{"id":727,"date":"2021-07-23T09:20:32","date_gmt":"2021-07-23T13:20:32","guid":{"rendered":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/reaction-mechanisms\/"},"modified":"2022-06-23T09:17:31","modified_gmt":"2022-06-23T13:17:31","slug":"reaction-mechanisms","status":"publish","type":"chapter","link":"https:\/\/pressbooks.bccampus.ca\/aperrott\/chapter\/reaction-mechanisms\/","title":{"raw":"12.6 Reaction Mechanisms","rendered":"12.6 Reaction Mechanisms"},"content":{"raw":"<strong><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1.602em;background-color: #cbd4b6;color: #000000\">Learning Objectives<\/span><\/strong>\r\n<div class=\"textbox textbox--learning-objectives\">\r\n\r\nBy the end of this section, you will be able to:\r\n<ul>\r\n \t<li>Distinguish net reactions from elementary reactions (steps)<\/li>\r\n \t<li>Identify the molecularity of elementary reactions<\/li>\r\n \t<li>Write a balanced chemical equation for a process given its reaction mechanism<\/li>\r\n \t<li>Derive the rate law consistent with a given reaction mechanism<\/li>\r\n<\/ul>\r\n<\/div>\r\n<p id=\"fs-idp19792192\">Chemical reactions very often occur in a step-wise fashion, involving two or more distinct reactions taking place in sequence. A balanced equation indicates what is reacting and what is produced, but it reveals no details about how the reaction actually takes place. The <strong>reaction mechanism<\/strong> (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs.<\/p>\r\n<p id=\"fs-idm10360272\">The decomposition of ozone, for example, appears to follow a mechanism with two steps:<\/p>\r\n\r\n<div id=\"fs-idp10305696\" style=\"text-align: center\" data-type=\"equation\">O<sub>3<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 O<sub>2<\/sub>(<em>g<\/em>) + O(<em>g<\/em>)<\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\">O(<em>g<\/em>) + O<sub>3<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 2O<sub>2<\/sub>(<em>g<\/em>)<\/div>\r\n<p id=\"fs-idm40865648\">Each of the steps in a reaction mechanism is an <strong>elementary reaction<\/strong>. These elementary reactions occur precisely as represented in the step equations, and they must sum to yield the balanced chemical equation representing the overall reaction:<\/p>\r\n\r\n<div id=\"fs-idp143616928\" style=\"text-align: center\" data-type=\"equation\">2O<sub>3<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 3O<sub>2<\/sub>(<em>g<\/em>)<\/div>\r\n<p id=\"fs-idp205634512\">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>.<\/p>\r\n<p id=\"fs-idp6340064\">While the overall reaction equation for the decomposition of ozone indicates that two molecules of ozone react to give three molecules of oxygen, the mechanism of the reaction <em data-effect=\"italics\">does not involve the direct collision and reaction of two ozone molecules<\/em>. Instead, one O<sub>3<\/sub> decomposes to yield O<sub>2<\/sub> and an oxygen atom, and a second O<sub>3<\/sub> molecule subsequently reacts with the oxygen atom to yield two additional O<sub>2<\/sub> molecules.<\/p>\r\n<p id=\"fs-idm500275472\">Unlike balanced equations representing an overall reaction, the equations for elementary reactions are explicit representations of the chemical change taking place. The reactant(s) in an elementary reaction\u2019s equation undergo only the bond-breaking and\/or making events depicted to yield the product(s). For this reason, <em data-effect=\"italics\">the rate law for an elementary reaction may be derived directly from the balanced chemical equation describing the reaction<\/em>. This is not the case for typical chemical reactions, for which rate laws may be reliably determined only via experimentation.<\/p>\r\n\r\n<div id=\"fs-idp262348128\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Unimolecular Elementary Reactions<\/strong><\/h3>\r\n<p id=\"fs-idp205522704\">The <strong>molecularity <\/strong>of an elementary reaction is the number of reactant species (atoms, molecules, or ions). For example, a <strong>unimolecular reaction<\/strong> involves the reaction of a <em data-effect=\"italics\">single<\/em> reactant species to produce one or more molecules of product:<\/p>\r\n\r\n<div id=\"fs-idp34074352\" style=\"text-align: center\" data-type=\"equation\"><em>A<\/em>\u00a0 \u27f6\u00a0 products<\/div>\r\n<p id=\"fs-idp13674832\">The rate law for a unimolecular reaction is first order:<\/p>\r\n\r\n<div id=\"fs-idm26736096\" style=\"text-align: center\" data-type=\"equation\">rate = <em>k<\/em>[<em>A<\/em>]<\/div>\r\n<p id=\"fs-idp203524640\">A unimolecular reaction may be one of several elementary reactions in a complex mechanism. For example, the reaction:<\/p>\r\n\r\n<div id=\"fs-idp16624720\" style=\"text-align: center\" data-type=\"equation\">O<sub>3<\/sub>\u00a0 \u27f6\u00a0 O<sub>2<\/sub> + O<\/div>\r\n<p id=\"fs-idp196763520\">illustrates a unimolecular elementary reaction that occurs as one part of a two-step reaction mechanism as described above. However, some unimolecular reactions may be the only step of a single-step reaction mechanism. (In other words, an \u201coverall\u201d reaction may also be an elementary reaction in some cases.) For example, the gas-phase decomposition of cyclobutane, C<sub>4<\/sub>H<sub>8<\/sub>, to ethylene, C<sub>2<\/sub>H<sub>4<\/sub>, is represented by the following chemical equation:<\/p>\r\n<span id=\"fs-idp32755824\" class=\"scaled-down\" data-type=\"media\" data-alt=\"In this figure, structural formulas are used to illustrate a chemical reaction. On the left, a structural formula for cyclobutane is shown. This structure is composed of 4 C atoms connected with single bonds in a square shape. Each C atom is bonded to two other C atoms in the structure, leaving two bonds for H atoms pointing outward above, below, left, and right. An arrow points right to two identical ethane molecules with a plus symbol between them. Each of these molecules contains two C atoms connected with a double bond oriented vertically between them. The C atom at the top of these molecules has H atoms bonded above to the right and left. Similarly, the lower C atom has two H atoms bonded below to the right and left.\"><img class=\"\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_06_CyclobD_img-2.jpg\" alt=\"In this figure, structural formulas are used to illustrate a chemical reaction. On the left, a structural formula for cyclobutane is shown. This structure is composed of 4 C atoms connected with single bonds in a square shape. Each C atom is bonded to two other C atoms in the structure, leaving two bonds for H atoms pointing outward above, below, left, and right. An arrow points right to two identical ethane molecules with a plus symbol between them. Each of these molecules contains two C atoms connected with a double bond oriented vertically between them. The C atom at the top of these molecules has H atoms bonded above to the right and left. Similarly, the lower C atom has two H atoms bonded below to the right and left.