{"id":10711,"date":"2026-09-26T13:54:29","date_gmt":"2026-09-26T12:54:29","guid":{"rendered":"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/maxwell-boltzmann-distribution\/"},"modified":"2026-10-04T23:03:16","modified_gmt":"2026-10-04T22:03:16","slug":"maxwell-boltzmann-distribution","status":"publish","type":"page","link":"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/maxwell-boltzmann-distribution\/","title":{"rendered":"The Maxwell\u2013Boltzmann Distribution"},"content":{"rendered":"\n<section class=\"ols-revision-page ols-kinetics-equilibria-page\">\n  <style>\n    .ols-revision-page {\n      --navy: #1C244B;\n      --blue: #2563eb;\n      --soft-blue: #eef4ff;\n      --soft-red: #fff7f7;\n      --soft-purple: #f7f0ff;\n      --soft-green: #f0f7f1;\n      --gold: #c9973a;\n      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20px;\n      box-shadow: var(--inner-shadow);\n    }\n.ols-faq-item h3 {\n      margin: 0 0 8px;\n      font-size: 20px;\n      line-height: 1.3;\n      color: var(--navy);\n    }\n.ols-faq-item p {\n      margin: 0;\n      font-size: 16px;\n      line-height: 1.65;\n      color: var(--body-text);\n    }\n.ols-faq-card,\n      .ols-quicksnap-card,\n      .ols-attribution-card {\n        padding: 24px 18px;\n        border-radius: 22px;\n      }\n  <\/style>\n\n    <aside class=\"ols-sidebar\">\n  <div class=\"ols-sidebar-header\">\n    <h3>Revision Notes<\/h3>\n    <p>A Level Chemistry<\/p>\n  <\/div>\n\n  <div class=\"ols-topic-group\">\n    <h4>Topic 9 Kinetics &amp; Equilibria<\/h4>\n\n    <ul class=\"ols-topic-list\">\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/\">Topic 9 Overview<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/\">Topic 9A Kinetics<\/a>\n        <ul class=\"ols-subtopic-list\">\n          <li>\n            <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/collision-theory-and-rates-of-reaction\/\">Collision Theory and Rates of Reaction<\/a>\n          <\/li>\n          <li>\n            <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/measuring-and-calculating-rates\/\">Measuring and Calculating Rates<\/a>\n          <\/li>\n          <li>\n            <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/maxwell-boltzmann-distribution\/\">The Maxwell\u2013Boltzmann Distribution<\/a>\n          <\/li>\n          <li>\n            <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/catalysts-and-reaction-profiles\/\">Catalysts and Reaction Profiles<\/a>\n          <\/li>\n          <li>\n            <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/core-practicals\/cp-9a-9b-iodine-propanone-and-clock-reaction-kinetics\/\">Core Practical 9A\/9B<\/a>\n          <\/li>\n        <\/ul>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9b-equilibria\/\">Topic 9B Equilibria<\/a>\n        <ul class=\"ols-subtopic-list\">\n          <li>\n            <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9b-equilibria\/dynamic-equilibrium\/\">Dynamic Equilibrium<\/a>\n          <\/li>\n          <li>\n            <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9b-equilibria\/le-chateliers-principle\/\">Le Chatelier's Principle<\/a>\n          <\/li>\n          <li>\n            <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9b-equilibria\/equilibria-in-industry\/\">Equilibria in Industry<\/a>\n          <\/li>\n        <\/ul>\n      <\/li>\n    <\/ul>\n  <\/div>\n\n  <div class=\"ols-topic-group\">\n    <h4>Other Topics<\/h4>\n\n    <ul class=\"ols-topic-list\">\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-6-energetics\/\">Topic 6 Energetics<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-7-intermolecular-forces\/\">Topic 7 Intermolecular Forces<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-8-redox-chemistry-and-groups-1-2-and-7\/\">Topic 8 Redox &amp; Groups 1, 2 and 7<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/core-practicals\/\">Core Practicals<\/a>\n     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}\r\n})();\r\n<\/script>\r\n\n\n    <main class=\"ols-main\">\n\n      <!