{"id":2254,"date":"2015-04-22T21:06:57","date_gmt":"2015-04-22T21:06:57","guid":{"rendered":"https:\/\/courses.candelalearning.com\/oschemtemp\/?post_type=chapter&#038;p=2254"},"modified":"2020-12-28T18:01:59","modified_gmt":"2020-12-28T18:01:59","slug":"chemical-equilibria","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/chapter\/chemical-equilibria\/","title":{"raw":"Chemical Equilibria","rendered":"Chemical Equilibria"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Outcomes<\/h3>\r\n<ul>\r\n \t<li>Describe the nature of equilibrium systems<\/li>\r\n \t<li>Explain the dynamic nature of a chemical equilibrium<\/li>\r\n<\/ul>\r\n<\/div>\r\nThe convention for writing chemical equations involves placing reactant formulas on the left side of a reaction arrow and product formulas on the right side. By this convention, and the definitions of \u201creactant\u201d and \u201cproduct,\u201d a chemical equation represents the reaction in question as proceeding from left to right.\u00a0<strong>Reversible reactions<\/strong>, however, may proceed in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at\u00a0<strong>equilibrium<\/strong>. The relative concentrations of reactants and products in equilibrium systems vary greatly; some systems contain mostly products at equilibrium, some contain mostly reactants, and some contain appreciable amounts of both.\r\n\r\nFigure 1 illustrates fundamental equilibrium concepts using the reversible decomposition of colorless dinitrogen tetroxide to yield brown nitrogen dioxide, an elementary reaction described by the equation:\r\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}{\\text{O}}_{4}\\left(g\\right)\\rightleftharpoons2{\\text{NO}}_{2}\\left(g\\right)[\/latex]<\/p>\r\nNote that a special double arrow is used to emphasize the reversible nature of the reaction.\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"650\"]<a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5371\/2015\/04\/27212334\/a352716381e7eafff6892bc5d3e1423ed707a2ca.jpg\"><img src=\"https:\/\/openstax.org\/resources\/a352716381e7eafff6892bc5d3e1423ed707a2ca\" alt=\"A three-part diagram is shown and labeled, \u201ca,\u201d \u201cb,\u201d and \u201cc.\u201d In part a, at the top of the diagram, three beakers are shown, and each one contains a sealed tube. The tube in the left beaker is labeled \u201ct equals 0.\u201d It is full of a colorless gas which is connected to a zoom-in view of the particles in the tube by a downward-facing arrow. This particle view shows seven particles, each composed of two connected blue spheres. Each blue sphere is connected to two red spheres. This type of particle is labeled \u201cN subscript 2 O subscript 4.\u201d The tube in the middle beaker is labeled \u201cpre-equilibrium.\u201d It is full of a light brown gas which is connected to a zoom-in view of the particles in the tube by a downward-facing arrow. This particle view shows nine particles, five of which are composed of two connected blue spheres. Each blue sphere is connected to two red spheres. This type of particle is labeled \u201cN subscript 2 O subscript 4.\u201d The remaining four are composed of two red spheres connected to a blue sphere. This type of particle is labeled \u201cN O subscript 2.\u201d The tube in the right beaker is labeled \u201cat equilibrium.\u201d It is full of a brown gas which is connected to a zoom-in view of the particles in the tube by a downward-facing arrow. This particle view shows eleven particles, three of which are composed of two connected blue spheres. Each blue sphere is connected to two red spheres. The remaining eight are composed of two red spheres connected to a blue sphere. In part b, in the middle of the image, is one graph. This graph has a y-axis labeled, \u201cConcentration,\u201d and an x-axis labeled, \u201cTime.\u201d A red line labeled, \u201cN O subscript 2,\u201d begins in the bottom left corner of the graph at a point labeled, \u201c0,\u201d and rises near the highest point on the y-axis before it levels off and becomes horizontal. A blue line labeled, \u201cN subscript 2 O subscript 4,\u201d begins near the highest point on the y-axis and drops below the midpoint of the y-axis before leveling off. In part c, at the bottom of the image is another graph. This graph has a y-axis labeled, \u201cRate,\u201d and an x-axis labeled, \u201cTime.