\" width=\"518\" height=\"161\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n<p id=\"fs-idp100963616\">This equation represents the overall reaction observed, and it might also represent a legitimate unimolecular elementary reaction. The rate law predicted from this equation, assuming it is an elementary reaction, turns out to be the same as the rate law derived experimentally for the overall reaction, namely, one showing first-order behavior:<\/p>\r\n\r\n<div id=\"fs-idp67724640\" data-type=\"equation\"><img class=\"wp-image-1747 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6a-300x82.png\" alt=\"\" width=\"238\" height=\"65\" \/><\/div>\r\n<p id=\"fs-idp128923296\">This agreement between observed and predicted rate laws is interpreted to mean that the proposed unimolecular, single-step process is a reasonable mechanism for the butadiene reaction.<\/p>\r\n\r\n<\/div>\r\n<div id=\"fs-idp108234736\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Bimolecular Elementary Reactions<\/strong><\/h3>\r\n<p id=\"fs-idp87793216\">A <strong>bimolecular reaction<\/strong> involves two reactant species, for example:<\/p>\r\n\r\n<div id=\"fs-idp211065760\" style=\"text-align: center\" data-type=\"equation\"><em>A<\/em> + <em>B<\/em>\u00a0 \u27f6\u00a0 products<\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\">and<\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\">2<em>A<\/em>\u00a0 \u27f6\u00a0 products<\/div>\r\n<p id=\"fs-idm80729584\">For the first type, in which the two reactant molecules are different, the rate law is first-order in <em data-effect=\"italics\">A<\/em> and first order in <em data-effect=\"italics\">B<\/em> (second-order overall):<\/p>\r\n\r\n<div id=\"fs-idm26928768\" style=\"text-align: center\" data-type=\"equation\">\u00a0rate = <em>k<\/em>[<em>A<\/em>][<em>B<\/em>]<\/div>\r\n<p id=\"fs-idp220120832\">For the second type, in which two identical molecules collide and react, the rate law is second order in <em data-effect=\"italics\">A<\/em>:<\/p>\r\n\r\n<div id=\"fs-idp93993280\" style=\"text-align: center\" data-type=\"equation\">rate = k[<em>A<\/em>][<em>A<\/em>] = k[<em>A<\/em>]<sup>2<\/sup><\/div>\r\n<p id=\"fs-idp43609744\">Some chemical reactions occur by mechanisms that consist of a single bimolecular elementary reaction. One example is the reaction of nitrogen dioxide with carbon monoxide:<\/p>\r\n\r\n<div id=\"fs-idm24253872\" style=\"text-align: center\" data-type=\"equation\">NO<sub>2<\/sub>(<em>g<\/em>) + CO(<em>g<\/em>)\u00a0 \u27f6\u00a0 NO(<em>g<\/em>) + CO<sub>2<\/sub>(<em>g<\/em>)<\/div>\r\n<p id=\"fs-idp38254032\">(see <a class=\"autogenerated-content\" href=\"#CNX_Chem_12_06_BimoElRe\">(Figure)<\/a>)<\/p>\r\n\r\n<div id=\"CNX_Chem_12_06_BimoElRe\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">The probable mechanism for the reaction between NO<sub>2<\/sub> and CO to yield NO and CO<sub>2<\/sub>.<\/div>\r\n<span id=\"fs-idp70495312\" data-type=\"media\" data-alt=\"This figure provides an illustration of a reaction between two H I molecules using space filling models. H atoms are shown as white spheres, and I atoms are shown as purple spheres. On the left, two H I molecules are shownwith a small white sphere bonded to a much larger purple sphere. The label, \u201cTwo H I molecules,\u201d appears below. An arrow points right to a similar structure in which the two molecules appear pushed together, so that the purple spheres of the two molecules are touching. Below appears the label, \u201cTransition state.\u201d Following another arrow, two white spheres are shown vertically oriented and bonded together with the label, \u201cH subscript 2\u201d above. The H subscript 2 molecule is followed by a plus sign and two purple spheres bonded together with the label, \u201cI subscript 2\u201d above. Below these structures is the label, \u201cHydrogen iodide molecules decompose to produce hydrogen H subscript 2 and iodine I subscript 2.\u201d\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_06_BimoElRe-2.jpg\" alt=\"This figure provides an illustration of a reaction between two H I molecules using space filling models. H atoms are shown as white spheres, and I atoms are shown as purple spheres. On the left, two H I molecules are shownwith a small white sphere bonded to a much larger purple sphere. The label, \u201cTwo H I molecules,\u201d appears below. An arrow points right to a similar structure in which the two molecules appear pushed together, so that the purple spheres of the two molecules are touching. Below appears the label, \u201cTransition state.\u201d Following another arrow, two white spheres are shown vertically oriented and bonded together with the label, \u201cH subscript 2\u201d above. The H subscript 2 molecule is followed by a plus sign and two purple spheres bonded together with the label, \u201cI subscript 2\u201d above. Below these structures is the label, \u201cHydrogen iodide molecules decompose to produce hydrogen H subscript 2 and iodine I subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idp38432416\">Bimolecular elementary reactions may also be involved as steps in a multistep reaction mechanism. The reaction of atomic oxygen with ozone is the second step of the two-step ozone decomposition mechanism discussed earlier in this section:<\/p>\r\n\r\n<div id=\"fs-idp100763440\" style=\"text-align: center\" data-type=\"equation\">O(<em>g<\/em>) + O<sub>3<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 2O<sub>2<\/sub>(<em>g<\/em>)<\/div>\r\n<\/div>\r\n<div id=\"fs-idp38909440\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Termolecular Elementary Reactions<\/strong><\/h3>\r\n<p id=\"fs-idm9155392\">An elementary<strong> termolecular reaction<\/strong> involves the simultaneous collision of three atoms, molecules, or ions. Termolecular elementary reactions are uncommon because the probability of three particles colliding simultaneously is less than one one-thousandth of the probability of two particles colliding. There are, however, a few established termolecular elementary reactions. The reaction of nitrogen monoxide with oxygen appears to involve termolecular steps:<\/p>\r\n\r\n<div id=\"fs-idp196238032\" style=\"text-align: center\" data-type=\"equation\">2NO + O<sub>2<\/sub>\u00a0 \u27f6\u00a0 2NO<sub>2<\/sub><\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\">rate = <em>k<\/em>[NO]<sup>2<\/sup>[O<sub>2<\/sub>]<\/div>\r\n<p id=\"fs-idp136937056\">Likewise, the reaction of nitrogen monoxide with chlorine appears to involve termolecular steps:<\/p>\r\n\r\n<div id=\"fs-idp128771280\" style=\"text-align: center\" data-type=\"equation\">2NO + Cl<sub>2<\/sub>\u00a0 \u27f6\u00a0 2NOCl<\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\">rate = <em>k<\/em>[NO]<sup>2<\/sup>[Cl<sub>2<\/sub>]<\/div>\r\n<\/div>\r\n<div id=\"fs-idp270477600\" class=\"bc-section section\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Relating Reaction Mechanisms to Rate Laws<\/strong><\/h3>\r\n<p id=\"fs-idp253615520\">It\u2019s often the case that one step in a multistep reaction mechanism is significantly slower than the others. Because a reaction cannot proceed faster than its slowest step, this step will limit the rate at which the overall reaction occurs. The slowest step is therefore called the <strong>rate-determining step<\/strong> (or rate-limiting step) of the reaction <a class=\"autogenerated-content\" href=\"#CNX_Chem_12_06_Cattle\">(Figure)<\/a>.