-- BREADCRUMBS - updated with full path and correct links -->\n      <nav class=\"ols-breadcrumbs\" aria-label=\"Breadcrumb\">\n<a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/\">Revision Notes<\/a> \/\n<a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/\">A Level Chemistry<\/a> \/\n<a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/\">Edexcel International<\/a> \/\n<a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/\">Topic 9 Kinetics and Equilibria<\/a> \/\n<a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/\">Topic 9A Kinetics<\/a> \/\n<span>The Maxwell\u2013Boltzmann Distribution<\/span>\n<\/nav>\n\n      <header class=\"ols-title-card\">\n        <h1>The Maxwell\u2013Boltzmann Distribution<\/h1>\n        <p class=\"ols-page-intro\">A concise revision guide to the Maxwell\u2013Boltzmann distribution: its shape and labels, the activation energy on the curve, why a small rise in temperature gives a large rise in rate, and how a catalyst changes the fraction of molecules able to react.<\/p>\n        <div class=\"ols-badges\">\n<div class=\"ols-badge\">Exam board: Edexcel International<\/div>\n<div class=\"ols-badge\">Unit 2: WCH12\/01<\/div>\n<div class=\"ols-badge\">Topic 9A Kinetics<\/div>\n<\/div>\n        <div class=\"ols-author\">\n\n    <img decoding=\"async\"\n      class=\"ols-author-avatar-img\"\n      src=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/05\/Author-Profile.jpeg\"\n      alt=\"Dr. Mohammed Al-Fatah\"\n    >\n\n    <div class=\"ols-author-content\">\n\n      <h2 class=\"ols-author-title\">\n        Written by: Dr. Mohammed Al-Fatah\n      <\/h2>\n\n      <p class=\"ols-author-description\">\n        Chemistry specialist revision notes for A Level Chemistry.\n      <\/p>\n\n      <a class=\"ols-linkedin-pill\" href=\"https:\/\/www.linkedin.com\/in\/doctormohammedfatah\/\" target=\"_blank\" rel=\"noopener noreferrer\">\n        <svg class=\"ols-linkedin-icon\" viewBox=\"0 0 24 24\" fill=\"currentColor\" aria-hidden=\"true\">\n          <path d=\"M4.98 3.5C4.98 4.88 3.86 6 2.48 6S0 4.88 0 3.5 1.12 1 2.48 1s2.5 1.12 2.5 2.5zM.5 8h4V24h-4V8zm7 0h3.8v2.2h.1c.5-.9 1.8-2.2 3.9-2.2 4.2 0 5 2.8 5 6.4V24h-4v-7.6c0-1.8 0-4.2-2.6-4.2s-3 2-3 4v7.8h-4V8z\"\/>\n        <\/svg>\n        View LinkedIn Profile\n      <\/a>\n\n    <\/div>\n\n  <\/div>\n      <\/header>\n\n      <article class=\"ols-note-card\">\n<div class=\"ols-note-title\">\n<div class=\"ols-note-icon\">1<\/div>\n<h2>What the Maxwell\u2013Boltzmann distribution Shows<\/h2>\n<\/div>\n<p>In a gas or a solution at a given temperature, the particles do not all have the same energy.<\/p><p>Collisions constantly transfer energy between them, so at any instant some are moving slowly and a few are moving very fast.<\/p><p>The <strong>Maxwell\u2013Boltzmann distribution<\/strong> is a graph of the number of molecules against their energy, and it shows how the energies are spread out.<\/p>\n<p>The curve has a characteristic shape. It starts at the origin, because no molecule has zero energy, and it rises to a peak at the <strong>most probable energy<\/strong>.<\/p><p>It falls away to the right in a long tail that gets closer and closer to the axis without ever touching it, because there is no upper limit to the energy a molecule could have.<\/p><p>The <strong>area under the curve<\/strong> is the total number of molecules.<\/p>\n<p>The activation energy, E\u2090, is marked as a vertical line well to the right of the peak. Only the molecules in the shaded area beyond that line have enough energy to react when they collide.<\/p><p>For most reactions at room temperature that is a small fraction of the total, which is why most collisions are not effective.<\/p>\n<div class=\"ols-key-box\">\n<p><strong>Sketching rule:<\/strong> Start at the origin, peak, then a tail that approaches the axis but never meets it. Label the axes &#8220;number of molecules&#8221; and &#8220;energy&#8221;, and mark E\u2090 to the right of the peak.<\/p>\n<\/div>\n<\/article>\n<section class=\"ols-h5p-card ols-h5p-inline\">\n<span class=\"ols-h5p-kicker\">Check your understanding<\/span>\n<h2>Check: Reading the Curve<\/h2>\n<p>Questions on the shape and labels of the distribution.<\/p>\n<div class=\"ols-h5p-frame\"><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-905\" class=\"h5p-iframe\" data-content-id=\"905\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Kinetics and Equilibria Summary: Reading the Curve\"><\/iframe><\/div><\/div>\n<\/section>\n<article class=\"ols-note-card soft\">\n<div class=\"ols-note-title\">\n<div class=\"ols-note-icon\">2<\/div>\n<h2>The Effect of Temperature<\/h2>\n<\/div>\n<p>When the temperature rises, the average energy of the molecules rises, so the whole curve shifts to the right.