{"id":3227,"date":"2016-08-25T19:34:27","date_gmt":"2016-08-25T19:34:27","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/?post_type=chapter&#038;p=3227"},"modified":"2016-08-26T19:20:08","modified_gmt":"2016-08-26T19:20:08","slug":"order-of-reaction","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/chapter\/order-of-reaction\/","title":{"raw":"Order of Reaction","rendered":"Order of Reaction"},"content":{"raw":"<div class=\"textbox learning-objectives\">\r\n<h3>Learning Objectives<\/h3>\r\n<div>\r\n<ul>\r\n \t<li>Describe the kinetic characteristics of a first-order reaction.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox examples\">\r\n<h3>How harmful are forest fires?<\/h3>\r\n[caption id=\"\" align=\"aligncenter\" width=\"400\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212847\/20140811155715136857.jpeg\" alt=\"The damage caused by a forest fire is proportional to the amount of material to burn\" width=\"400\" height=\"335\" \/> Tropical forest fire. Courtesy of Ramos Keith, <a href=\"http:\/\/Courtesy of Ramos Keith, US Fish and Wildlife Service\">US Fish and Wildlife Service<\/a>.[\/caption]\r\n\r\nForest fires cause extensive damage when they occur. Both plant and animal life are harmed during these events. The severity of a forest fire depends on how much plant life is available to burn \u2013 the more available dry plant material, the more serious the fire and the more rapidly it will spread.\r\n\r\n<\/div>\r\n<h2>Order of Reaction<\/h2>\r\nIn the reaction <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212848\/e78f9d6f7f862d083e5cc919f835deec.png\" alt=\"A rightarrow B\" width=\"56\" height=\"13\" \/> , the rate of the reaction is directly proportional to the concentration of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> raised to the first power. That is to say, <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212849\/027c627d709439ea922cf8d6ba3b29a7.png\" alt=\"[A]=[A]^1\" width=\"75\" height=\"20\" \/> . A <strong> first-order reaction <\/strong> is a reaction in which the rate is proportional to the concentration of only one reactant. As a first-order reaction proceeds, the rate of reaction decreases because the concentration of the reactant decreases). The graph of concentration versus time is curved. The reaction rate <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212850\/33726a6d3ebe2d79c87452aafcf3ac5b.png\" alt=\"left(frac{Delta [A]}{Delta t} right)\" width=\"47\" height=\"34\" \/> can be determined graphically by the slope of a tangent to the curve at any point. The rate of the reaction at the time shown with the red triangle is given by:\r\n\r\n<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212851\/9154cd30b05f82ee3247f5d782e03769.png\" alt=\"text{rate}=-frac{[A]_{text{final}}-[A]_{text{initial}}}{Delta t}=-frac{0.35 text{ M} - 0.63 text{ M}}{3.0 text{ s} - 1.0 text{ s}}=0.14 text{ M\/s}\" width=\"468\" height=\"39\" \/>\r\n<div>\r\n\r\n[caption id=\"\" align=\"aligncenter\" width=\"512\"]<img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212853\/20140811155715307115.png\" alt=\"The instantaneous rate of a reaction can be measured by the slope of the tangent line at that point\" width=\"512\" height=\"297\" longdesc=\"This%20graph%20shows%20how%20the%20concentration%20of%20a%20reactant%20changes%20as%20a%20reaction%20proceeds.%20The%20rate%20of%20the%20reaction%20is%20determined%20at%20any%20point%20by%20measuring%20the%20slope%20of%20a%20tangent%20to%20the%20curve.\" \/> Figure 1. This graph shows how the concentration of a reactant changes as a reaction proceeds. The rate of the reaction is determined at any point by measuring the slope of a tangent to the curve. Figure from the CK-12 Foundation - Christopher Auyeung.[\/caption]\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\nThe rates of some reactions depend on the concentrations of more than one reactant. Consider a reaction in which a molecule of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> collides with a molecule of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/00025e2ee78e7b712fbb42f74f2d6cb7.png\" alt=\"B\" width=\"14\" height=\"12\" \/> to form product <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211834\/e97e00897680a9985f8688553bb4ca5f.png\" alt=\"C\" width=\"14\" height=\"12\" \/> .\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212854\/da6971f6babe573e4e767e5a31ea5f81.png\" alt=\"A+B rightarrow C\" width=\"92\" height=\"13\" \/>\r\n\r\nDoubling the concentration of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> alone would double the reaction rate. Likewise, doubling the concentration of <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/00025e2ee78e7b712fbb42f74f2d6cb7.png\" alt=\"B\" width=\"14\" height=\"12\" \/> alone would also double the rate. The rate law must reflect the rate dependence on both reactants.