{"id":1329,"date":"2020-06-23T16:33:14","date_gmt":"2020-06-23T20:33:14","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chbe220\/?post_type=chapter&#038;p=1329"},"modified":"2020-08-11T15:43:33","modified_gmt":"2020-08-11T19:43:33","slug":"reaction-order","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chbe220\/chapter\/reaction-order\/","title":{"raw":"Reaction Order","rendered":"Reaction Order"},"content":{"raw":"<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\">\r\n<div class=\"textbox textbox--learning-objectives\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Learning Objectives<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nBy the end of this section, you should be able to:\r\n\r\n<strong>Define<\/strong> r<span style=\"font-size: 1em\">eaction order and o<\/span><span style=\"font-size: 1em\">verall order<\/span>\r\n\r\n<strong>Determine <\/strong>the\u00a0r<span style=\"font-size: 1em\">eaction order and the rate constant from kinetic data<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\nThe dependence of the rate of reaction on the reactant concentrations can often be expressed as a direct proportionality, in which the concentrations may be raised to be the zeroth, first, or second power. The exponent is known as the order of the reaction with respect to that substance.[latex]^{[1]}[\/latex]\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">The overall order of a reaction is the sum of the orders with respect to the sum of the exponents<\/span>\r\n\r\n<\/div>\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n<p style=\"text-align: left\">For example:<\/p>\r\n<p style=\"text-align: center\">[latex]r = k_{r}[A]^3[B]^{1\/2}[\/latex]<\/p>\r\n<p style=\"text-align: left\">The reaction is:<\/p>\r\n\r\n<ul>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">Third-order in A<\/span><\/li>\r\n \t<li>One-half order in B<\/li>\r\n \t<li>Three and a half order overall<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\"><\/div>\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n\r\nIn the more complicated example for the reaction previously given between hydrogen and bromine:\r\n<p style=\"text-align: center\">[latex]r = \\frac{k_{a}[H_{2}][Br_{2}]^{3\/2}}{[Br_{2}]+k_{b}[H\\!Br]}[\/latex]<\/p>\r\nThe reaction is:\r\n<ul>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">First order in [latex]H_{2}[\/latex]<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">Indeterminate order in [latex]Br_{2}[\/latex]<\/span><span style=\"text-align: initial;font-size: 1em\">(as it's not in a single term)<\/span><\/li>\r\n \t<li>Indeterminate order in [latex]H\\!Br[\/latex] (as it cannot be isolated to a single term raised to a power)<\/li>\r\n \t<li>Indeterminate order overall (as some orders are indeterminate)<\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\"><\/div>\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n<h2 id=\"Determining-the-Rate-Law\">Determining the Rate Law<\/h2>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n<h3 id=\"Isolation-Method-for-Determining-the-Rate-Law\">Isolation Method for Determining the Rate Law<\/h3>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n\r\nOne of the simplest methods for determining the rate law is the isolation method.\r\n\r\nSay we have a reaction with two reactants, A and B. We put a <strong>large amount of B<\/strong> in our reactor compared to A; so much that the <strong>concentration barely changes<\/strong>.\r\n\r\nIf the true rate law is: [latex]r = k_{r}[A][B]^2[\/latex]\r\n\r\nWhat we would observe is [latex]r = k_{eff}[A][\/latex], where [latex]k_{eff}=k_{r}[B_{0}]^2[\/latex]\r\n<ul>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">[latex]k_{eff}[\/latex] = the effective rate constant<\/span><\/li>\r\n \t<li><span style=\"text-align: initial;font-size: 1em\">[latex][B]_{0}[\/latex]indicating the concentration of B at the start of the reaction (or time zero) or also called B naught (with naught meaning nothing or zero in this case)<\/span><\/li>\r\n<\/ul>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\"><img class=\"wp-image-1075 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order-300x149.png\" alt=\"\" width=\"833\" height=\"413\" \/><\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\"><\/div>\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n\r\nWith B in great excess: [latex]r = k_{eff}[A][\/latex] where [latex]k_{eff}=k_{r}[B_{0}]^2[\/latex], reaction appears <strong>first order<\/strong>.\r\n\r\nWith A in great excess: [latex]r' = k'_{eff}[B]^2[\/latex] where [latex]k'_{eff}=k_{r}[A_{0}][\/latex], reaction appears <strong>second order<\/strong>.