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<title>Arrhenius plot</title>

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<span id="openzim-page-title" class="mw-page-title-main"><span class="mw-page-title-main">Arrhenius plot</span></span>

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<p>In <a href="Chemical_kinetics" title="Chemical kinetics">chemical kinetics</a>, an <b>Arrhenius plot</b> displays the logarithm of a <a href="Reaction_rate_constant" title="Reaction rate constant">reaction rate constant</a>, <span class="nowrap">(<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ln(k)}">

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<annotation encoding="application/x-tex">{\displaystyle \ln(k)}</annotation>

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</math></span><img src="./7a3fbbb4019a9d7380367230d4ccd08d973fbe87.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:4.96ex; height:2.843ex;" alt="{\displaystyle \ln(k)}" loading="lazy"></span>,</span> <a href="Ordinate" class="mw-redirect" title="Ordinate">ordinate</a> axis) plotted against reciprocal of the temperature <span class="nowrap">(<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle 1/T}">

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<annotation encoding="application/x-tex">{\displaystyle 1/T}</annotation>

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</math></span><img src="./ee06bfe8f48b840ea1c11f78977a90f661f2375e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:3.961ex; height:2.843ex;" alt="{\displaystyle 1/T}" loading="lazy"></span>,</span> <a href="Abscissa" class="mw-redirect" title="Abscissa">abscissa</a>).<sup id="cite_ref-1" class="reference"><a href="#cite_note-1"><span class="cite-bracket">[</span>1<span class="cite-bracket">]</span></a></sup> Arrhenius plots are often used to analyze the effect of temperature on the rates of chemical reactions. For a single rate-limited thermally activated process, an Arrhenius plot gives a straight line, from which the <a href="Activation_energy" title="Activation energy">activation energy</a> and the <a href="Pre-exponential_factor" title="Pre-exponential factor">pre-exponential factor</a> can both be determined.

</p><p>The <a href="Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a> can be given in the form:

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<mfrac>

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<annotation encoding="application/x-tex">{\displaystyle k=A\exp \left({\frac {-E_{\text{a}}}{RT}}\right)=A\exp \left({\frac {-E_{\text{a}}'}{k_{\text{B}}T}}\right)}</annotation>

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where:

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<annotation encoding="application/x-tex">{\displaystyle k}</annotation>

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</math></span><img src="./c3c9a2c7b599b37105512c5d570edc034056dd40.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" loading="lazy"></span> = <a href="Rate_constant" class="mw-redirect" title="Rate constant">rate constant</a></li>

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span> = <a href="Pre-exponential_factor" title="Pre-exponential factor">pre-exponential factor</a></li>

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<annotation encoding="application/x-tex">{\displaystyle E_{\text{a}}}</annotation>

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</math></span><img src="./ff4a7ab091ebb02b9f0a1abb030d0177ac682dd4.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{\text{a}}}" loading="lazy"></span> = (molar) <a href="Activation_energy" title="Activation energy">activation energy</a></li>

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<annotation encoding="application/x-tex">{\displaystyle R}</annotation>

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</math></span><img src="./4b0bfb3769bf24d80e15374dc37b0441e2616e33.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" loading="lazy"></span> = <a href="Gas_constant" title="Gas constant">gas constant</a>, (<span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R=k_{\text{B}}N_{\text{A}}}">

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<annotation encoding="application/x-tex">{\displaystyle R=k_{\text{B}}N_{\text{A}}}</annotation>

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</math></span><img src="./b11d47d8f096170dac6b12bbcf733a4521871245.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:10.801ex; height:2.509ex;" alt="{\displaystyle R=k_{\text{B}}N_{\text{A}}}" loading="lazy"></span>, where <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle N_{\text{A}}}">

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<annotation encoding="application/x-tex">{\displaystyle N_{\text{A}}}</annotation>

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</math></span><img src="./037f8d054f445451d8fee1b440cddba989e66ea1.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:3.331ex; height:2.509ex;" alt="{\displaystyle N_{\text{A}}}" loading="lazy"></span> is the <a href="Avogadro_constant" title="Avogadro constant">Avogadro constant</a>).</li>

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<annotation encoding="application/x-tex">{\displaystyle E_{\text{a}}'}</annotation>