<\/p>\r\n&nbsp;\r\n<div id=\"CNX_Chem_12_06_Cattle\" class=\"scaled-down\">\r\n<div class=\"bc-figcaption figcaption\">A cattle chute is a nonchemical example of a rate-determining step. Cattle can only be moved from one holding pen to another as quickly as one animal can make its way through the chute. (credit: Loren Kerns)<\/div>\r\n<span id=\"fs-idp96445120\" data-type=\"media\" data-alt=\"A photo is shown of cattle passing through a narrow chute into a holding pen. A person directs them through the gate with a long white and red pole.\"><img src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_06_Cattle-2.jpg\" alt=\"A photo is shown of cattle passing through a narrow chute into a holding pen. A person directs them through the gate with a long white and red pole.\" data-media-type=\"image\/jpeg\" \/><\/span>\r\n\r\n<\/div>\r\n<p id=\"fs-idp41680064\">As described earlier, rate laws may be derived directly from the chemical equations for elementary reactions. This is not the case, however, for ordinary chemical reactions. The balanced equations most often encountered represent the overall change for some chemical system, and very often this is the result of some multistep reaction mechanisms. In every case, the rate law must be determined from experimental data and the reaction mechanism subsequently deduced from the rate law (and sometimes from other data). The reaction of NO<sub>2<\/sub> and CO provides an illustrative example:<\/p>\r\n\r\n<div id=\"fs-idp193034480\" style=\"text-align: center\" data-type=\"equation\">NO<sub>2<\/sub>(<em>g<\/em>) + CO(<em>g<\/em>)\u00a0 \u27f6\u00a0 \u00a0CO<sub>2<\/sub>(<em>g<\/em>) + NO(<em>g<\/em>)<\/div>\r\n<p id=\"fs-idp18907792\">For temperatures above 225 \u00b0C, the rate law has been found to be:<\/p>\r\n\r\n<div id=\"fs-idp70556928\" style=\"text-align: center\" data-type=\"equation\">\u00a0rate = <em>k<\/em>[NO<sub>2<\/sub>][CO]<\/div>\r\n<p id=\"fs-idp43466688\">The reaction is first order with respect to NO<sub>2<\/sub> and first-order with respect to CO. This is consistent with a single-step bimolecular mechanism and it is <em data-effect=\"italics\">possible<\/em> that this is the mechanism for this reaction at high temperatures.<\/p>\r\n<p id=\"fs-idp232335904\">At temperatures below 225 \u00b0C<em data-effect=\"italics\">,<\/em> the reaction is described by a rate law that is second order with respect to NO<sub>2<\/sub>:<\/p>\r\n\r\n<div id=\"fs-idm80864896\" style=\"text-align: center\" data-type=\"equation\">rate = <em>k<\/em>[NO<sub>2<\/sub>]<sup>2<\/sup><\/div>\r\n<p id=\"fs-idp70725520\">This rate law is not consistent with the single-step mechanism, but is consistent with the following two-step mechanism:<\/p>\r\n\r\n<div id=\"fs-idp34145072\" style=\"text-align: center\" data-type=\"equation\">NO<sub>2<\/sub>(<em>g<\/em>) + NO<sub>2<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 NO<sub>3<\/sub>(<em>g<\/em>) + NO(<em>g<\/em>)\u00a0 \u00a0 \u00a0(slow)<\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\">NO<sub>3<\/sub>(<em>g<\/em>) + CO(<em>g<\/em>)\u00a0 \u27f6\u00a0 NO<sub>2<\/sub>(<em>g<\/em>)+CO<sub>2<\/sub>(<em>g<\/em>)\u00a0 \u00a0 \u00a0(fast)<\/div>\r\n<p id=\"fs-idp107509104\">The rate-determining (slower) step gives a rate law showing second-order dependence on the NO<sub>2<\/sub> concentration, and the sum of the two equations gives the net overall reaction.<\/p>\r\n<p id=\"fs-idp37457664\">In general, when the rate-determining (slower) step is the first step in a mechanism, the rate law for the overall reaction is the same as the rate law for this step. However, when the rate-determining step is preceded by a step involving a rapidly reversible reaction the rate law for the overall reaction may be more difficult to derive.<\/p>\r\n<p id=\"fs-idp17102832\">As discussed in several chapters of this text, a reversible reaction is at <em data-effect=\"italics\">equilibrium<\/em> when the rates of the forward and reverse processes are equal. Consider the reversible elementary reaction in which NO dimerizes to yield an intermediate species N<sub>2<\/sub>O<sub>2<\/sub>. When this reaction is at equilibrium:<\/p>\r\n\r\n<div id=\"fs-idp65516752\" style=\"text-align: center\" data-type=\"equation\">NO + NO\u00a0 \u21cc\u00a0 N<sub>2<\/sub>O<sub>2<\/sub><\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\">rate<sub>forward<\/sub> = rate<sub>reverse<\/sub><\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\">k<sub>1<\/sub>[NO]<sup>2<\/sup> = k<sub>-1<\/sub>[N<sub>2<\/sub>O<sub>2<\/sub>]<\/div>\r\n<p id=\"fs-idm76069968\">This expression may be rearranged to express the concentration of the intermediate in terms of the reactant NO:<\/p>\r\n\r\n<div id=\"fs-idp95214240\" data-type=\"equation\"><img class=\"wp-image-1748 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6b-300x113.png\" alt=\"\" width=\"199\" height=\"75\" \/><\/div>\r\n<p id=\"fs-idp32322000\">Since intermediate species concentrations are not used in formulating rate laws for overall reactions, this approach is sometimes necessary, as illustrated in the following example exercise.<\/p>\r\n\r\n<div id=\"fs-idp252983408\" class=\"textbox textbox--examples\" data-type=\"example\">\r\n<p id=\"fs-idm378927696\"><strong>Deriving a Rate Law from a Reaction Mechanism:<\/strong><\/p>\r\nThe two-step mechanism below has been proposed for a reaction between nitrogen monoxide and molecular chlorine:\r\n<div id=\"fs-idm496065264\" style=\"padding-left: 40px\" data-type=\"equation\">Step 1:\u00a0 NO(<em>g<\/em>) + Cl<sub>2<\/sub>(<em>g<\/em>)\u00a0 \u21cc\u00a0 NOCl<sub>2<\/sub>(<em>g<\/em>)\u00a0 \u00a0 \u00a0(fast)<\/div>\r\n<div style=\"padding-left: 40px\" data-type=\"equation\">Step 2:\u00a0 NOCl<sub>2<\/sub>(<em>g<\/em>) + NO(<em>g<\/em>)\u00a0 \u27f6\u00a0 2NOCl(<em>g<\/em>)\u00a0 \u00a0 \u00a0(slow)<\/div>\r\n<p id=\"fs-idm352158848\">Use this mechanism to derive the equation and predicted rate law for the overall reaction.<\/p>\r\n<p id=\"fs-idm359312208\"><strong>Solution:<\/strong><\/p>\r\nThe equation for the overall reaction is obtained by adding the two elementary reactions:\r\n<div id=\"fs-idm345484992\" style=\"text-align: center\" data-type=\"equation\">2NO(<em>g<\/em>) + Cl2(<em>g<\/em>)\u00a0 \u27f6\u00a0 2NOCl(<em>g<\/em>)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm345501040\">To derive a rate law from this mechanism, first write rate laws for each of the two steps.