\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">[latex]k'_{eff}[\/latex] is read as k prime effective<\/span>\r\n\r\nIt is easier to analyse these individual effective rate laws than the more complex combined rate law when both concentrations change significantly.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\"><\/div>\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n<h3 id=\"Method-of-Initial-Rates\">Method of Initial Rates<\/h3>\r\nThe method of initial rates is commonly used in conjunction with the isolation methods to determine reaction order.\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\"><\/div>\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise: Method of Initial Rates<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n<p style=\"text-align: left\">Say we have a reaction with two species, A and B. We put in the same amount of B into the reactor each time. The following is our initial rates are observed with different concentrations of A. What is the reaction order in A?<\/p>\r\n\r\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 70.7889%;height: 104px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px;text-align: center\"><strong>[A] (mol\/L)<\/strong><\/td>\r\n<td style=\"width: 50%;height: 15px;text-align: center\"><strong>Initial rate(mol\/L\u00b7s)<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px;text-align: center\">1<\/td>\r\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]1\u00d710^{-2}[\/latex]<\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 50%;height: 15px;text-align: center\">2<\/td>\r\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]4\u00d710^{-2}[\/latex]<\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Solution<\/h3>\r\nAs the concentration of A doubles, the reaction rate quadruples\r\n<p style=\"text-align: center\">[latex]r_{0}=k_{eff}[A]^2[\/latex]<\/p>\r\nSo the reaction is second order in A.\r\n\r\n<\/div>\r\n&nbsp;\r\n<div>\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">If we take the logarithm of the general equation for reaction rate, we can linearize the equation:<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n\r\n\\begin{align*}\r\nr_{0} &amp; = k_{eff}[A_{0}]^a \\\\\r\nlog(r_{0})&amp; = log(k_{eff}) + a*log([A_{0}])\\\\\r\ny &amp; = intercept + slope * x\r\n\\end{align*}\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">Plot [latex]log(r_{0})[\/latex] vs [latex]log([A_{0}])[\/latex], where the slope is the reaction order in A; and y-intercept equals to [latex]log(k_{eff})[\/latex]<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\"><\/div>\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n\r\n&nbsp;\r\n<div>\r\n<div class=\"textbox textbox--exercises\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Exercise: Reaction Order and Rate Constant<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nSulfuryl chloride ([latex]SO_{2}Cl_{2}[\/latex]) decomposes to [latex]SO_{2}[\/latex] and [latex]Cl_{2}[\/latex] by the following reaction:\r\n<p style=\"text-align: center\">[latex]SO_{2}Cl_{2(g)} \u2192 SO_{2(g)}+Cl_{2(g)}[\/latex]<\/p>\r\n<p style=\"text-align: left\">Data for the reaction at 320\u00b0C are listed in the following table. Calculate the reaction order with regard to sulfuryl chloride and determine the rate constant for the reaction.<span style=\"font-size: 1em\">[latex]^{[2]}[\/latex]<\/span><\/p>\r\n\r\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 70.4691%;height: 75px\" border=\"0\">\r\n<tbody>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><strong>Experiment<\/strong><\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><strong><span style=\"text-align: initial;font-size: 1em\">[latex][SO_{2}Cl_{2}]_{0}[\/latex]<\/span><\/strong><\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><strong>Initial rate(M\/s)<\/strong><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">1<\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">0.0050<\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]1.10\u00d710^{-7}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">2<\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">0.0075<\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]1.65\u00d710^{-7}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">3<\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">0.0100<\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]2.20\u00d710^{-7}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<tr style=\"height: 