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</math></span><img src="./469ad462d35fa15c98971a49dcfdf2519d473624.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.769ex; height:2.509ex;" alt="{\displaystyle E_{\text{a}}'}" loading="lazy"></span> = <a href="Activation_energy" title="Activation energy">activation energy</a> (for a single reaction event)</li>

<msub>

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<annotation encoding="application/x-tex">{\displaystyle k_{\text{B}}}</annotation>

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</math></span><img src="./9582c7c795d2def2c061f0dfa3a6f0fb3dd2de44.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.607ex; height:2.509ex;" alt="{\displaystyle k_{\text{B}}}" loading="lazy"></span> = <a href="Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a></li>

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<annotation encoding="application/x-tex">{\displaystyle T}</annotation>

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</math></span><img src="./ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" loading="lazy"></span> = <a href="Absolute_temperature" class="mw-redirect" title="Absolute temperature">absolute temperature</a></li></ul>

<p>The only difference between the two forms of the expression is the quantity used for the activation energy: the former would have the unit <a href="Joule" title="Joule">joule</a>/<a href="Mole_(unit)" title="Mole (unit)">mole</a>, which is common in chemistry, while the latter would have the unit <a href="Joule" title="Joule">joule</a> and would be for one molecular reaction event, which is common in physics. The different units are accounted for in using either the <a href="Gas_constant" title="Gas constant">gas constant</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle R}">

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<annotation encoding="application/x-tex">{\displaystyle R}</annotation>

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</math></span><img src="./4b0bfb3769bf24d80e15374dc37b0441e2616e33.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.764ex; height:2.176ex;" alt="{\displaystyle R}" loading="lazy"></span> or the <a href="Boltzmann_constant" title="Boltzmann constant">Boltzmann constant</a> <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k_{\text{B}}}">

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<annotation encoding="application/x-tex">{\displaystyle k_{\text{B}}}</annotation>

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</math></span><img src="./9582c7c795d2def2c061f0dfa3a6f0fb3dd2de44.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:2.607ex; height:2.509ex;" alt="{\displaystyle k_{\text{B}}}" loading="lazy"></span>.

</p><p>Taking the <a href="Natural_logarithm" title="Natural logarithm">natural logarithm</a> of the former equation gives:

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<annotation encoding="application/x-tex">{\displaystyle \ln(k)=\ln(A)-{\frac {E_{\text{a}}}{R}}\left({\frac {1}{T}}\right)}</annotation>

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</p><p>When plotted in the manner described above, the value of the <a href="Y-intercept" title="Y-intercept">y-intercept</a> (at <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle x=1/T=0}">

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<annotation encoding="application/x-tex">{\displaystyle x=1/T=0}</annotation>

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</math></span><img src="./c20fe9246dd43477ca83e689eec7353a61d9a38f.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:12.65ex; height:2.843ex;" alt="{\displaystyle x=1/T=0}" loading="lazy"></span>) will correspond to <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \ln(A)}">

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<annotation encoding="application/x-tex">{\displaystyle \ln(A)}</annotation>

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</math></span><img src="./80f078da677978f3f2ba70d91db0d457b53e9dfe.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:5.492ex; height:2.843ex;" alt="{\displaystyle \ln(A)}" loading="lazy"></span>, and the <a href="Slope" title="Slope">slope</a> of the line will be equal to <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle -E_{\text{a}}/R}">

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<annotation encoding="application/x-tex">{\displaystyle -E_{\text{a}}/R}</annotation>

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</math></span><img src="./2c733fed482b2c13411b50d4093264d416f4251e.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:7.504ex; height:2.843ex;" alt="{\displaystyle -E_{\text{a}}/R}" loading="lazy"></span>. The values of y-intercept and slope can be determined from the experimental points using <a href="Simple_linear_regression" title="Simple linear regression">simple linear regression</a> with a <a href="Spreadsheet" title="Spreadsheet">spreadsheet</a>.

</p><p>The pre-exponential factor, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span>, is an empirical constant of proportionality which has been estimated by various theories which take into account factors such as the frequency of collision between reacting particles, their relative orientation, and the <a href="Entropy_of_activation" title="Entropy of activation">entropy of activation</a>.