<\/p><p>The peak moves to a higher energy and becomes lower, because the same number of molecules is now spread over a wider range of energies.<\/p><p>The area under the curve is unchanged: heating does not create molecules.<\/p>\n<p>The important change is at the activation energy line. Because the tail of the higher-temperature curve is higher, the shaded area beyond E\u2090 is much larger.<\/p><p>A much greater <strong>proportion of molecules has energy greater than or equal to E\u2090<\/strong>. This is why a small rise in temperature produces a large rise in rate.<\/p><p>The collision frequency rises only slightly, but the fraction of collisions that are effective rises a great deal.<\/p>\n<div class=\"ols-key-box\">\n<p><strong>Exam wording:<\/strong> For a temperature rise, give both points: &#8220;the peak moves to a higher energy and is lower&#8221; and &#8220;a greater proportion of molecules have energy \u2265 E\u2090, so a greater proportion of collisions are successful and the rate increases&#8221;. The activation energy itself does not move.<\/p>\n<\/div>\n<div class=\"ols-figure-card ols-zoom-pop\">\n<div class=\"ols-figure-image\">\n<a class=\"ols-image-fullscreen-link\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/t9x-tempchain.jpg\" target=\"_blank\" rel=\"noopener\" aria-label=\"Open image fullscreen\">\n<img decoding=\"async\" src=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/t9x-tempchain.jpg\" alt=\"Cause-and-effect chain for the effect of temperature on rate, with distribution changes and a temperature versus catalyst table.\" data-fullscreen-src=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/t9x-tempchain.jpg\">\n<\/a>\n<\/div>\n<div class=\"ols-figure-caption\"><p>Heating raises the collision frequency only slightly but greatly increases the proportion of molecules with energy at least equal to the activation energy, which is why a small temperature rise gives a large rise in rate.<\/p><\/div>\n<\/div>\n<\/article>\n<section class=\"ols-h5p-card ols-h5p-inline\">\n<span class=\"ols-h5p-kicker\">Check your understanding<\/span>\n<h2>Check: Temperature and the Distribution<\/h2>\n<p>Explain temperature effects for a reaction not discussed above.<\/p>\n<div class=\"ols-h5p-frame\"><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-906\" class=\"h5p-iframe\" data-content-id=\"906\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Kinetics and Equilibria Explain: Temperature and the Distribution\"><\/iframe><\/div><\/div>\n<\/section>\n<article class=\"ols-note-card\">\n<div class=\"ols-note-title\">\n<div class=\"ols-note-icon\">3<\/div>\n<h2>The Effect of a Catalyst<\/h2>\n<\/div>\n<p>A catalyst does not change the energies of the molecules, so the curve stays exactly where it is.<\/p><p>Instead the catalyst provides a different route for the reaction with a <strong>lower activation energy<\/strong>, so the E\u2090 line moves to the left.<\/p><p>A larger part of the same distribution now lies beyond the line. A greater proportion of the molecules already have enough energy to react by the catalysed route, so more collisions are effective and the rate increases.<\/p>\n<p>The two effects are easy to confuse in an exam. Temperature moves the curve and leaves E\u2090 where it is; a catalyst leaves the curve where it is and moves E\u2090.<\/p>\n<div class=\"ols-figure-card ols-zoom-pop\">\n<div class=\"ols-figure-image\">\n<a class=\"ols-image-fullscreen-link\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/kinetics-equilibria-boltzmann-temperature-catalyst.jpg\" target=\"_blank\" rel=\"noopener\" aria-label=\"Open image fullscreen\">\n<img decoding=\"async\" src=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/kinetics-equilibria-boltzmann-temperature-catalyst.jpg\" alt=\"Maxwell\u2013Boltzmann distributions: the effect of a higher temperature and the effect of a catalyst lowering the activation energy\" data-fullscreen-src=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/kinetics-equilibria-boltzmann-temperature-catalyst.jpg\">\n<\/a>\n<\/div>\n<div class=\"ols-figure-caption\"><p>The Maxwell\u2013Boltzmann distribution at two temperatures with the fraction beyond E\u2090 shaded, and the same curve with the lower activation energy of a catalysed route.