15px\">\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">4<\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">0.0125<\/td>\r\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]2.75\u00d710^{-7}[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<\/div>\r\n<\/div>\r\n<div class=\"textbox\">\r\n<h3>Solution<\/h3>\r\n<strong>Step 1:<\/strong> determine the reaction order with respect to sulfuryl chloride\r\n\r\nComparing Experiments 1 and 3, for example, shows that doubling the concentration doubles the reaction rate <span style=\"text-align: initial;font-size: 1em\">[latex](2.20\u00d710^{-7}) \u00f7 (1.10\u00d710^{-7}) = 2.0[\/latex]<\/span>, which means that the reaction rate is proportional to <span style=\"text-align: initial;font-size: 1em\">[latex][SO_{2}Cl_{2}][\/latex]<\/span>.\r\n\r\nThe reaction is first order with respect to \u00a0<span style=\"text-align: initial;font-size: 1em\">[latex][SO_{2}Cl_{2}][\/latex]<\/span>.\r\n\r\n<strong>Step 2:<\/strong> calculate <span style=\"text-align: initial;font-size: 1em\">[latex]k_{r}[\/latex]<\/span>\r\n\r\nWe have <span style=\"text-align: initial;font-size: 1em\">[latex]rate = k_{r}[SO_{2}Cl_{2}][\/latex]<\/span>. We can calculate the rate constant (<span style=\"text-align: initial;font-size: 1em\">[latex]k_{r}[\/latex]<\/span>) using data from any experiment in the table.\r\n\\begin{align*}\r\nrate &amp; = k_{r}[SO_{2}Cl_{2}] \\\\\r\n1.10\u00d710^{-7} M\/s&amp; = k_{r}\u00d70.0050M \\\\\r\n2.2\u00d710^{-5}s^{-1} &amp; = k_{r}\r\n\\end{align*}\r\n\r\n&nbsp;\r\n\r\n<strong>Method 2<\/strong>\r\n\r\nThe following graph is produced when plotting <span style=\"text-align: initial;font-size: 1em\">[latex]log(r_{0})[\/latex]<\/span> vs <span style=\"text-align: initial;font-size: 1em\">[latex]log([A_{0}])[\/latex]\u00a0<\/span>\r\n\r\n<img class=\"wp-image-1077 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-reaction-order-example-300x181.png\" alt=\"\" width=\"532\" height=\"321\" \/>\r\n\r\nFrom the line of best fit, we can see the slope is 1 (meaning a first order relationship) and <span style=\"text-align: initial;font-size: 1em\">[latex]log(k_{r})=-4.6576[\/latex]\u00a0<\/span>\r\n\r\nTherefore the reaction is first order in <span style=\"text-align: initial;font-size: 1em\">[latex]SO_{2}Cl_{2}[\/latex] <\/span>, <span style=\"text-align: initial;font-size: 1em\">[latex]k_{r}=10^{-4.6576} = 2.2\u00d710^{-5}s^{-1}[\/latex]<\/span>.\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div class=\"cell border-box-sizing text_cell rendered\">\r\n<div class=\"prompt input_prompt\">\r\n<div class=\"textbox shaded\">\r\n<h2>References<\/h2>\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n\r\n[1] Chemistry LibreTexts. 2020. <i>The Rate Law.<\/i> [online] Available at: &lt;<a href=\"https:\/\/chem.libretexts.org\/Bookshelves\/Physical_and_Theoretical_Chemistry_Textbook_Maps\/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)\/Kinetics\/Rate_Laws\/The_Rate_Law\">https:\/\/chem.libretexts.org\/Bookshelves\/Physical_and_Theoretical_Chemistry_Textbook_Maps\/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)\/Kinetics\/Rate_Laws\/The_Rate_Law<\/a>&gt; [Accessed 23 April 2020].\r\n\r\n[2] Chemistry LibreTexts. 2020.\u00a0<i>14.4: The Change Of Concentration With Time (Integrated Rate Laws)<\/i>. [online] Available at: &lt;<a href=\"https:\/\/chem.libretexts.org\/Bookshelves\/General_Chemistry\/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)\/14%3A_Chemical_Kinetics\/14.4%3A_The_Change_of_Concentration_with_Time_(Integrated_Rate_Laws)\">https:\/\/chem.libretexts.org\/Bookshelves\/General_Chemistry\/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)\/14%3A_Chemical_Kinetics\/14.4%3A_The_Change_of_Concentration_with_Time_(Integrated_Rate_Laws)<\/a>&gt; [Accessed 23 April 2020].\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<\/div>","rendered":"<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n<div class=\"textbox textbox--learning-objectives\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Learning Objectives<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>By the end of this section, you should be able to:<\/p>\n<p><strong>Define<\/strong> r<span style=\"font-size: 1em\">eaction order and o<\/span><span style=\"font-size: 1em\">verall order<\/span><\/p>\n<p><strong>Determine <\/strong>the\u00a0r<span style=\"font-size: 1em\">eaction order and the rate constant from kinetic data<\/span><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The dependence of the rate of reaction on the reactant concentrations can often be expressed as a direct proportionality, in which the concentrations may be raised to be the zeroth, first, or second power. The exponent is known as the order of the reaction with respect to that substance.