{"id":1348,"date":"2020-06-23T17:45:42","date_gmt":"2020-06-23T21:45:42","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/chbe220\/?post_type=chapter&#038;p=1348"},"modified":"2020-08-11T18:14:28","modified_gmt":"2020-08-11T22:14:28","slug":"reaction-mechanisms-elementary-reactions","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/chbe220\/chapter\/reaction-mechanisms-elementary-reactions\/","title":{"raw":"Reaction Mechanisms - Elementary Reactions","rendered":"Reaction Mechanisms &#8211; Elementary Reactions"},"content":{"raw":"<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<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>Analyze<\/strong> <span style=\"font-size: 1em\">elementary reactions and <\/span><span style=\"font-size: 1em\">reaction molecularity<\/span>\r\n\r\n<\/div>\r\n<\/div>\r\n&nbsp;\r\n\r\nThe sequence of events that occur at the molecular level during a reaction is the <strong>mechanism of the reaction<\/strong>. It describes how individual atoms, ions, or molecules interact to form particular products. The <strong>stepwise changes<\/strong>\u00a0are collectively called the reaction mechanism. <strong>Each step of the reaction<\/strong> is called an <strong>elementary reaction<\/strong>. The sum of the elementary reactions in the mechanism must give the balanced chemical equation for the overall reaction. [latex]^{[1]}[\/latex]\r\n\r\nThe decomposition of ozone, for example, appears to follow a mechanism with two steps:\r\n<p style=\"text-align: center\">[latex]O_{3}\u2192O_{2}+O[\/latex]\r\n[latex]O+O_{3}\u21922O_{2}[\/latex]<\/p>\r\nElementary reactions add up to the overall reaction:\r\n<p style=\"text-align: center\">[latex]2O_{3(g)}\u21923O_{2(g)}[\/latex]<\/p>\r\nWith the elementary reactions, we do not specify phases, and the formula represents specific processes occurring with individual molecules or atoms.\r\n\r\nNotice that the oxygen atom produced in the first step of this mechanism is consumed in the second step and therefore does not appear as a product in the overall reaction. Species that are produced in one step and consumed in a subsequent step are called <strong>intermediates<\/strong>. [latex]^{[2]}[\/latex]\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<h2 id=\"Molecularity\">Molecularity<\/h2>\r\nThe <strong>molecularity<\/strong> is the number of molecules or atoms coming together to react in an elementary reaction.\r\n<ul>\r\n \t<li><strong>Uni<\/strong>molecular reaction \u2013 Only <strong>one<\/strong> molecule is involved, examples might include an isomerization or decomposition<\/li>\r\n<\/ul>\r\n<div>\r\n<blockquote><strong>Example<\/strong>: isomerization of cyclopropane to propene\r\n\r\n<img class=\"size-medium wp-image-1102 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-Cyclopropane-to-propene-300x104.png\" alt=\"\" width=\"300\" height=\"104\" \/>\r\n\r\n<strong>Example<\/strong>: decomposition of cyclobutane\r\n\r\n<img class=\" wp-image-2425 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/06\/Capture-decomposition-of-cyclobutane-300x92.png\" alt=\"\" width=\"362\" height=\"111\" \/><\/blockquote>\r\n<\/div>\r\n<ul>\r\n \t<li><strong>Bi<\/strong>molecular reaction \u2013 <strong>two<\/strong> molecules collide, interact, and undergo some kind of change. It can be two of the same or different molecules.<\/li>\r\n<\/ul>\r\n<strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 \u00a0 \u00a0 Example<\/strong><span style=\"text-align: initial;font-size: 1em\">: Hydrogen attacking a bromine molecule <\/span>\r\n<p style=\"text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]H+Br_{2}\u2192HBr+Br[\/latex]<\/span><\/p>\r\n&nbsp;\r\n\r\n<strong><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1.602em\">Reaction Order vs. Molecularity<\/span><\/strong>\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Reaction order<\/strong><span style=\"text-align: initial;font-size: 1em\"> \u2013 An empirical quantity obtained from experimentally determined rate law<\/span>\r\n\r\n<strong style=\"text-align: initial;font-size: 1em\">Molecularity<\/strong><span style=\"text-align: initial;font-size: 1em\"> \u2013 Number of molecules coming together in an elementary reaction proposed as an individual step in a mechanism<\/span>\r\n\r\n<span style=\"text-align: initial;font-size: 1em\">The order of the elementary reaction is the same as its molecularity. In contrast, the rate law cannot be determined from the balanced chemical equation for the overall reaction (unless it is a single step mechanism and is therefore also an elementary step).