\r\n\r\n<img class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212855\/b42f819ddbe9e65f3bcb1e7a6dc297d3.png\" alt=\"text{rate}=k[A][B]\" width=\"110\" height=\"18\" \/>\r\n\r\nThis reaction is said to be first order with respect to <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> and first order with respect to <img src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/00025e2ee78e7b712fbb42f74f2d6cb7.png\" alt=\"B\" width=\"14\" height=\"12\" \/> . Overall, it is a second-order reaction. The rate law and the order of a reaction must be determined experimentally.\r\n<div class=\"textbox key-takeaways\">\r\n<h3>Summary<\/h3>\r\n<ul>\r\n \t<li>A first-order reaction is described.<\/li>\r\n<\/ul>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Practice<\/h3>\r\nRead the material at the link below and answer the following questions:\r\n<ol>\r\n \t<li>What is a zero-order reaction?<\/li>\r\n \t<li>What is a second-order reaction?<\/li>\r\n \t<li>How is the order of a two-reactant reaction determined?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<div class=\"textbox exercises\">\r\n<h3>Review<\/h3>\r\n<ol>\r\n \t<li>What is a first-order reaction?<\/li>\r\n \t<li>How is the instantaneous rate determined?<\/li>\r\n \t<li>How do we determine rate law and reaction order?<\/li>\r\n<\/ol>\r\n<\/div>\r\n<h2>\u00a0Glossary<\/h2>\r\n<div>\r\n<ul>\r\n \t<li><strong> first-order reaction: <\/strong> A reaction in which the rate is proportional to the concentration of only one reactant.<\/li>\r\n<\/ul>\r\n<\/div>","rendered":"<div class=\"textbox learning-objectives\">\n<h3>Learning Objectives<\/h3>\n<div>\n<ul>\n<li>Describe the kinetic characteristics of a first-order reaction.<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<div class=\"textbox examples\">\n<h3>How harmful are forest fires?<\/h3>\n<div style=\"width: 410px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212847\/20140811155715136857.jpeg\" alt=\"The damage caused by a forest fire is proportional to the amount of material to burn\" width=\"400\" height=\"335\" \/><\/p>\n<p class=\"wp-caption-text\">Tropical forest fire. Courtesy of Ramos Keith, <a href=\"http:\/\/Courtesy of Ramos Keith, US Fish and Wildlife Service\">US Fish and Wildlife Service<\/a>.<\/p>\n<\/div>\n<p>Forest fires cause extensive damage when they occur. Both plant and animal life are harmed during these events. The severity of a forest fire depends on how much plant life is available to burn \u2013 the more available dry plant material, the more serious the fire and the more rapidly it will spread.<\/p>\n<\/div>\n<h2>Order of Reaction<\/h2>\n<p>In the reaction <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212848\/e78f9d6f7f862d083e5cc919f835deec.png\" alt=\"A rightarrow B\" width=\"56\" height=\"13\" \/> , the rate of the reaction is directly proportional to the concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> raised to the first power. That is to say, <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212849\/027c627d709439ea922cf8d6ba3b29a7.png\" alt=\"[A]=[A]^1\" width=\"75\" height=\"20\" \/> . A <strong> first-order reaction <\/strong> is a reaction in which the rate is proportional to the concentration of only one reactant. As a first-order reaction proceeds, the rate of reaction decreases because the concentration of the reactant decreases). The graph of concentration versus time is curved. The reaction rate <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212850\/33726a6d3ebe2d79c87452aafcf3ac5b.png\" alt=\"left(frac{Delta [A]}{Delta t} right)\" width=\"47\" height=\"34\" \/> can be determined graphically by the slope of a tangent to the curve at any point. The rate of the reaction at the time shown with the red triangle is given by:<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212851\/9154cd30b05f82ee3247f5d782e03769.png\" alt=\"text{rate}=-frac{[A]_{text{final}}-[A]_{text{initial}}}{Delta t}=-frac{0.35 text{ M} - 0.63 text{ M}}{3.0 text{ s} - 1.0 text{ s}}=0.14 text{ M\/s}\" width=\"468\" height=\"39\" \/><\/p>\n<div>\n<div style=\"width: 522px\" class=\"wp-caption aligncenter\"><img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212853\/20140811155715307115.png\" alt=\"The instantaneous rate of a reaction can be measured by the slope of the tangent line at that point\" width=\"512\" height=\"297\" longdesc=\"This%20graph%20shows%20how%20the%20concentration%20of%20a%20reactant%20changes%20as%20a%20reaction%20proceeds.%20The%20rate%20of%20the%20reaction%20is%20determined%20at%20any%20point%20by%20measuring%20the%20slope%20of%20a%20tangent%20to%20the%20curve.\" \/><\/p>\n<p class=\"wp-caption-text\">Figure 1. This graph shows how the concentration of a reactant changes as a reaction proceeds. The rate of the reaction is determined at any point by measuring the slope of a tangent to the curve. Figure from the CK-12 Foundation &#8211; Christopher Auyeung.