\u201d A red line labeled, \u201ck subscript f, [ N subscript 2 O subscript 4 ],\u201d begins in the bottom left corner of the graph at a point labeled, \u201c0,\u201d and rises near the middle of the y-axis before it levels off and becomes horizontal. A blue line labeled, \u201ck subscript f, [ N O subscript 2 ] superscript 2,\u201d begins near the highest point on the y-axis and drops to the same point on the y-axis as the red line before leveling off. The point where both lines become horizontal is labeled, \u201cEquilibrium achieved.\u201d\" width=\"650\" height=\"1285\" \/><\/a> Figure 1: (a) A sealed tube containing colorless N<sub>2<\/sub>O<sub>4<\/sub> darkens as it decomposes to yield brown NO<sub>2<\/sub>. (b) Changes in concentration over time as the decomposition reaction achieves equilibrium. (c) At equilibrium, the forward and reverse reaction rates are equal.[\/caption]\r\n\r\n[caption id=\"attachment_4876\" align=\"alignright\" width=\"300\"]<img class=\"wp-image-4876\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214438\/CNX_Chem_13_01_dynamic.jpg\" alt=\"Two people are shown throwing juggling pins back and forth to one another.\" width=\"300\" height=\"223\" \/> Figure\u00a02. A two-person juggling act illustrates the dynamic aspect of chemical equilibria. Each person is throwing and catching clubs at the same rate, and each holds a (approximately) constant number of clubs.[\/caption]\r\n<p id=\"fs-idp53505568\">For this elementary process, rate laws for the forward and reverse reactions may be derived directly from the reaction stoichiometry:<\/p>\r\n\r\n<center>[latex]\\text{rate}_f=k_f[\\text{N}_2\\text{O}_4][\/latex]<\/center><center>[latex]\\text{rate}_r=k_r[\\text{NO}_2]^2[\/latex]<\/center>As the reaction begins (<em>t<\/em>\u00a0= 0), the concentration of the N<sub>2<\/sub>O<sub>4<\/sub>\u00a0reactant is finite and that of the NO<sub>2<\/sub>\u00a0product is zero, so the forward reaction proceeds at a finite rate while the reverse reaction rate is zero. As time passes, N<sub>2<\/sub>O<sub>4<\/sub>\u00a0is consumed and its concentration falls, while NO<sub>2<\/sub>\u00a0is produced and its concentration increases (Figure 1b). The decreasing concentration of the reactant slows the forward reaction rate, and the increasing product concentration speeds the reverse reaction rate (Figure 1c). This process continues until\u00a0<em>the forward and reverse reaction rates become equal<\/em>, at which time the reaction has reached equilibrium, as characterized by constant concentrations of its reactants and products (shaded areas of Figure 1b\u00a0and Figure 1c). It\u2019s important to emphasize that chemical equilibria are dynamic; a reaction at equilibrium has not \u201cstopped,\u201d but is proceeding in the forward and reverse directions at the same rate. This dynamic nature is essential to understanding equilibrium behavior as discussed in this and subsequent chapters of the text.\r\n\r\n[caption id=\"attachment_5833\" align=\"alignright\" width=\"350\"]<img class=\"wp-image-5833\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/13200744\/CNX_Chem_13_01_bromine-1024x742.png\" alt=\"A glass container is shown that is filled with an orange-brown gas and a small amount of dark orange liquid.\" width=\"350\" height=\"253\" \/> Figure 4. A sealed tube containing an equilibrium mixture of liquid and gaseous bromine. (credit: http:\/\/images-of-elements.com\/bromine.php)[\/caption]\r\n\r\nPhysical changes, such as phase transitions, are also reversible and may establish equilibria. This concept was introduced in another chapter of this text through discussion of the vapor pressure of a condensed phase (liquid or solid). As one example, consider the vaporization of bromine:\r\n<p style=\"text-align: center;\">[latex]{\\text{Br}}_{2}\\left(l\\right)\\rightleftharpoons{\\text{Br}}_{2}\\left(g\\right)[\/latex]<\/p>\r\nWhen liquid bromine is added to an otherwise empty container and the container is sealed, the forward process depicted above (vaporization) will commence and continue at a roughly constant rate as long as the exposed surface area of the liquid and its temperature remain constant. As increasing amounts of gaseous bromine are produced, the rate of the reverse process (condensation) will increase until it equals the rate of vaporization and equilibrium is established. A photograph showing this phase transition equilibrium is provided in Figure 4.