[latex]^{[1]}[\/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<h2 id=\"Rate-Laws-for-Elementary-Reactions\">Rate Laws for Elementary Reactions<\/h2>\r\n<h3 id=\"Unimolecular\">Unimolecular<\/h3>\r\n<p style=\"text-align: left\">[latex]A\u2192P[\/latex] (can be several products):<\/p>\r\n\r\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 33.4613%;height: 63px\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 100%;text-align: center\"><span style=\"font-size: 16px\">[latex]-\\frac{d[A]}{dt}=k_{r}*[A][\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<h3 id=\"Bimolecular\">Bimolecular<\/h3>\r\n<p style=\"text-align: left\">[latex]A+B\u2192P[\/latex] (can be several products):<\/p>\r\n\r\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 37.9609%;height: 57px\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 100%;text-align: center\"><span style=\"font-size: 16px\">[latex]-\\frac{d[A]}{dt}=k_{r}*[A]*[B][\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\n<p style=\"text-align: left\">[latex]A+A\u2192P[\/latex] (can be several products):<\/p>\r\n\r\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 33.876%;height: 58px\" border=\"0\">\r\n<tbody>\r\n<tr>\r\n<td style=\"width: 100%;text-align: center\"><span style=\"font-size: 16px\">[latex]-\\frac{d[A]}{dt}=k_{r}*[A]^2[\/latex]<\/span><\/td>\r\n<\/tr>\r\n<\/tbody>\r\n<\/table>\r\nGenerally these depend on concentration of reactants. However, these rate laws must be tested against experimental data.\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<h2 id=\"Consecutive-Elementary-Reactions\">Consecutive Elementary Reactions<\/h2>\r\nSome reactions proceed through the formation of an intermediate (I). One example of this with irreversible reactions is:\r\n<p style=\"text-align: center\">[latex]A\u2192I\u2192P[\/latex]<\/p>\r\nThe intermediate([latex]I[\/latex]) is present in the reaction steps but does not appear in the overall reaction: [latex]A\u2192P[\/latex]\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--examples\"><header class=\"textbox__header\">\r\n<p class=\"textbox__title\">Example: Express Rate of Formation for Reactive Compounds<\/p>\r\n\r\n<\/header>\r\n<div class=\"textbox__content\">\r\n\r\nGiven the consecutive elementary reaction:\r\n<p style=\"text-align: center\">[latex]A\\xrightarrow{\\text{ka}}I\\xrightarrow{\\text{kb}}P[\/latex]<\/p>\r\nThe rate of change for [A] is: [latex]\\frac{d[A]}{dt}=-k_{a}*[A][\/latex]\r\n\r\nWhat are the equations for the rates of change for the other two species, [latex]I[\/latex] and [latex]P[\/latex], in terms of their concentrations and the reaction rate constants?\r\n\r\n&nbsp;\r\n\r\n<strong>Solution<\/strong>\r\n\r\nthe intermediate I is produced by the reaction that converts A to I and consumed by the reaction that produces P:\r\n<p style=\"text-align: center\">[latex]\\frac{d[I]}{dt}=k_{a}*[A]-k_{b}*[I][\/latex]<\/p>\r\n<p style=\"text-align: left\">P is produced by the reaction that converts I to P:<\/p>\r\n<p style=\"text-align: center\">[latex]\\frac{d[P]}{dt}=k_{b}*[I][\/latex]<\/p>\r\n\r\n<\/div>\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\"><\/div>\r\n<div class=\"inner_cell\">\r\n<div class=\"text_cell_render border-box-sizing rendered_html\">\r\n\r\nTaking 3 sets of arbitary values for [latex]k_{a}[\/latex] and [latex]k_{b}[\/latex], we can plot the following graphs of concentration vs.time:\r\n\r\n&nbsp;\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\"><img class=\" wp-image-1104 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison-300x79.png\" alt=\"\" width=\"923\" height=\"243\" \/><\/div>\r\n<div class=\"textbox shaded\">\r\n<h2>References<\/h2>\r\n<span style=\"font-size: 1em\">[1] Chemistry LibreTexts. 