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<p>The rates of some reactions depend on the concentrations of more than one reactant. Consider a reaction in which a molecule of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> collides with a molecule of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/00025e2ee78e7b712fbb42f74f2d6cb7.png\" alt=\"B\" width=\"14\" height=\"12\" \/> to form product <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211834\/e97e00897680a9985f8688553bb4ca5f.png\" alt=\"C\" width=\"14\" height=\"12\" \/> .<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212854\/da6971f6babe573e4e767e5a31ea5f81.png\" alt=\"A+B rightarrow C\" width=\"92\" height=\"13\" \/><\/p>\n<p>Doubling the concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> alone would double the reaction rate. Likewise, doubling the concentration of <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/00025e2ee78e7b712fbb42f74f2d6cb7.png\" alt=\"B\" width=\"14\" height=\"12\" \/> alone would also double the rate. The rate law must reflect the rate dependence on both reactants.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"aligncenter\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19212855\/b42f819ddbe9e65f3bcb1e7a6dc297d3.png\" alt=\"text{rate}=k[A][B]\" width=\"110\" height=\"18\" \/><\/p>\n<p>This reaction is said to be first order with respect to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/d5ebd507fac84fdb3364e6593d198a76.png\" alt=\"A\" width=\"13\" height=\"12\" \/> and first order with respect to <img loading=\"lazy\" decoding=\"async\" src=\"https:\/\/s3-us-west-2.amazonaws.com\/courses-images-archive-read-only\/wp-content\/uploads\/sites\/53\/2014\/08\/19211811\/00025e2ee78e7b712fbb42f74f2d6cb7.png\" alt=\"B\" width=\"14\" height=\"12\" \/> . Overall, it is a second-order reaction. The rate law and the order of a reaction must be determined experimentally.<\/p>\n<div class=\"textbox key-takeaways\">\n<h3>Summary<\/h3>\n<ul>\n<li>A first-order reaction is described.<\/li>\n<\/ul>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Practice<\/h3>\n<p>Read the material at the link below and answer the following questions:<\/p>\n<ol>\n<li>What is a zero-order reaction?<\/li>\n<li>What is a second-order reaction?<\/li>\n<li>How is the order of a two-reactant reaction determined?<\/li>\n<\/ol>\n<\/div>\n<div class=\"textbox exercises\">\n<h3>Review<\/h3>\n<ol>\n<li>What is a first-order reaction?<\/li>\n<li>How is the instantaneous rate determined?<\/li>\n<li>How do we determine rate law and reaction order?<\/li>\n<\/ol>\n<\/div>\n<h2>\u00a0Glossary<\/h2>\n<div>\n<ul>\n<li><strong> first-order reaction: <\/strong> A reaction in which the rate is proportional to the concentration of only one reactant.<\/li>\n<\/ul>\n<\/div>\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-3227\">\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 Concepts Intermediate. <strong>Authored by<\/strong>: Calbreath, Baxter, et al.. <strong>Provided by<\/strong>: CK12.org. <strong>Located at<\/strong>: <a target=\"_blank\" href=\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\">http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/<\/a>. <strong>License<\/strong>: <em><a target=\"_blank\" rel=\"license\" href=\"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/\">CC BY-NC: Attribution-NonCommercial<\/a><\/em><\/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":29,"menu_order":9,"template":"","meta":{"_candela_citation":"[{\"type\":\"cc\",\"description\":\"Chemistry Concepts Intermediate\",\"author\":\"Calbreath, Baxter, et al.\",\"organization\":\"CK12.org\",\"url\":\"http:\/\/www.ck12.org\/book\/CK-12-Chemistry-Concepts-Intermediate\/\",\"project\":\"\",\"license\":\"cc-by-nc\",\"license_terms\":\"\"}]","CANDELA_OUTCOMES_GUID":"","pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-3227","chapter","type-chapter","status-publish","hentry"],"part":2339,"_links":{"self":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/3227","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/users\/29"}],"version-history":[{"count":4,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/3227\/revisions"}],"predecessor-version":[{"id":3435,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/3227\/revisions\/3435"}],"part":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/parts\/2339"}],"metadata":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapters\/3227\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/media?parent=3227"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/pressbooks\/v2\/chapter-type?post=3227"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/contributor?post=3227"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/courses.lumenlearning.com\/umes-cheminter\/wp-json\/wp\/v2\/license?post=3227"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}