\r\n\r\n&nbsp;\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Key Concepts and Summary<\/h3>\r\nA reversible reaction is at equilibrium when the forward and reverse processes occur at equal rates. Chemical equilibria are dynamic processes characterized by constant amounts of reactant and product species.\r\n\r\n<\/div>\r\n<h2>Glossary<\/h2>\r\n<strong>equilibrium: <\/strong>in chemical reactions, the state in which the conversion of reactants into products and the conversion of products back into reactants occur simultaneously at the same rate; state of balance\r\n\r\n<strong>reversible reaction: <\/strong>chemical reaction that can proceed in both the forward and reverse directions under given conditions","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Outcomes<\/h3>\n<ul>\n<li>Describe the nature of equilibrium systems<\/li>\n<li>Explain the dynamic nature of a chemical equilibrium<\/li>\n<\/ul>\n<\/div>\n<p>The convention for writing chemical equations involves placing reactant formulas on the left side of a reaction arrow and product formulas on the right side. By this convention, and the definitions of \u201creactant\u201d and \u201cproduct,\u201d a chemical equation represents the reaction in question as proceeding from left to right.\u00a0<strong>Reversible reactions<\/strong>, however, may proceed in both forward (left to right) and reverse (right to left) directions. When the rates of the forward and reverse reactions are equal, the concentrations of the reactant and product species remain constant over time and the system is at\u00a0<strong>equilibrium<\/strong>. The relative concentrations of reactants and products in equilibrium systems vary greatly; some systems contain mostly products at equilibrium, some contain mostly reactants, and some contain appreciable amounts of both.<\/p>\n<p>Figure 1 illustrates fundamental equilibrium concepts using the reversible decomposition of colorless dinitrogen tetroxide to yield brown nitrogen dioxide, an elementary reaction described by the equation:<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{N}}_{2}{\\text{O}}_{4}\\left(g\\right)\\rightleftharpoons2{\\text{NO}}_{2}\\left(g\\right)[\/latex]<\/p>\n<p>Note that a special double arrow is used to emphasize the reversible nature of the reaction.<\/p>\n<div style=\"width: 660px\" class=\"wp-caption aligncenter\"><a href=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/5371\/2015\/04\/27212334\/a352716381e7eafff6892bc5d3e1423ed707a2ca.jpg\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/openstax.org\/resources\/a352716381e7eafff6892bc5d3e1423ed707a2ca\" alt=\"A three-part diagram is shown and labeled, \u201ca,\u201d \u201cb,\u201d and \u201cc.\u201d In part a, at the top of the diagram, three beakers are shown, and each one contains a sealed tube. The tube in the left beaker is labeled \u201ct equals 0.\u201d It is full of a colorless gas which is connected to a zoom-in view of the particles in the tube by a downward-facing arrow. This particle view shows seven particles, each composed of two connected blue spheres. Each blue sphere is connected to two red spheres. This type of particle is labeled \u201cN subscript 2 O subscript 4.\u201d The tube in the middle beaker is labeled \u201cpre-equilibrium.\u201d It is full of a light brown gas which is connected to a zoom-in view of the particles in the tube by a downward-facing arrow. This particle view shows nine particles, five of which are composed of two connected blue spheres. Each blue sphere is connected to two red spheres. This type of particle is labeled \u201cN subscript 2 O subscript 4.\u201d The remaining four are composed of two red spheres connected to a blue sphere. This type of particle is labeled \u201cN O subscript 2.\u201d The tube in the right beaker is labeled \u201cat equilibrium.