2020. <\/span><i style=\"font-size: 1em\">14.6 Reaction Mechanisms.<\/i><span style=\"font-size: 1em\"> [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\/14.6%3A_Reaction_Mechanisms#:~:text=A%20balanced%20chemical%20reaction%20does,step%20is%20an%20elementary%20reaction.\">https:\/\/chem.libretexts.org\/Bookshelves\/General_Chemistry\/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)\/14%3A_Chemical_Kinetics\/14.6%3A_Reaction_Mechanisms#:~:text=A%20balanced%20chemical%20reaction%20does,step%20is%20an%20elementary%20reaction.<\/a>&gt; [Accessed 24 April, 2020].<\/span>\r\n\r\n<span style=\"font-size: 1em\">[2] OpenStax Chemistry 2016. <\/span><i style=\"font-size: 1em\">12.6 Reaction Mechanisms.<\/i><span style=\"font-size: 1em\"> [online] Available at: &lt;<a href=\"https:\/\/opentextbc.ca\/chemistry\/chapter\/12-6-reaction-mechanisms\">https:\/\/opentextbc.ca\/chemistry\/chapter\/12-6-reaction-mechanisms<\/a>&gt; [Accessed 27 April, 2020].<\/span>\r\n\r\n<\/div>\r\n&nbsp;\r\n\r\n<\/div>","rendered":"<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<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>Analyze<\/strong> <span style=\"font-size: 1em\">elementary reactions and <\/span><span style=\"font-size: 1em\">reaction molecularity<\/span><\/p>\n<\/div>\n<\/div>\n<p>&nbsp;<\/p>\n<p>The sequence of events that occur at the molecular level during a reaction is the <strong>mechanism of the reaction<\/strong>. It describes how individual atoms, ions, or molecules interact to form particular products. The <strong>stepwise changes<\/strong>\u00a0are collectively called the reaction mechanism. <strong>Each step of the reaction<\/strong> is called an <strong>elementary reaction<\/strong>. The sum of the elementary reactions in the mechanism must give the balanced chemical equation for the overall reaction. [latex]^{[1]}[\/latex]<\/p>\n<p>The decomposition of ozone, for example, appears to follow a mechanism with two steps:<\/p>\n<p style=\"text-align: center\">[latex]O_{3}\u2192O_{2}+O[\/latex]<br \/>\n[latex]O+O_{3}\u21922O_{2}[\/latex]<\/p>\n<p>Elementary reactions add up to the overall reaction:<\/p>\n<p style=\"text-align: center\">[latex]2O_{3(g)}\u21923O_{2(g)}[\/latex]<\/p>\n<p>With the elementary reactions, we do not specify phases, and the formula represents specific processes occurring with individual molecules or atoms.<\/p>\n<p>Notice that the oxygen atom produced in the first step of this mechanism is consumed in the second step and therefore does not appear as a product in the overall reaction. Species that are produced in one step and consumed in a subsequent step are called <strong>intermediates<\/strong>. [latex]^{[2]}[\/latex]<\/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<h2 id=\"Molecularity\">Molecularity<\/h2>\n<p>The <strong>molecularity<\/strong> is the number of molecules or atoms coming together to react in an elementary reaction.<\/p>\n<ul>\n<li><strong>Uni<\/strong>molecular reaction \u2013 Only <strong>one<\/strong> molecule is involved, examples might include an isomerization or decomposition<\/li>\n<\/ul>\n<div>\n<blockquote><p><strong>Example<\/strong>: isomerization of cyclopropane to propene<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-medium wp-image-1102 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-Cyclopropane-to-propene-300x104.png\" alt=\"\" width=\"300\" height=\"104\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-Cyclopropane-to-propene-300x104.png 300w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-Cyclopropane-to-propene-65x23.png 65w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-Cyclopropane-to-propene-225x78.png 225w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-Cyclopropane-to-propene-350x122.png 350w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-Cyclopropane-to-propene.png 391w\" sizes=\"auto, (max-width: 300px) 100vw, 300px\" \/><\/p>\n<p><strong>Example<\/strong>: decomposition of cyclobutane<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-2425 