<\/p><\/div>\n<\/div>\n<div class=\"ols-key-box\">\n<p><strong>Key idea:<\/strong> Temperature: the curve moves. Catalyst: the E\u2090 line moves. Both increase the proportion of collisions with energy \u2265 E\u2090.<\/p>\n<\/div>\n<\/article>\n<section class=\"ols-h5p-card ols-h5p-inline\">\n<span class=\"ols-h5p-kicker\">Check your understanding<\/span>\n<h2>Check: Catalyst or Temperature?<\/h2>\n<p>Decide which change is being described from the effect on the distribution.<\/p>\n<div class=\"ols-h5p-frame\"><div class=\"h5p-iframe-wrapper\"><iframe id=\"h5p-iframe-907\" class=\"h5p-iframe\" data-content-id=\"907\" style=\"height:1px\" src=\"about:blank\" frameBorder=\"0\" scrolling=\"no\" title=\"Kinetics and Equilibria Quick Choice: Catalyst or Temperature?\"><\/iframe><\/div><\/div>\n<\/section>\n<section class=\"ols-faq-card\">\n<h2>FAQs<\/h2>\n<p>Use these quick answers to check the Maxwell\u2013Boltzmann distribution.<\/p>\n\n<div class=\"ols-faq-list\">\n<div class=\"ols-faq-item\">\n<h3>Why does the curve start at the origin?<\/h3>\n<p>No molecule has zero energy, so the number of molecules with zero energy is zero.<\/p>\n<\/div>\n\n<div class=\"ols-faq-item\">\n<h3>Why does the curve never touch the axis at high energy?<\/h3>\n<p>There is no upper limit to the energy a molecule could have, so the number of molecules with very high energy approaches zero but never reaches it.<\/p>\n<\/div>\n\n<div class=\"ols-faq-item\">\n<h3>What happens to the area under the curve when the temperature rises?<\/h3>\n<p>Nothing. The area is the total number of molecules, which does not change. The curve becomes flatter and its peak moves to a higher energy.<\/p>\n<\/div>\n\n<div class=\"ols-faq-item\">\n<h3>Does heating lower the activation energy?<\/h3>\n<p>No. Heating moves the curve so that more molecules have energy above E\u2090; the value of E\u2090 itself is fixed for a given route. Only a catalyst changes it.<\/p>\n<\/div>\n\n<div class=\"ols-faq-item\">\n<h3>What is the most probable energy?<\/h3>\n<p>The energy at the peak of the curve, the energy that more molecules have than any other. It is lower than the average energy because of the long tail.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"ols-related-card\">\n<h2>Related Topic 9A Kinetics Pages<\/h2>\n<p>Use these pages to connect the ideas across kinetics and the rest of Topic 9.<\/p>\n<div class=\"ols-related-grid\">\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/collision-theory-and-rates-of-reaction\/\">Collision Theory and Rates of Reaction<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/measuring-and-calculating-rates\/\">Measuring and Calculating Rates<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/catalysts-and-reaction-profiles\/\">Catalysts and Reaction Profiles<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/\">Topic 9A Kinetics Overview<\/a>\n<\/div>\n<\/section>\n<section class=\"ols-attribution-card\">\n        <p><strong>Copyright notice:<\/strong> This OLS revision content, including the explanations, layout, diagrams, tables and embedded learning structure, is authored for Online Learning System by Dr. Mohammed Al-Fatah. It may not be copied, reproduced, redistributed or adapted without written permission.<\/p>\n      <\/section>\n    <\/main>\n  \n\n<script type=\"application\/ld+json\">\n{\n  \"@context\": \"https:\/\/schema.org\",\n  \"@graph\": [\n    {\n      \"@type\": \"WebPage\",\n      \"@id\": \"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/maxwell-boltzmann-distribution\/#webpage\",\n      \"url\": \"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/edexcel-international\/topic-9-kinetics-and-equilibria\/9a-kinetics\/maxwell-boltzmann-distribution\/\",\n      \"name\": \"The Maxwell\u2013Boltzmann Distribution | Topic 9A Kinetics | Online Learning System\",\n      \"description\": \"Edexcel International A Level Chemistry revision notes on the Maxwell\u2013Boltzmann distribution: shape, activation energy, the effect of temperature and the effect of a catalyst 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\/ Topic 9 Kinetics and Equilibria \/ Topic 9A Kinetics \/ The Maxwell\u2013Boltzmann Distribution The Maxwell\u2013Boltzmann Distribution A concise revision guide to the Maxwell\u2013Boltzmann distribution: its shape and labels, the activation energy on the curve, why a small rise in temperature gives a large rise in 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