<\/p>\r\n\r\n<div id=\"fs-idm514969616\" style=\"padding-left: 40px\" data-type=\"equation\">rate<sub>1<\/sub> = <em>k<\/em><sub>1<\/sub>[NO][Cl<sub>2<\/sub>]\u00a0 \u00a0 \u00a0(for the forward reaction of step 1)<\/div>\r\n<div style=\"padding-left: 40px\" data-type=\"equation\">rate<sub>-1<\/sub> = <em>k<\/em><sub>-1<\/sub>[NOCl<sub>2<\/sub>]\u00a0 \u00a0 \u00a0(for the reverse reaction of step 1)<\/div>\r\n<div style=\"padding-left: 40px\" data-type=\"equation\">rate<sub>2<\/sub> = <em>k<\/em><sub>2<\/sub>[NOCl<sub>2<\/sub>][NO]\u00a0 \u00a0 \u00a0(for step 2)<\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm328804768\">Step 2 is the rate-determining step, and so the rate law for the overall reaction should be the same as for this step. However, the step 2 rate law, as written, contains an intermediate species concentration, [NOCl<sub>2<\/sub>]. To remedy this, use the first step\u2019s rate laws to derive an expression for the intermediate concentration in terms of the reactant concentrations.<\/p>\r\n<p id=\"fs-idm328530432\">Assuming step 1 is at equilibrium:<\/p>\r\n\r\n<div id=\"fs-idm386271152\" data-type=\"equation\">\r\n<div style=\"text-align: center\" data-type=\"equation\">rate<sub>1<\/sub> = rate<sub>-1<\/sub><\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\"><em>k<\/em><sub>1<\/sub>[NO][Cl<sub>2<\/sub>] = <em>k<\/em><sub>-1<\/sub>[NOCl<sub>2<\/sub>]<\/div>\r\n<div style=\"text-align: center\" data-type=\"equation\"><img class=\"alignnone wp-image-1749\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6c-300x53.png\" alt=\"\" width=\"255\" height=\"45\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<\/div>\r\n<p id=\"fs-idm385514496\">Substituting this expression into the rate law for step 2 yields:<\/p>\r\n\r\n<div id=\"fs-idm373566368\" data-type=\"equation\"><img class=\"wp-image-1750 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/d-300x59.png\" alt=\"\" width=\"259\" height=\"51\" \/><\/div>\r\n<div data-type=\"equation\"><\/div>\r\n<p id=\"fs-idm328658256\"><strong>Check Your Learning:<\/strong><\/p>\r\nThe first step of a proposed multistep mechanism is:\r\n<div id=\"fs-idm389297024\" style=\"text-align: center\" data-type=\"equation\">F<sub>2<\/sub>(g) \u21cc\u00a0 2F(g)\u00a0 \u00a0 \u00a0(fast)<\/div>\r\n<p id=\"fs-idm373041168\">Derive the equation relating atomic fluorine concentration to molecular fluorine concentration.<\/p>\r\n&nbsp;\r\n<div id=\"fs-idm330964176\" data-type=\"note\">\r\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\r\n<p id=\"fs-idm361032656\"><img class=\"alignnone wp-image-1751\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6d.png\" alt=\"\" width=\"177\" height=\"60\" \/><\/p>\r\n\r\n<\/div>\r\n<\/div>\r\n<\/div>\r\n<div id=\"fs-idp145811120\" class=\"summary\" data-depth=\"1\">\r\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\r\n<p id=\"fs-idp240124176\">The sequence of individual steps, or elementary reactions, by which reactants are converted into products during the course of a reaction is called the reaction mechanism. The molecularity of an elementary reaction is the number of reactant species involved, typically one (unimolecular), two (bimolecular), or, less commonly, three (termolecular). The overall rate of a reaction is determined by the rate of the slowest in its mechanism, called the rate-determining step. Unimolecular elementary reactions have first-order rate laws, while bimolecular elementary reactions have second-order rate laws. By comparing the rate laws derived from a reaction mechanism to that determined experimentally, the mechanism may be deemed either incorrect or plausible.<\/p>\r\n\r\n<\/div>\r\n<div data-type=\"footnote-refs\">\r\n\r\n&nbsp;\r\n\r\n<\/div>\r\n<div class=\"textbox shaded\" data-type=\"glossary\">\r\n<h3 data-type=\"glossary-title\"><strong>Glossary<\/strong><\/h3>\r\n<dl id=\"fs-idp131244384\">\r\n \t<dt>bimolecular reaction<\/dt>\r\n \t<dd id=\"fs-idm21928512\">elementary reaction involving two reactant species<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp36862592\">\r\n \t<dt>elementary reaction<\/dt>\r\n \t<dd id=\"fs-idp56117440\">reaction that takes place in a single step, precisely as depicted in its chemical equation<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp63453216\">\r\n \t<dt>intermediate<\/dt>\r\n \t<dd id=\"fs-idp42175008\">species produced in one step of a reaction mechanism and consumed in a subsequent step<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp7133520\">\r\n \t<dt>molecularity<\/dt>\r\n \t<dd id=\"fs-idp108318064\">number of reactant species involved in an elementary reaction<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp105000160\">\r\n \t<dt>rate-determining step<\/dt>\r\n \t<dd id=\"fs-idp105335120\">(also, rate-limiting step) slowest elementary reaction in a reaction mechanism; determines the rate of the overall reaction<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp154473568\">\r\n \t<dt>reaction mechanism<\/dt>\r\n \t<dd id=\"fs-idp74962800\">stepwise sequence of elementary reactions by which a chemical change takes place<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idp251542624\">\r\n \t<dt>termolecular reaction<\/dt>\r\n \t<dd id=\"fs-idp96748560\">elementary reaction involving three reactant species<\/dd>\r\n<\/dl>\r\n<dl id=\"fs-idm2926992\">\r\n \t<dt>unimolecular reaction<\/dt>\r\n \t<dd id=\"fs-idp46376128\">elementary reaction involving a single reactant species<\/dd>\r\n<\/dl>\r\n<\/div>","rendered":"<p><strong><span style=\"font-family: 'Cormorant Garamond', serif;font-size: 1.602em;background-color: #cbd4b6;color: #000000\">Learning Objectives<\/span><\/strong><\/p>\n<div class=\"textbox textbox--learning-objectives\">\n<p>By the end of this section, you will be able to:<\/p>\n<ul>\n<li>Distinguish net reactions from elementary reactions (steps)<\/li>\n<li>Identify the molecularity of elementary reactions<\/li>\n<li>Write a balanced chemical equation for a process given its reaction mechanism<\/li>\n<li>Derive the rate law consistent with a given reaction mechanism<\/li>\n<\/ul>\n<\/div>\n<p id=\"fs-idp19792192\">Chemical reactions very often occur in a step-wise fashion, involving two or more distinct reactions taking place in sequence. A balanced equation indicates what is reacting and what is produced, but it reveals no details about how the reaction actually takes place. The <strong>reaction mechanism<\/strong> (or reaction path) provides details regarding the precise, step-by-step process by which a reaction occurs.