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/06\/Capture-decomposition-of-cyclobutane-300x92.png\" alt=\"\" width=\"362\" height=\"111\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/06\/Capture-decomposition-of-cyclobutane-300x92.png 300w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/06\/Capture-decomposition-of-cyclobutane-65x20.png 65w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/06\/Capture-decomposition-of-cyclobutane-225x69.png 225w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/06\/Capture-decomposition-of-cyclobutane-350x107.png 350w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/06\/Capture-decomposition-of-cyclobutane.png 716w\" sizes=\"auto, (max-width: 362px) 100vw, 362px\" \/><\/p><\/blockquote>\n<\/div>\n<ul>\n<li><strong>Bi<\/strong>molecular reaction \u2013 <strong>two<\/strong> molecules collide, interact, and undergo some kind of change. It can be two of the same or different molecules.<\/li>\n<\/ul>\n<p><strong style=\"text-align: initial;font-size: 1em\">\u00a0 \u00a0 \u00a0 \u00a0 Example<\/strong><span style=\"text-align: initial;font-size: 1em\">: Hydrogen attacking a bromine molecule <\/span><\/p>\n<p style=\"text-align: center\"><span style=\"text-align: initial;font-size: 1em\">[latex]H+Br_{2}\u2192HBr+Br[\/latex]<\/span><\/p>\n<p>&nbsp;<\/p>\n<p><strong><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1.602em\">Reaction Order vs. Molecularity<\/span><\/strong><\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Reaction order<\/strong><span style=\"text-align: initial;font-size: 1em\"> \u2013 An empirical quantity obtained from experimentally determined rate law<\/span><\/p>\n<p><strong style=\"text-align: initial;font-size: 1em\">Molecularity<\/strong><span style=\"text-align: initial;font-size: 1em\"> \u2013 Number of molecules coming together in an elementary reaction proposed as an individual step in a mechanism<\/span><\/p>\n<p><span style=\"text-align: initial;font-size: 1em\">The order of the elementary reaction is the same as its molecularity. In contrast, the rate law cannot be determined from the balanced chemical equation for the overall reaction (unless it is a single step mechanism and is therefore also an elementary step).[latex]^{[1]}[\/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<h2 id=\"Rate-Laws-for-Elementary-Reactions\">Rate Laws for Elementary Reactions<\/h2>\n<h3 id=\"Unimolecular\">Unimolecular<\/h3>\n<p style=\"text-align: left\">[latex]A\u2192P[\/latex] (can be several products):<\/p>\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 33.4613%;height: 63px\">\n<tbody>\n<tr>\n<td style=\"width: 100%;text-align: center\"><span style=\"font-size: 16px\">[latex]-\\frac{d[A]}{dt}=k_{r}*[A][\/latex]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h3 id=\"Bimolecular\">Bimolecular<\/h3>\n<p style=\"text-align: left\">[latex]A+B\u2192P[\/latex] (can be several products):<\/p>\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 37.9609%;height: 57px\">\n<tbody>\n<tr>\n<td style=\"width: 100%;text-align: center\"><span style=\"font-size: 16px\">[latex]-\\frac{d[A]}{dt}=k_{r}*[A]*[B][\/latex]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p style=\"text-align: left\">[latex]A+A\u2192P[\/latex] (can be several products):<\/p>\n<table class=\"grid aligncenter\" style=\"border-collapse: collapse;width: 33.876%;height: 58px\">\n<tbody>\n<tr>\n<td style=\"width: 100%;text-align: center\"><span style=\"font-size: 16px\">[latex]-\\frac{d[A]}{dt}=k_{r}*[A]^2[\/latex]<\/span><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>Generally these depend on concentration of reactants. However, these rate laws must be tested against experimental data.