[latex]^{[1]}[\/latex]<\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">The overall order of a reaction is the sum of the orders with respect to the sum of the exponents<\/span><\/p>\n<\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p style=\"text-align: left\">For example:<\/p>\n<p style=\"text-align: center\">[latex]r = k_{r}[A]^3[B]^{1\/2}[\/latex]<\/p>\n<p style=\"text-align: left\">The reaction is:<\/p>\n<ul>\n<li><span style=\"text-align: initial;font-size: 1em\">Third-order in A<\/span><\/li>\n<li>One-half order in B<\/li>\n<li>Three and a half order overall<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>In the more complicated example for the reaction previously given between hydrogen and bromine:<\/p>\n<p style=\"text-align: center\">[latex]r = \\frac{k_{a}[H_{2}][Br_{2}]^{3\/2}}{[Br_{2}]+k_{b}[H\\!Br]}[\/latex]<\/p>\n<p>The reaction is:<\/p>\n<ul>\n<li><span style=\"text-align: initial;font-size: 1em\">First order in [latex]H_{2}[\/latex]<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">Indeterminate order in [latex]Br_{2}[\/latex]<\/span><span style=\"text-align: initial;font-size: 1em\">(as it&#8217;s not in a single term)<\/span><\/li>\n<li>Indeterminate order in [latex]H\\!Br[\/latex] (as it cannot be isolated to a single term raised to a power)<\/li>\n<li>Indeterminate order overall (as some orders are indeterminate)<\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h2 id=\"Determining-the-Rate-Law\">Determining the Rate Law<\/h2>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"Isolation-Method-for-Determining-the-Rate-Law\">Isolation Method for Determining the Rate Law<\/h3>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>One of the simplest methods for determining the rate law is the isolation method.<\/p>\n<p>Say we have a reaction with two reactants, A and B. We put a <strong>large amount of B<\/strong> in our reactor compared to A; so much that the <strong>concentration barely changes<\/strong>.<\/p>\n<p>If the true rate law is: [latex]r = k_{r}[A][B]^2[\/latex]<\/p>\n<p>What we would observe is [latex]r = k_{eff}[A][\/latex], where [latex]k_{eff}=k_{r}[B_{0}]^2[\/latex]<\/p>\n<ul>\n<li><span style=\"text-align: initial;font-size: 1em\">[latex]k_{eff}[\/latex] = the effective rate constant<\/span><\/li>\n<li><span style=\"text-align: initial;font-size: 1em\">[latex][B]_{0}[\/latex]indicating the concentration of B at the start of the reaction (or time zero) or also called B naught (with naught meaning nothing or zero in this case)<\/span><\/li>\n<\/ul>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1075 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order-300x149.png\" alt=\"\" width=\"833\" height=\"413\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order-300x149.png 300w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order-1024x509.png 1024w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order-768x382.png 768w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order-65x32.png 65w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order-225x112.png 225w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order-350x174.png 350w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-isolation-method-reaction-order.png 1510w\" sizes=\"auto, (max-width: 833px) 100vw, 833px\" \/><\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>With B in great excess: [latex]r = k_{eff}[A][\/latex] where [latex]k_{eff}=k_{r}[B_{0}]^2[\/latex], reaction appears <strong>first order<\/strong>.<\/p>\n<p>With A in great excess: [latex]r' = k'_{eff}[B]^2[\/latex] where [latex]k'_{eff}=k_{r}[A_{0}][\/latex], reaction appears <strong>second order<\/strong>.<\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">[latex]k'_{eff}[\/latex] is read as k prime effective<\/span><\/p>\n<p>It is easier to analyse these individual effective rate laws than the more complex combined rate law when both concentrations change significantly.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<h3 id=\"Method-of-Initial-Rates\">Method of Initial Rates<\/h3>\n<p>The method of initial rates is commonly used in conjunction with the isolation methods to determine reaction order.<\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise: Method of Initial Rates<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p style=\"text-align: left\">Say we have a reaction with two species, A and B. We put in the same amount of B into the reactor each time. The following is our initial rates are observed with different concentrations of A. What is the reaction order in A?