<\/p>\n<p id=\"fs-idm10360272\">The decomposition of ozone, for example, appears to follow a mechanism with two steps:<\/p>\n<div id=\"fs-idp10305696\" style=\"text-align: center\" data-type=\"equation\">O<sub>3<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 O<sub>2<\/sub>(<em>g<\/em>) + O(<em>g<\/em>)<\/div>\n<div style=\"text-align: center\" data-type=\"equation\">O(<em>g<\/em>) + O<sub>3<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 2O<sub>2<\/sub>(<em>g<\/em>)<\/div>\n<p id=\"fs-idm40865648\">Each of the steps in a reaction mechanism is an <strong>elementary reaction<\/strong>. These elementary reactions occur precisely as represented in the step equations, and they must sum to yield the balanced chemical equation representing the overall reaction:<\/p>\n<div id=\"fs-idp143616928\" style=\"text-align: center\" data-type=\"equation\">2O<sub>3<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 3O<sub>2<\/sub>(<em>g<\/em>)<\/div>\n<p id=\"fs-idp205634512\">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>.<\/p>\n<p id=\"fs-idp6340064\">While the overall reaction equation for the decomposition of ozone indicates that two molecules of ozone react to give three molecules of oxygen, the mechanism of the reaction <em data-effect=\"italics\">does not involve the direct collision and reaction of two ozone molecules<\/em>. Instead, one O<sub>3<\/sub> decomposes to yield O<sub>2<\/sub> and an oxygen atom, and a second O<sub>3<\/sub> molecule subsequently reacts with the oxygen atom to yield two additional O<sub>2<\/sub> molecules.<\/p>\n<p id=\"fs-idm500275472\">Unlike balanced equations representing an overall reaction, the equations for elementary reactions are explicit representations of the chemical change taking place. The reactant(s) in an elementary reaction\u2019s equation undergo only the bond-breaking and\/or making events depicted to yield the product(s). For this reason, <em data-effect=\"italics\">the rate law for an elementary reaction may be derived directly from the balanced chemical equation describing the reaction<\/em>. This is not the case for typical chemical reactions, for which rate laws may be reliably determined only via experimentation.<\/p>\n<div id=\"fs-idp262348128\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Unimolecular Elementary Reactions<\/strong><\/h3>\n<p id=\"fs-idp205522704\">The <strong>molecularity <\/strong>of an elementary reaction is the number of reactant species (atoms, molecules, or ions). For example, a <strong>unimolecular reaction<\/strong> involves the reaction of a <em data-effect=\"italics\">single<\/em> reactant species to produce one or more molecules of product:<\/p>\n<div id=\"fs-idp34074352\" style=\"text-align: center\" data-type=\"equation\"><em>A<\/em>\u00a0 \u27f6\u00a0 products<\/div>\n<p id=\"fs-idp13674832\">The rate law for a unimolecular reaction is first order:<\/p>\n<div id=\"fs-idm26736096\" style=\"text-align: center\" data-type=\"equation\">rate = <em>k<\/em>[<em>A<\/em>]<\/div>\n<p id=\"fs-idp203524640\">A unimolecular reaction may be one of several elementary reactions in a complex mechanism. For example, the reaction:<\/p>\n<div id=\"fs-idp16624720\" style=\"text-align: center\" data-type=\"equation\">O<sub>3<\/sub>\u00a0 \u27f6\u00a0 O<sub>2<\/sub> + O<\/div>\n<p id=\"fs-idp196763520\">illustrates a unimolecular elementary reaction that occurs as one part of a two-step reaction mechanism as described above. However, some unimolecular reactions may be the only step of a single-step reaction mechanism. (In other words, an \u201coverall\u201d reaction may also be an elementary reaction in some cases.) For example, the gas-phase decomposition of cyclobutane, C<sub>4<\/sub>H<sub>8<\/sub>, to ethylene, C<sub>2<\/sub>H<sub>4<\/sub>, is represented by the following chemical equation:<\/p>\n<p><span id=\"fs-idp32755824\" class=\"scaled-down\" data-type=\"media\" data-alt=\"In this figure, structural formulas are used to illustrate a chemical reaction. On the left, a structural formula for cyclobutane is shown. This structure is composed of 4 C atoms connected with single bonds in a square shape. Each C atom is bonded to two other C atoms in the structure, leaving two bonds for H atoms pointing outward above, below, left, and right. An arrow points right to two identical ethane molecules with a plus symbol between them. Each of these molecules contains two C atoms connected with a double bond oriented vertically between them. The C atom at the top of these molecules has H atoms bonded above to the right and left. Similarly, the lower C atom has two H atoms bonded below to the right and left.\"><img loading=\"lazy\" decoding=\"async\" class=\"\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_06_CyclobD_img-2.jpg\" alt=\"In this figure, structural formulas are used to illustrate a chemical reaction. On the left, a structural formula for cyclobutane is shown. This structure is composed of 4 C atoms connected with single bonds in a square shape. Each C atom is bonded to two other C atoms in the structure, leaving two bonds for H atoms pointing outward above, below, left, and right. An arrow points right to two identical ethane molecules with a plus symbol between them. Each of these molecules contains two C atoms connected with a double bond oriented vertically between them. The C atom at the top of these molecules has H atoms bonded above to the right and left. Similarly, the lower C atom has two H atoms bonded below to the right and left.\" width=\"518\" height=\"161\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<p id=\"fs-idp100963616\">This equation represents the overall reaction observed, and it might also represent a legitimate unimolecular elementary reaction. The rate law predicted from this equation, assuming it is an elementary reaction, turns out to be the same as the rate law derived experimentally for the overall reaction, namely, one showing first-order behavior:<\/p>\n<div id=\"fs-idp67724640\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1747 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6a-300x82.png\" alt=\"\" width=\"238\" height=\"65\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6a-300x82.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6a-65x18.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6a-225x61.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6a-350x95.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6a.png 466w\" sizes=\"auto, (max-width: 238px) 100vw, 238px\" \/><\/div>\n<p id=\"fs-idp128923296\">This agreement between observed and predicted rate laws is interpreted to mean that the proposed unimolecular, single-step process is a reasonable mechanism for the butadiene reaction.