\u201d It is full of a brown gas which is connected to a zoom-in view of the particles in the tube by a downward-facing arrow. This particle view shows eleven particles, three of which are composed of two connected blue spheres. Each blue sphere is connected to two red spheres. The remaining eight are composed of two red spheres connected to a blue sphere. In part b, in the middle of the image, is one graph. This graph has a y-axis labeled, \u201cConcentration,\u201d and an x-axis labeled, \u201cTime.\u201d A red line labeled, \u201cN O subscript 2,\u201d begins in the bottom left corner of the graph at a point labeled, \u201c0,\u201d and rises near the highest point on the y-axis before it levels off and becomes horizontal. A blue line labeled, \u201cN subscript 2 O subscript 4,\u201d begins near the highest point on the y-axis and drops below the midpoint of the y-axis before leveling off. In part c, at the bottom of the image is another graph. This graph has a y-axis labeled, \u201cRate,\u201d and an x-axis labeled, \u201cTime.\u201d A red line labeled, \u201ck subscript f, [ N subscript 2 O subscript 4 ],\u201d begins in the bottom left corner of the graph at a point labeled, \u201c0,\u201d and rises near the middle of the y-axis before it levels off and becomes horizontal. A blue line labeled, \u201ck subscript f, [ N O subscript 2 ] superscript 2,\u201d begins near the highest point on the y-axis and drops to the same point on the y-axis as the red line before leveling off. The point where both lines become horizontal is labeled, \u201cEquilibrium achieved.\u201d\" width=\"650\" height=\"1285\" \/><\/a><\/p>\n<p class=\"wp-caption-text\">Figure 1: (a) A sealed tube containing colorless N<sub>2<\/sub>O<sub>4<\/sub> darkens as it decomposes to yield brown NO<sub>2<\/sub>. (b) Changes in concentration over time as the decomposition reaction achieves equilibrium. (c) At equilibrium, the forward and reverse reaction rates are equal.<\/p>\n<\/div>\n<div id=\"attachment_4876\" style=\"width: 310px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-4876\" class=\"wp-image-4876\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/887\/2015\/08\/23214438\/CNX_Chem_13_01_dynamic.jpg\" alt=\"Two people are shown throwing juggling pins back and forth to one another.\" width=\"300\" height=\"223\" \/><\/p>\n<p id=\"caption-attachment-4876\" class=\"wp-caption-text\">Figure\u00a02. A two-person juggling act illustrates the dynamic aspect of chemical equilibria. Each person is throwing and catching clubs at the same rate, and each holds a (approximately) constant number of clubs.<\/p>\n<\/div>\n<p id=\"fs-idp53505568\">For this elementary process, rate laws for the forward and reverse reactions may be derived directly from the reaction stoichiometry:<\/p>\n<div style=\"text-align: center;\">[latex]\\text{rate}_f=k_f[\\text{N}_2\\text{O}_4][\/latex]<\/div>\n<div style=\"text-align: center;\">[latex]\\text{rate}_r=k_r[\\text{NO}_2]^2[\/latex]<\/div>\n<p>As the reaction begins (<em>t<\/em>\u00a0= 0), the concentration of the N<sub>2<\/sub>O<sub>4<\/sub>\u00a0reactant is finite and that of the NO<sub>2<\/sub>\u00a0product is zero, so the forward reaction proceeds at a finite rate while the reverse reaction rate is zero. As time passes, N<sub>2<\/sub>O<sub>4<\/sub>\u00a0is consumed and its concentration falls, while NO<sub>2<\/sub>\u00a0is produced and its concentration increases (Figure 1b). The decreasing concentration of the reactant slows the forward reaction rate, and the increasing product concentration speeds the reverse reaction rate (Figure 1c). This process continues until\u00a0<em>the forward and reverse reaction rates become equal<\/em>, at which time the reaction has reached equilibrium, as characterized by constant concentrations of its reactants and products (shaded areas of Figure 1b\u00a0and Figure 1c). It\u2019s important to emphasize that chemical equilibria are dynamic; a reaction at equilibrium has not \u201cstopped,\u201d but is proceeding in the forward and reverse directions at the same rate. This dynamic nature is essential to understanding equilibrium behavior as discussed in this and subsequent chapters of the text.