</p><p>The expression <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle \exp(-E_{\text{a}}/RT)}">

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<annotation encoding="application/x-tex">{\displaystyle \exp(-E_{\text{a}}/RT)}</annotation>

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</math></span><img src="./232c97657b3c0dac2e99c29b9fb467d81de35f5d.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.838ex; width:14.502ex; height:2.843ex;" alt="{\displaystyle \exp(-E_{\text{a}}/RT)}" loading="lazy"></span> represents the fraction of the molecules present in a gas which have energies equal to or in excess of activation energy at a particular temperature. In almost all practical cases, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{a}}\gg RT}">

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<annotation encoding="application/x-tex">{\displaystyle E_{\text{a}}\gg RT}</annotation>

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</math></span><img src="./90a33f70949797ab4880eafad2fedaabca952911.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.784ex; height:2.509ex;" alt="{\displaystyle E_{\text{a}}\gg RT}" loading="lazy"></span>, so that this fraction is very small and increases rapidly with <span class="nowrap"><span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}">

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<annotation encoding="application/x-tex">{\displaystyle T}</annotation>

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</math></span><img src="./ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" loading="lazy"></span>.</span> In consequence, the reaction rate constant <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}">

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<annotation encoding="application/x-tex">{\displaystyle k}</annotation>

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</math></span><img src="./c3c9a2c7b599b37105512c5d570edc034056dd40.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" loading="lazy"></span> increases rapidly with temperature <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}">

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<annotation encoding="application/x-tex">{\displaystyle T}</annotation>

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</math></span><img src="./ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" loading="lazy"></span>, as shown in the direct plot of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}">

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<annotation encoding="application/x-tex">{\displaystyle k}</annotation>

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</math></span><img src="./c3c9a2c7b599b37105512c5d570edc034056dd40.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" loading="lazy"></span> against <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle T}">

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<annotation encoding="application/x-tex">{\displaystyle T}</annotation>

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</math></span><img src="./ec7200acd984a1d3a3d7dc455e262fbe54f7f6e0.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.636ex; height:2.176ex;" alt="{\displaystyle T}" loading="lazy"></span>. (Mathematically, at very high temperatures so that <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle E_{\text{a}}\ll RT}">

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<annotation encoding="application/x-tex">{\displaystyle E_{\text{a}}\ll RT}</annotation>

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</math></span><img src="./56843da305afce1848bff7dcb7b803718e497366.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.671ex; width:9.784ex; height:2.509ex;" alt="{\displaystyle E_{\text{a}}\ll RT}" loading="lazy"></span>, <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k}">

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<annotation encoding="application/x-tex">{\displaystyle k}</annotation>

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</math></span><img src="./c3c9a2c7b599b37105512c5d570edc034056dd40.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.211ex; height:2.176ex;" alt="{\displaystyle k}" loading="lazy"></span> would level off and approach <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle A}">

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<annotation encoding="application/x-tex">{\displaystyle A}</annotation>

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</math></span><img src="./7daff47fa58cdfd29dc333def748ff5fa4c923e3.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.743ex; height:2.176ex;" alt="{\displaystyle A}" loading="lazy"></span> as a limit, but this case does not occur under practical conditions.)

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<div class="mw-heading mw-heading2"><h2 id="Worked_example">Worked example</h2></div>

<p>Considering as example the decomposition of <a href="Nitrogen_dioxide" title="Nitrogen dioxide">nitrogen dioxide</a> into <a href="Nitrogen_monoxide" class="mw-redirect" title="Nitrogen monoxide">nitrogen monoxide</a> and molecular <a href="Oxygen" title="Oxygen">oxygen</a>:

</p>

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</style><span class="chemf nowrap">2 NO<sub class="template-chem2-sub">2</sub> → 2 NO + O<sub class="template-chem2-sub">2</sub></span></dd></dl>

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</style><div class="thumb tmulti tnone center"><div class="thumbinner multiimageinner" style="width:592px;max-width:592px"><div class="trow"><div class="tsingle" style="width:275px;max-width:275px"><div class="thumbimage" style="height:207px;overflow:hidden"><span typeof="mw:File"></span></div><div class="thumbcaption">Direct plot: <var style="padding-right: 1px;">k</var> against <var style="padding-right: 1px;">T</var></div></div><div class="tsingle" style="width:313px;max-width:313px"><div class="thumbimage" style="height:207px;overflow:hidden"><span typeof="mw:File"></span></div><div class="thumbcaption">Arrhenius plot: ln(<var style="padding-right: 1px;">k</var>) against 1/<var style="padding-right: 1px;">T</var>.</div></div></div></div></div></div>