<\/p>\n<\/div>\n<div id=\"fs-idp108234736\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Bimolecular Elementary Reactions<\/strong><\/h3>\n<p id=\"fs-idp87793216\">A <strong>bimolecular reaction<\/strong> involves two reactant species, for example:<\/p>\n<div id=\"fs-idp211065760\" style=\"text-align: center\" data-type=\"equation\"><em>A<\/em> + <em>B<\/em>\u00a0 \u27f6\u00a0 products<\/div>\n<div style=\"text-align: center\" data-type=\"equation\">and<\/div>\n<div style=\"text-align: center\" data-type=\"equation\">2<em>A<\/em>\u00a0 \u27f6\u00a0 products<\/div>\n<p id=\"fs-idm80729584\">For the first type, in which the two reactant molecules are different, the rate law is first-order in <em data-effect=\"italics\">A<\/em> and first order in <em data-effect=\"italics\">B<\/em> (second-order overall):<\/p>\n<div id=\"fs-idm26928768\" style=\"text-align: center\" data-type=\"equation\">\u00a0rate = <em>k<\/em>[<em>A<\/em>][<em>B<\/em>]<\/div>\n<p id=\"fs-idp220120832\">For the second type, in which two identical molecules collide and react, the rate law is second order in <em data-effect=\"italics\">A<\/em>:<\/p>\n<div id=\"fs-idp93993280\" style=\"text-align: center\" data-type=\"equation\">rate = k[<em>A<\/em>][<em>A<\/em>] = k[<em>A<\/em>]<sup>2<\/sup><\/div>\n<p id=\"fs-idp43609744\">Some chemical reactions occur by mechanisms that consist of a single bimolecular elementary reaction. One example is the reaction of nitrogen dioxide with carbon monoxide:<\/p>\n<div id=\"fs-idm24253872\" style=\"text-align: center\" data-type=\"equation\">NO<sub>2<\/sub>(<em>g<\/em>) + CO(<em>g<\/em>)\u00a0 \u27f6\u00a0 NO(<em>g<\/em>) + CO<sub>2<\/sub>(<em>g<\/em>)<\/div>\n<p id=\"fs-idp38254032\">(see <a class=\"autogenerated-content\" href=\"#CNX_Chem_12_06_BimoElRe\">(Figure)<\/a>)<\/p>\n<div id=\"CNX_Chem_12_06_BimoElRe\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">The probable mechanism for the reaction between NO<sub>2<\/sub> and CO to yield NO and CO<sub>2<\/sub>.<\/div>\n<p><span id=\"fs-idp70495312\" data-type=\"media\" data-alt=\"This figure provides an illustration of a reaction between two H I molecules using space filling models. H atoms are shown as white spheres, and I atoms are shown as purple spheres. On the left, two H I molecules are shownwith a small white sphere bonded to a much larger purple sphere. The label, \u201cTwo H I molecules,\u201d appears below. An arrow points right to a similar structure in which the two molecules appear pushed together, so that the purple spheres of the two molecules are touching. Below appears the label, \u201cTransition state.\u201d Following another arrow, two white spheres are shown vertically oriented and bonded together with the label, \u201cH subscript 2\u201d above. The H subscript 2 molecule is followed by a plus sign and two purple spheres bonded together with the label, \u201cI subscript 2\u201d above. Below these structures is the label, \u201cHydrogen iodide molecules decompose to produce hydrogen H subscript 2 and iodine I subscript 2.\u201d\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_06_BimoElRe-2.jpg\" alt=\"This figure provides an illustration of a reaction between two H I molecules using space filling models. H atoms are shown as white spheres, and I atoms are shown as purple spheres. On the left, two H I molecules are shownwith a small white sphere bonded to a much larger purple sphere. The label, \u201cTwo H I molecules,\u201d appears below. An arrow points right to a similar structure in which the two molecules appear pushed together, so that the purple spheres of the two molecules are touching. Below appears the label, \u201cTransition state.\u201d Following another arrow, two white spheres are shown vertically oriented and bonded together with the label, \u201cH subscript 2\u201d above. The H subscript 2 molecule is followed by a plus sign and two purple spheres bonded together with the label, \u201cI subscript 2\u201d above. Below these structures is the label, \u201cHydrogen iodide molecules decompose to produce hydrogen H subscript 2 and iodine I subscript 2.\u201d\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idp38432416\">Bimolecular elementary reactions may also be involved as steps in a multistep reaction mechanism. The reaction of atomic oxygen with ozone is the second step of the two-step ozone decomposition mechanism discussed earlier in this section:<\/p>\n<div id=\"fs-idp100763440\" style=\"text-align: center\" data-type=\"equation\">O(<em>g<\/em>) + O<sub>3<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 2O<sub>2<\/sub>(<em>g<\/em>)<\/div>\n<\/div>\n<div id=\"fs-idp38909440\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Termolecular Elementary Reactions<\/strong><\/h3>\n<p id=\"fs-idm9155392\">An elementary<strong> termolecular reaction<\/strong> involves the simultaneous collision of three atoms, molecules, or ions. Termolecular elementary reactions are uncommon because the probability of three particles colliding simultaneously is less than one one-thousandth of the probability of two particles colliding. There are, however, a few established termolecular elementary reactions. The reaction of nitrogen monoxide with oxygen appears to involve termolecular steps:<\/p>\n<div id=\"fs-idp196238032\" style=\"text-align: center\" data-type=\"equation\">2NO + O<sub>2<\/sub>\u00a0 \u27f6\u00a0 2NO<sub>2<\/sub><\/div>\n<div style=\"text-align: center\" data-type=\"equation\">rate = <em>k<\/em>[NO]<sup>2<\/sup>[O<sub>2<\/sub>]<\/div>\n<p id=\"fs-idp136937056\">Likewise, the reaction of nitrogen monoxide with chlorine appears to involve termolecular steps:<\/p>\n<div id=\"fs-idp128771280\" style=\"text-align: center\" data-type=\"equation\">2NO + Cl<sub>2<\/sub>\u00a0 \u27f6\u00a0 2NOCl<\/div>\n<div style=\"text-align: center\" data-type=\"equation\">rate = <em>k<\/em>[NO]<sup>2<\/sup>[Cl<sub>2<\/sub>]<\/div>\n<\/div>\n<div id=\"fs-idp270477600\" class=\"bc-section section\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Relating Reaction Mechanisms to Rate Laws<\/strong><\/h3>\n<p id=\"fs-idp253615520\">It\u2019s often the case that one step in a multistep reaction mechanism is significantly slower than the others. Because a reaction cannot proceed faster than its slowest step, this step will limit the rate at which the overall reaction occurs. The slowest step is therefore called the <strong>rate-determining step<\/strong> (or rate-limiting step) of the reaction <a class=\"autogenerated-content\" href=\"#CNX_Chem_12_06_Cattle\">(Figure)<\/a>.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"CNX_Chem_12_06_Cattle\" class=\"scaled-down\">\n<div class=\"bc-figcaption figcaption\">A cattle chute is a nonchemical example of a rate-determining step. Cattle can only be moved from one holding pen to another as quickly as one animal can make its way through the chute. (credit: Loren Kerns)<\/div>\n<p><span id=\"fs-idp96445120\" data-type=\"media\" data-alt=\"A photo is shown of cattle passing through a narrow chute into a holding pen. A person directs them through the gate with a long white and red pole.\"><img decoding=\"async\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/CNX_Chem_12_06_Cattle-2.jpg\" alt=\"A photo is shown of cattle passing through a narrow chute into a holding pen. A person directs them through the gate with a long white and red pole.