<\/p>\n<div id=\"attachment_5833\" style=\"width: 360px\" class=\"wp-caption alignright\"><img loading=\"lazy\" decoding=\"async\" aria-describedby=\"caption-attachment-5833\" class=\"wp-image-5833\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images\/wp-content\/uploads\/sites\/218\/2016\/10\/13200744\/CNX_Chem_13_01_bromine-1024x742.png\" alt=\"A glass container is shown that is filled with an orange-brown gas and a small amount of dark orange liquid.\" width=\"350\" height=\"253\" \/><\/p>\n<p id=\"caption-attachment-5833\" class=\"wp-caption-text\">Figure 4. A sealed tube containing an equilibrium mixture of liquid and gaseous bromine. (credit: http:\/\/images-of-elements.com\/bromine.php)<\/p>\n<\/div>\n<p>Physical changes, such as phase transitions, are also reversible and may establish equilibria. This concept was introduced in another chapter of this text through discussion of the vapor pressure of a condensed phase (liquid or solid). As one example, consider the vaporization of bromine:<\/p>\n<p style=\"text-align: center;\">[latex]{\\text{Br}}_{2}\\left(l\\right)\\rightleftharpoons{\\text{Br}}_{2}\\left(g\\right)[\/latex]<\/p>\n<p>When liquid bromine is added to an otherwise empty container and the container is sealed, the forward process depicted above (vaporization) will commence and continue at a roughly constant rate as long as the exposed surface area of the liquid and its temperature remain constant. As increasing amounts of gaseous bromine are produced, the rate of the reverse process (condensation) will increase until it equals the rate of vaporization and equilibrium is established. A photograph showing this phase transition equilibrium is provided in Figure 4.<\/p>\n<p>&nbsp;<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Key Concepts and Summary<\/h3>\n<p>A reversible reaction is at equilibrium when the forward and reverse processes occur at equal rates. Chemical equilibria are dynamic processes characterized by constant amounts of reactant and product species.<\/p>\n<\/div>\n<h2>Glossary<\/h2>\n<p><strong>equilibrium: <\/strong>in chemical reactions, the state in which the conversion of reactants into products and the conversion of products back into reactants occur simultaneously at the same rate; state of balance<\/p>\n<p><strong>reversible reaction: <\/strong>chemical reaction that can proceed in both the forward and reverse directions under given conditions<\/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-2254\">\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 2e. <strong>Provided by<\/strong>: OpenStax. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"https:\/\/openstax.org\/\">https:\/\/openstax.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>: Access for free at https:\/\/openstax.org\/books\/chemistry-2e\/pages\/1-introduction<\/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":2,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry 2e\",\"author\":\"\",\"organization\":\"OpenStax\",\"url\":\"https:\/\/openstax.org\/\",\"project\":\"\",\"license\":\"cc-by\",\"license_terms\":\"Access for free at https:\/\/openstax.org\/books\/chemistry-2e\/pages\/1-introduction\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-2254","chapter","type-chapter","status-publish","hentry"],"part":2989,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/pressbooks\/v2\/chapters\/2254","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/wp\/v2\/users\/17"}],"version-history":[{"count":24,"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/pressbooks\/v2\/chapters\/2254\/revisions"}],"predecessor-version":[{"id":6953,"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/pressbooks\/v2\/chapters\/2254\/revisions\/6953"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/pressbooks\/v2\/parts\/2989"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/pressbooks\/v2\/chapters\/2254\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/wp\/v2\/media?parent=2254"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/pressbooks\/v2\/chapter-type?post=2254"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/wp\/v2\/contributor?post=2254"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/chemistryformajors\/wp-json\/wp\/v2\/license?post=2254"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}