\"arr\",\"license_terms\":\"Standard YouTube License\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3400","chapter","type-chapter","status-publish","hentry"],"part":3000,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3400","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":10,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3400\/revisions"}],"predecessor-version":[{"id":5789,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3400\/revisions\/5789"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/parts\/3000"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapters\/3400\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/media?parent=3400"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/pressbooks\/v2\/chapter-type?post=3400"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/contributor?post=3400"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/suny-chem-atoms-first\/wp-json\/wp\/v2\/license?post=3400"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}