<p>Based on the red "line of best fit" plotted in the graph given above:

</p>

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</style><div class="block-indent" style="padding-left: 1.5em;">Let y = ln(k [10<sup>−4</sup> cm<sup>3</sup> mol<sup>−1</sup> s<sup>−1</sup>])</div>

<p>Points read from graph:

</p>

<p>Slope of red line = (4.1 − 2.2) / (0.0015 − 0.00165) = −12,667

</p><p>Intercept [<i>y-value at x = 0</i>] of red line = 4.1 + (0.0015 × 12667) = 23.1

</p><p>Inserting these values into the form above:

<mfrac>

<msub>

</mrow>

</msub>

</mfrac>

</mrow>

<mrow>

<mfrac>

</mfrac>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \ln(k)=\ln(A)-{\frac {E_{a}}{R}}\left({\frac {1}{T}}\right)}</annotation>

</semantics>

</math></span></span>

yields:

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle \ln(k)=23.1-12,667(1/T)}</annotation>

</semantics>

</math></span></span>

</p>

<msup>

</mrow>

</msup>

<msup>

</mrow>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle k=e^{23.1}\cdot e^{-12,667/T}}</annotation>

</semantics>

</math></span></span>

</p><p>as shown in the plot at the right.

</p><p><span class="mwe-math-element mwe-math-element-block"><span class="mwe-math-mathml-display mwe-math-mathml-a11y" style="display: none;"><math display="block" xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle k=1.08\times 10^{10}\cdot e^{-12,667/T}}">

<msup>

</mrow>

</msup>

<msup>

</mrow>

</mrow>

</msup>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle k=1.08\times 10^{10}\cdot e^{-12,667/T}}</annotation>

</semantics>

</math></span></span>

for:

</p>

<p>Substituting for the quotient in the exponent of <span class="mwe-math-element mwe-math-element-inline"><span class="mwe-math-mathml-inline mwe-math-mathml-a11y" style="display: none;"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\displaystyle e}">

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle e}</annotation>

</semantics>

</math></span><img src="./cd253103f0876afc68ebead27a5aa9867d927467.svg" class="mwe-math-fallback-image-inline mw-invert skin-invert" aria-hidden="true" style="vertical-align: -0.338ex; width:1.083ex; height:1.676ex;" alt="{\displaystyle e}" loading="lazy"></span>:

<msub>

</mrow>

</msub>

</mrow>

</mrow>

</mstyle>

</mrow>

<annotation encoding="application/x-tex">{\displaystyle E_{a}/R=-12\,667\,\mathrm {K} }</annotation>

</semantics>

</math></span></span>

where the approximate value for <a href="Gas_constant" title="Gas constant">R</a> is 8.31446 J K<sup>−1</sup> mol<sup>−1</sup>

</p><p>The activation energy of this reaction from these data is then:

</p>

<ul><li><a href="Arrhenius_equation" title="Arrhenius equation">Arrhenius equation</a></li>

<li><a href="Eyring_equation" title="Eyring equation">Eyring equation</a></li>

<li><a href="Polymer_degradation" title="Polymer degradation">Polymer degradation</a></li></ul>

<div class="mw-heading mw-heading2"><h2 id="References">References</h2></div>

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</style><cite class="citation web cs1"><a rel="nofollow" class="external text" href="https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Supplemental_Modules_(Physical_and_Theoretical_Chemistry)/Kinetics/06%3A_Modeling_Reaction_Kinetics/6.02%3A_Temperature_Dependence_of_Reaction_Rates/6.2.03%3A_The_Arrhenius_Law/6.2.3.04%3A_The_Arrhenius_Law_-_Arrhenius_Plots">"6.2.3.4: The Arrhenius Law – Arrhenius Plots"</a>. <i>Chemistry LibreTexts</i>. 2013-10-02<span class="reference-accessdate">. Retrieved <span class="nowrap">2023-10-14</span></span>.</cite></span>

</li>

</ol></div></div></div><div><div class="zim-footer">

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