<\/p>\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 70.7889%;height: 104px\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px;text-align: center\"><strong>[A] (mol\/L)<\/strong><\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\"><strong>Initial rate(mol\/L\u00b7s)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px;text-align: center\">1<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]1\u00d710^{-2}[\/latex]<\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 50%;height: 15px;text-align: center\">2<\/td>\n<td style=\"width: 50%;height: 15px;text-align: center\">[latex]4\u00d710^{-2}[\/latex]<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<h3>Solution<\/h3>\n<p>As the concentration of A doubles, the reaction rate quadruples<\/p>\n<p style=\"text-align: center\">[latex]r_{0}=k_{eff}[A]^2[\/latex]<\/p>\n<p>So the reaction is second order in A.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<div>\n<p><span style=\"text-align: initial;font-size: 1em\">If we take the logarithm of the general equation for reaction rate, we can linearize the equation:<\/span><\/p>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>\\begin{align*}<br \/>\nr_{0} &amp; = k_{eff}[A_{0}]^a \\\\<br \/>\nlog(r_{0})&amp; = log(k_{eff}) + a*log([A_{0}])\\\\<br \/>\ny &amp; = intercept + slope * x<br \/>\n\\end{align*}<\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">Plot [latex]log(r_{0})[\/latex] vs [latex]log([A_{0}])[\/latex], where the slope is the reaction order in A; and y-intercept equals to [latex]log(k_{eff})[\/latex]<\/span><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\"><\/div>\n<div class=\"inner_cell\">\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>&nbsp;<\/p>\n<div>\n<div class=\"textbox textbox--exercises\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Exercise: Reaction Order and Rate Constant<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Sulfuryl chloride ([latex]SO_{2}Cl_{2}[\/latex]) decomposes to [latex]SO_{2}[\/latex] and [latex]Cl_{2}[\/latex] by the following reaction:<\/p>\n<p style=\"text-align: center\">[latex]SO_{2}Cl_{2(g)} \u2192 SO_{2(g)}+Cl_{2(g)}[\/latex]<\/p>\n<p style=\"text-align: left\">Data for the reaction at 320\u00b0C are listed in the following table. Calculate the reaction order with regard to sulfuryl chloride and determine the rate constant for the reaction.<span style=\"font-size: 1em\">[latex]^{[2]}[\/latex]<\/span><\/p>\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 70.4691%;height: 75px\">\n<tbody>\n<tr style=\"height: 15px\">\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><strong>Experiment<\/strong><\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><strong><span style=\"text-align: initial;font-size: 1em\">[latex][SO_{2}Cl_{2}]_{0}[\/latex]<\/span><\/strong><\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><strong>Initial rate(M\/s)<\/strong><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">1<\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">0.0050<\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]1.10\u00d710^{-7}[\/latex]<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">2<\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">0.0075<\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]1.65\u00d710^{-7}[\/latex]<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">3<\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">0.0100<\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]2.20\u00d710^{-7}[\/latex]<\/span><\/td>\n<\/tr>\n<tr style=\"height: 15px\">\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">4<\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\">0.0125<\/td>\n<td style=\"width: 33.3333%;height: 15px;text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]2.75\u00d710^{-7}[\/latex]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<\/div>\n<div class=\"textbox\">\n<h3>Solution<\/h3>\n<p><strong>Step 1:<\/strong> determine the reaction order with respect to sulfuryl chloride<\/p>\n<p>Comparing Experiments 1 and 3, for example, shows that doubling the concentration doubles the reaction rate <span style=\"text-align: initial;font-size: 1em\">[latex](2.20\u00d710^{-7}) \u00f7 (1.10\u00d710^{-7}) = 2.0[\/latex]<\/span>, which means that the reaction rate is proportional to <span style=\"text-align: initial;font-size: 1em\">[latex][SO_{2}Cl_{2}][\/latex]<\/span>.<\/p>\n<p>The reaction is first order with respect to \u00a0<span style=\"text-align: initial;font-size: 1em\">[latex][SO_{2}Cl_{2}][\/latex]<\/span>.