\" data-media-type=\"image\/jpeg\" \/><\/span><\/p>\n<\/div>\n<p id=\"fs-idp41680064\">As described earlier, rate laws may be derived directly from the chemical equations for elementary reactions. This is not the case, however, for ordinary chemical reactions. The balanced equations most often encountered represent the overall change for some chemical system, and very often this is the result of some multistep reaction mechanisms. In every case, the rate law must be determined from experimental data and the reaction mechanism subsequently deduced from the rate law (and sometimes from other data). The reaction of NO<sub>2<\/sub> and CO provides an illustrative example:<\/p>\n<div id=\"fs-idp193034480\" style=\"text-align: center\" data-type=\"equation\">NO<sub>2<\/sub>(<em>g<\/em>) + CO(<em>g<\/em>)\u00a0 \u27f6\u00a0 \u00a0CO<sub>2<\/sub>(<em>g<\/em>) + NO(<em>g<\/em>)<\/div>\n<p id=\"fs-idp18907792\">For temperatures above 225 \u00b0C, the rate law has been found to be:<\/p>\n<div id=\"fs-idp70556928\" style=\"text-align: center\" data-type=\"equation\">\u00a0rate = <em>k<\/em>[NO<sub>2<\/sub>][CO]<\/div>\n<p id=\"fs-idp43466688\">The reaction is first order with respect to NO<sub>2<\/sub> and first-order with respect to CO. This is consistent with a single-step bimolecular mechanism and it is <em data-effect=\"italics\">possible<\/em> that this is the mechanism for this reaction at high temperatures.<\/p>\n<p id=\"fs-idp232335904\">At temperatures below 225 \u00b0C<em data-effect=\"italics\">,<\/em> the reaction is described by a rate law that is second order with respect to NO<sub>2<\/sub>:<\/p>\n<div id=\"fs-idm80864896\" style=\"text-align: center\" data-type=\"equation\">rate = <em>k<\/em>[NO<sub>2<\/sub>]<sup>2<\/sup><\/div>\n<p id=\"fs-idp70725520\">This rate law is not consistent with the single-step mechanism, but is consistent with the following two-step mechanism:<\/p>\n<div id=\"fs-idp34145072\" style=\"text-align: center\" data-type=\"equation\">NO<sub>2<\/sub>(<em>g<\/em>) + NO<sub>2<\/sub>(<em>g<\/em>)\u00a0 \u27f6\u00a0 NO<sub>3<\/sub>(<em>g<\/em>) + NO(<em>g<\/em>)\u00a0 \u00a0 \u00a0(slow)<\/div>\n<div style=\"text-align: center\" data-type=\"equation\">NO<sub>3<\/sub>(<em>g<\/em>) + CO(<em>g<\/em>)\u00a0 \u27f6\u00a0 NO<sub>2<\/sub>(<em>g<\/em>)+CO<sub>2<\/sub>(<em>g<\/em>)\u00a0 \u00a0 \u00a0(fast)<\/div>\n<p id=\"fs-idp107509104\">The rate-determining (slower) step gives a rate law showing second-order dependence on the NO<sub>2<\/sub> concentration, and the sum of the two equations gives the net overall reaction.<\/p>\n<p id=\"fs-idp37457664\">In general, when the rate-determining (slower) step is the first step in a mechanism, the rate law for the overall reaction is the same as the rate law for this step. However, when the rate-determining step is preceded by a step involving a rapidly reversible reaction the rate law for the overall reaction may be more difficult to derive.<\/p>\n<p id=\"fs-idp17102832\">As discussed in several chapters of this text, a reversible reaction is at <em data-effect=\"italics\">equilibrium<\/em> when the rates of the forward and reverse processes are equal. Consider the reversible elementary reaction in which NO dimerizes to yield an intermediate species N<sub>2<\/sub>O<sub>2<\/sub>. When this reaction is at equilibrium:<\/p>\n<div id=\"fs-idp65516752\" style=\"text-align: center\" data-type=\"equation\">NO + NO\u00a0 \u21cc\u00a0 N<sub>2<\/sub>O<sub>2<\/sub><\/div>\n<div style=\"text-align: center\" data-type=\"equation\">rate<sub>forward<\/sub> = rate<sub>reverse<\/sub><\/div>\n<div style=\"text-align: center\" data-type=\"equation\">k<sub>1<\/sub>[NO]<sup>2<\/sup> = k<sub>-1<\/sub>[N<sub>2<\/sub>O<sub>2<\/sub>]<\/div>\n<p id=\"fs-idm76069968\">This expression may be rearranged to express the concentration of the intermediate in terms of the reactant NO:<\/p>\n<div id=\"fs-idp95214240\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1748 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6b-300x113.png\" alt=\"\" width=\"199\" height=\"75\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6b-300x113.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6b-65x25.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6b-225x85.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6b.png 350w\" sizes=\"auto, (max-width: 199px) 100vw, 199px\" \/><\/div>\n<p id=\"fs-idp32322000\">Since intermediate species concentrations are not used in formulating rate laws for overall reactions, this approach is sometimes necessary, as illustrated in the following example exercise.<\/p>\n<div id=\"fs-idp252983408\" class=\"textbox textbox--examples\" data-type=\"example\">\n<p id=\"fs-idm378927696\"><strong>Deriving a Rate Law from a Reaction Mechanism:<\/strong><\/p>\n<p>The two-step mechanism below has been proposed for a reaction between nitrogen monoxide and molecular chlorine:<\/p>\n<div id=\"fs-idm496065264\" style=\"padding-left: 40px\" data-type=\"equation\">Step 1:\u00a0 NO(<em>g<\/em>) + Cl<sub>2<\/sub>(<em>g<\/em>)\u00a0 \u21cc\u00a0 NOCl<sub>2<\/sub>(<em>g<\/em>)\u00a0 \u00a0 \u00a0(fast)<\/div>\n<div style=\"padding-left: 40px\" data-type=\"equation\">Step 2:\u00a0 NOCl<sub>2<\/sub>(<em>g<\/em>) + NO(<em>g<\/em>)\u00a0 \u27f6\u00a0 2NOCl(<em>g<\/em>)\u00a0 \u00a0 \u00a0(slow)<\/div>\n<p id=\"fs-idm352158848\">Use this mechanism to derive the equation and predicted rate law for the overall reaction.<\/p>\n<p id=\"fs-idm359312208\"><strong>Solution:<\/strong><\/p>\n<p>The equation for the overall reaction is obtained by adding the two elementary reactions:<\/p>\n<div id=\"fs-idm345484992\" style=\"text-align: center\" data-type=\"equation\">2NO(<em>g<\/em>) + Cl2(<em>g<\/em>)\u00a0 \u27f6\u00a0 2NOCl(<em>g<\/em>)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm345501040\">To derive a rate law from this mechanism, first write rate laws for each of the two steps.<\/p>\n<div id=\"fs-idm514969616\" style=\"padding-left: 40px\" data-type=\"equation\">rate<sub>1<\/sub> = <em>k<\/em><sub>1<\/sub>[NO][Cl<sub>2<\/sub>]\u00a0 \u00a0 \u00a0(for the forward reaction of step 1)<\/div>\n<div style=\"padding-left: 40px\" data-type=\"equation\">rate<sub>-1<\/sub> = <em>k<\/em><sub>-1<\/sub>[NOCl<sub>2<\/sub>]\u00a0 \u00a0 \u00a0(for the reverse reaction of step 1)<\/div>\n<div style=\"padding-left: 40px\" data-type=\"equation\">rate<sub>2<\/sub> = <em>k<\/em><sub>2<\/sub>[NOCl<sub>2<\/sub>][NO]\u00a0 \u00a0 \u00a0(for step 2)<\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm328804768\">Step 2 is the rate-determining step, and so the rate law for the overall reaction should be the same as for this step. However, the step 2 rate law, as written, contains an intermediate species concentration, [NOCl<sub>2<\/sub>]. To remedy this, use the first step\u2019s rate laws to derive an expression for the intermediate concentration in terms of the reactant concentrations.