<\/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<h2 id=\"Consecutive-Elementary-Reactions\">Consecutive Elementary Reactions<\/h2>\n<p>Some reactions proceed through the formation of an intermediate (I). One example of this with irreversible reactions is:<\/p>\n<p style=\"text-align: center\">[latex]A\u2192I\u2192P[\/latex]<\/p>\n<p>The intermediate([latex]I[\/latex]) is present in the reaction steps but does not appear in the overall reaction: [latex]A\u2192P[\/latex]<\/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--examples\">\n<header class=\"textbox__header\">\n<p class=\"textbox__title\">Example: Express Rate of Formation for Reactive Compounds<\/p>\n<\/header>\n<div class=\"textbox__content\">\n<p>Given the consecutive elementary reaction:<\/p>\n<p style=\"text-align: center\">[latex]A\\xrightarrow{\\text{ka}}I\\xrightarrow{\\text{kb}}P[\/latex]<\/p>\n<p>The rate of change for [A] is: [latex]\\frac{d[A]}{dt}=-k_{a}*[A][\/latex]<\/p>\n<p>What are the equations for the rates of change for the other two species, [latex]I[\/latex] and [latex]P[\/latex], in terms of their concentrations and the reaction rate constants?<\/p>\n<p>&nbsp;<\/p>\n<p><strong>Solution<\/strong><\/p>\n<p>the intermediate I is produced by the reaction that converts A to I and consumed by the reaction that produces P:<\/p>\n<p style=\"text-align: center\">[latex]\\frac{d[I]}{dt}=k_{a}*[A]-k_{b}*[I][\/latex]<\/p>\n<p style=\"text-align: left\">P is produced by the reaction that converts I to P:<\/p>\n<p style=\"text-align: center\">[latex]\\frac{d[P]}{dt}=k_{b}*[I][\/latex]<\/p>\n<\/div>\n<\/div>\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>Taking 3 sets of arbitary values for [latex]k_{a}[\/latex] and [latex]k_{b}[\/latex], we can plot the following graphs of concentration vs.time:<\/p>\n<p>&nbsp;<\/p>\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-1104 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison-300x79.png\" alt=\"\" width=\"923\" height=\"243\" srcset=\"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison-300x79.png 300w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison-1024x269.png 1024w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison-768x202.png 768w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison-65x17.png 65w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison-225x59.png 225w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison-350x92.png 350w, https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-content\/uploads\/sites\/1010\/2020\/05\/Capture-ka-kb-comparison.png 1072w\" sizes=\"auto, (max-width: 923px) 100vw, 923px\" \/><\/div>\n<div class=\"textbox shaded\">\n<h2>References<\/h2>\n<p><span style=\"font-size: 1em\">[1] Chemistry LibreTexts. 2020. <\/span><i style=\"font-size: 1em\">14.6 Reaction Mechanisms.<\/i><span style=\"font-size: 1em\"> [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\/14.6%3A_Reaction_Mechanisms#:~:text=A%20balanced%20chemical%20reaction%20does,step%20is%20an%20elementary%20reaction.\">https:\/\/chem.libretexts.org\/Bookshelves\/General_Chemistry\/Map%3A_Chemistry_-_The_Central_Science_(Brown_et_al.)\/14%3A_Chemical_Kinetics\/14.6%3A_Reaction_Mechanisms#:~:text=A%20balanced%20chemical%20reaction%20does,step%20is%20an%20elementary%20reaction.<\/a>&gt; [Accessed 24 April, 2020].<\/span><\/p>\n<p><span style=\"font-size: 1em\">[2] OpenStax Chemistry 2016. <\/span><i style=\"font-size: 1em\">12.6 Reaction Mechanisms.<\/i><span style=\"font-size: 1em\"> [online] Available at: &lt;<a href=\"https:\/\/opentextbc.ca\/chemistry\/chapter\/12-6-reaction-mechanisms\">https:\/\/opentextbc.ca\/chemistry\/chapter\/12-6-reaction-mechanisms<\/a>&gt; [Accessed 27 April, 2020].<\/span><\/p>\n<\/div>\n<p>&nbsp;<\/p>\n<\/div>\n","protected":false},"author":948,"menu_order":7,"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-1348","chapter","type-chapter","status-publish","hentry"],"part":1286,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1348","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=1348"}],"version-history":[{"count":10,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1348\/revisions"}],"predecessor-version":[{"id":2648,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapters\/1348\/revisions\/2648"}],"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\/1348\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/media?parent=1348"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/pressbooks\/v2\/chapter-type?post=1348"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/contributor?post=1348"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/chbe220\/wp-json\/wp\/v2\/license?post=1348"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}