<\/p>\n<p><strong>Step 2:<\/strong> calculate <span style=\"text-align: initial;font-size: 1em\">[latex]k_{r}[\/latex]<\/span><\/p>\n<p>We have <span style=\"text-align: initial;font-size: 1em\">[latex]rate = k_{r}[SO_{2}Cl_{2}][\/latex]<\/span>. We can calculate the rate constant (<span style=\"text-align: initial;font-size: 1em\">[latex]k_{r}[\/latex]<\/span>) using data from any experiment in the table.<br \/>\n\\begin{align*}<br \/>\nrate &amp; = k_{r}[SO_{2}Cl_{2}] \\\\<br \/>\n1.10\u00d710^{-7} M\/s&amp; = k_{r}\u00d70.0050M \\\\<br \/>\n2.2\u00d710^{-5}s^{-1} &amp; = k_{r}<br \/>\n\\end{align*}<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Method 2<\/strong><\/p>\n<p>The following graph is produced when plotting <span style=\"text-align: initial;font-size: 1em\">[latex]log(r_{0})[\/latex]<\/span> vs <span style=\"text-align: initial;font-size: 1em\">[latex]log([A_{0}])[\/latex]\u00a0<\/span><\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1077 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-reaction-order-example-300x181.png\" alt=\"\" width=\"532\" height=\"321\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-reaction-order-example-300x181.png 300w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-reaction-order-example-65x39.png 65w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-reaction-order-example-225x136.png 225w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-reaction-order-example-350x211.png 350w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-reaction-order-example.png 592w\" sizes=\"auto, (max-width: 532px) 100vw, 532px\" \/><\/p>\n<p>From the line of best fit, we can see the slope is 1 (meaning a first order relationship) and <span style=\"text-align: initial;font-size: 1em\">[latex]log(k_{r})=-4.6576[\/latex]\u00a0<\/span><\/p>\n<p>Therefore the reaction is first order in <span style=\"text-align: initial;font-size: 1em\">[latex]SO_{2}Cl_{2}[\/latex] <\/span>, <span style=\"text-align: initial;font-size: 1em\">[latex]k_{r}=10^{-4.6576} = 2.2\u00d710^{-5}s^{-1}[\/latex]<\/span>.<\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n<div class=\"cell border-box-sizing text_cell rendered\">\n<div class=\"prompt input_prompt\">\n<div class=\"textbox shaded\">\n<h2>References<\/h2>\n<div class=\"text_cell_render border-box-sizing rendered_html\">\n<p>[1] Chemistry LibreTexts. 2020. <i>The Rate Law.<\/i> [online] Available at: &lt;<a href=\"https:\/\/chem.libretexts.org\/Bookshelves\/Physical_and_Theoretical_Chemistry_Textbook_Maps\/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)\/Kinetics\/Rate_Laws\/The_Rate_Law\">https:\/\/chem.libretexts.org\/Bookshelves\/Physical_and_Theoretical_Chemistry_Textbook_Maps\/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)\/Kinetics\/Rate_Laws\/The_Rate_Law<\/a>&gt; [Accessed 23 April 2020].<\/p>\n<p>[2] Chemistry LibreTexts. 2020.\u00a0<i>14.4: The Change Of Concentration With Time (Integrated Rate Laws)<\/i>. [online] Available at: &lt;<a href=\"https:\/\/chem.libretexts.org\/Bookshelves\/General_Chemistry\/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)\/14%3A_Chemical_Kinetics\/14.4%3A_The_Change_of_Concentration_with_Time_(Integrated_Rate_Laws)\">https:\/\/chem.libretexts.org\/Bookshelves\/General_Chemistry\/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)\/14%3A_Chemical_Kinetics\/14.4%3A_The_Change_of_Concentration_with_Time_(Integrated_Rate_Laws)<\/a>&gt; [Accessed 23 April 2020].<\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n<\/div>\n<\/div>\n<\/div>\n","protected":false},"author":948,"menu_order":3,"comment_status":"closed","ping_status":"closed","template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[],"contributor":[],"license":[],"class_list":["post-1329","chapter","type-chapter","status-publish","hentry"],"part":1286,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1329","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/users\/948"}],"replies":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/comments?post=1329"}],"version-history":[{"count":14,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1329\/revisions"}],"predecessor-version":[{"id":2605,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1329\/revisions\/2605"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/parts\/1286"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1329\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/media?parent=1329"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapter-type?post=1329"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/contributor?post=1329"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/license?post=1329"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}