<\/p>\n<p id=\"fs-idm328530432\">Assuming step 1 is at equilibrium:<\/p>\n<div id=\"fs-idm386271152\" data-type=\"equation\">\n<div style=\"text-align: center\" data-type=\"equation\">rate<sub>1<\/sub> = rate<sub>-1<\/sub><\/div>\n<div style=\"text-align: center\" data-type=\"equation\"><em>k<\/em><sub>1<\/sub>[NO][Cl<sub>2<\/sub>] = <em>k<\/em><sub>-1<\/sub>[NOCl<sub>2<\/sub>]<\/div>\n<div style=\"text-align: center\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1749\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6c-300x53.png\" alt=\"\" width=\"255\" height=\"45\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6c-300x53.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6c-65x11.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6c-225x40.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6c-350x62.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6c.png 483w\" sizes=\"auto, (max-width: 255px) 100vw, 255px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<\/div>\n<p id=\"fs-idm385514496\">Substituting this expression into the rate law for step 2 yields:<\/p>\n<div id=\"fs-idm373566368\" data-type=\"equation\"><img loading=\"lazy\" decoding=\"async\" class=\"wp-image-1750 aligncenter\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/d-300x59.png\" alt=\"\" width=\"259\" height=\"51\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/d-300x59.png 300w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/d-65x13.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/d-225x44.png 225w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/d-350x68.png 350w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/d.png 594w\" sizes=\"auto, (max-width: 259px) 100vw, 259px\" \/><\/div>\n<div data-type=\"equation\"><\/div>\n<p id=\"fs-idm328658256\"><strong>Check Your Learning:<\/strong><\/p>\n<p>The first step of a proposed multistep mechanism is:<\/p>\n<div id=\"fs-idm389297024\" style=\"text-align: center\" data-type=\"equation\">F<sub>2<\/sub>(g) \u21cc\u00a0 2F(g)\u00a0 \u00a0 \u00a0(fast)<\/div>\n<p id=\"fs-idm373041168\">Derive the equation relating atomic fluorine concentration to molecular fluorine concentration.<\/p>\n<p>&nbsp;<\/p>\n<div id=\"fs-idm330964176\" data-type=\"note\">\n<div data-type=\"title\"><strong>Answer:<\/strong><\/div>\n<p id=\"fs-idm361032656\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-1751\" src=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6d.png\" alt=\"\" width=\"177\" height=\"60\" srcset=\"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6d.png 256w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6d-65x22.png 65w, https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-content\/uploads\/sites\/1463\/2021\/07\/12.6d-225x76.png 225w\" sizes=\"auto, (max-width: 177px) 100vw, 177px\" \/><\/p>\n<\/div>\n<\/div>\n<\/div>\n<div id=\"fs-idp145811120\" class=\"summary\" data-depth=\"1\">\n<h3 data-type=\"title\"><strong>Key Concepts and Summary<\/strong><\/h3>\n<p id=\"fs-idp240124176\">The sequence of individual steps, or elementary reactions, by which reactants are converted into products during the course of a reaction is called the reaction mechanism. The molecularity of an elementary reaction is the number of reactant species involved, typically one (unimolecular), two (bimolecular), or, less commonly, three (termolecular). The overall rate of a reaction is determined by the rate of the slowest in its mechanism, called the rate-determining step. Unimolecular elementary reactions have first-order rate laws, while bimolecular elementary reactions have second-order rate laws. By comparing the rate laws derived from a reaction mechanism to that determined experimentally, the mechanism may be deemed either incorrect or plausible.<\/p>\n<\/div>\n<div data-type=\"footnote-refs\">\n<p>&nbsp;<\/p>\n<\/div>\n<div class=\"textbox shaded\" data-type=\"glossary\">\n<h3 data-type=\"glossary-title\"><strong>Glossary<\/strong><\/h3>\n<dl id=\"fs-idp131244384\">\n<dt>bimolecular reaction<\/dt>\n<dd id=\"fs-idm21928512\">elementary reaction involving two reactant species<\/dd>\n<\/dl>\n<dl id=\"fs-idp36862592\">\n<dt>elementary reaction<\/dt>\n<dd id=\"fs-idp56117440\">reaction that takes place in a single step, precisely as depicted in its chemical equation<\/dd>\n<\/dl>\n<dl id=\"fs-idp63453216\">\n<dt>intermediate<\/dt>\n<dd id=\"fs-idp42175008\">species produced in one step of a reaction mechanism and consumed in a subsequent step<\/dd>\n<\/dl>\n<dl id=\"fs-idp7133520\">\n<dt>molecularity<\/dt>\n<dd id=\"fs-idp108318064\">number of reactant species involved in an elementary reaction<\/dd>\n<\/dl>\n<dl id=\"fs-idp105000160\">\n<dt>rate-determining step<\/dt>\n<dd id=\"fs-idp105335120\">(also, rate-limiting step) slowest elementary reaction in a reaction mechanism; determines the rate of the overall reaction<\/dd>\n<\/dl>\n<dl id=\"fs-idp154473568\">\n<dt>reaction mechanism<\/dt>\n<dd id=\"fs-idp74962800\">stepwise sequence of elementary reactions by which a chemical change takes place<\/dd>\n<\/dl>\n<dl id=\"fs-idp251542624\">\n<dt>termolecular reaction<\/dt>\n<dd id=\"fs-idp96748560\">elementary reaction involving three reactant species<\/dd>\n<\/dl>\n<dl id=\"fs-idm2926992\">\n<dt>unimolecular reaction<\/dt>\n<dd id=\"fs-idp46376128\">elementary reaction involving a single reactant species<\/dd>\n<\/dl>\n<\/div>\n","protected":false},"author":1392,"menu_order":7,"template":"","meta":{"pb_show_title":"on","pb_short_title":"","pb_subtitle":"","pb_authors":[],"pb_section_license":""},"chapter-type":[48],"contributor":[],"license":[],"class_list":["post-727","chapter","type-chapter","status-publish","hentry","chapter-type-numberless"],"part":695,"_links":{"self":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/727","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters"}],"about":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/types\/chapter"}],"author":[{"embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/users\/1392"}],"version-history":[{"count":10,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/727\/revisions"}],"predecessor-version":[{"id":2164,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/727\/revisions\/2164"}],"part":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/parts\/695"}],"metadata":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapters\/727\/metadata\/"}],"wp:attachment":[{"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/media?parent=727"}],"wp:term":[{"taxonomy":"chapter-type","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/pressbooks\/v2\/chapter-type?post=727"},{"taxonomy":"contributor","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/contributor?post=727"},{"taxonomy":"license","embeddable":true,"href":"https:\/\/pressbooks.bccampus.ca\/aperrott\/wp-json\/wp\/v2\/license?post=727"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}