{"id":12498,"date":"2026-10-03T08:33:19","date_gmt":"2026-10-03T07:33:19","guid":{"rendered":"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/calculating-entropy-changes\/"},"modified":"2026-10-03T10:00:48","modified_gmt":"2026-10-03T09:00:48","slug":"calculating-entropy-changes","status":"publish","type":"page","link":"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/calculating-entropy-changes\/","title":{"rendered":"Calculating Entropy Changes"},"content":{"rendered":"\n<section class=\"ols-revision-page ols-nature-of-covalent-bonding-9ch0-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      --soft-orange: #fff7ed;\n      --grey-text: #667085;\n      --body-text: #1f2937;\n      --border: rgba(28, 36, 75, 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cover; object-position: center; flex-shrink: 0; border: 4px solid #ffffff; box-shadow: 0 14px 32px rgba(28,36,75,0.18), 0 0 0 1px rgba(28,36,75,0.10); transition: transform 0.25s ease, box-shadow 0.25s ease; }\n    .ols-author:hover .ols-author-avatar-img { transform: scale(1.04); box-shadow: 0 20px 42px rgba(28,36,75,0.22), 0 0 0 1px rgba(28,36,75,0.10); }\n    .ols-author-content { min-width: 0; }\n    .ols-author-title { margin: 0 0 4px; font-size: clamp(24px,3vw,34px); line-height: 1.15; font-weight: 700; color: var(--navy); letter-spacing: -0.03em; }\n    .ols-author-description { margin: 0; font-size: 17px; line-height: 1.7; font-weight: 300; color: var(--grey-text); }\n    .ols-linkedin-pill { display: inline-flex; align-items: center; justify-content: center; gap: 10px; margin-top: 16px; padding: 11px 18px; border-radius: 999px; background: linear-gradient(135deg,#0A66C2,#004182); color: #ffffff; text-decoration: none; font-size: 14px; line-height: 1; font-weight: 700; 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linear-gradient(135deg, #ffffff 0%, var(--soft-orange) 100%); }\n    .ols-note-title { display: flex; align-items: center; gap: 14px; margin-bottom: 20px; }\n    .ols-note-icon { width: 52px; height: 52px; border-radius: 16px; background: var(--navy); color: #ffffff; display: grid; place-items: center; font-size: 24px; font-weight: 800; flex-shrink: 0; }\n    .ols-note-title h2, .ols-h5p-card h2, .ols-related-card h2, .ols-faq-card h2 { margin: 0; font-size: clamp(28px, 3.5vw, 42px); line-height: 1.15; font-weight: 800; color: #111827; letter-spacing: -0.03em; }\n    .ols-h5p-card h2, .ols-related-card h2, .ols-faq-card h2 { margin-bottom: 14px; }\n    .ols-note-card p, .ols-note-card li { font-size: clamp(15px, 1.25vw, 17px); line-height: 1.65; font-weight: 300; color: var(--body-text); }\n    .ols-h5p-card p, .ols-related-card p, .ols-faq-card p { font-size: clamp(15px, 1.3vw, 18px); line-height: 1.65; font-weight: 300; color: var(--body-text); }\n    .ols-note-card strong, .ols-h5p-card strong, .ols-related-card strong, .ols-faq-card strong { font-weight: 700; color: var(--navy); }\n    .ols-note-card ul, .ols-note-card ol { margin: 0; padding-left: 22px; }\n\n    .ols-key-box { margin-top: 20px; background: var(--soft-green); border: 1px solid rgba(63, 143, 70, 0.25); border-radius: 20px; padding: 18px 20px; }\n    .ols-key-box p { margin: 0; font-weight: 400; color: var(--navy); }\n    .ols-definition-box { background: linear-gradient(135deg, #ffffff, var(--soft-purple)); border: 2px dashed rgba(122, 62, 157, 0.35); border-radius: 24px; padding: 22px 24px; margin-top: 22px; }\n    .ols-definition-box p { margin: 0; color: var(--navy); font-weight: 400; }\n\n    .ols-rule-list { display: grid; gap: 14px; margin-top: 18px; }\n    .ols-rule-item { background: #ffffff; border: 1px solid var(--border); border-left: 5px solid var(--blue); border-radius: 18px; padding: 18px; box-shadow: var(--inner-shadow); }\n    .ols-rule-item h3 { margin: 0 0 8px; font-size: 20px; line-height: 1.25; color: var(--navy); }\n    .ols-rule-item p { margin: 0; font-size: 15px; line-height: 1.6; }\n\n    .ols-figure-card { margin: 26px auto 4px; border: 1px solid var(--border); border-radius: 26px; overflow: hidden; background: #ffffff; box-shadow: var(--inner-shadow); max-width: 100%; }\n    .ols-figure-card.medium { max-width: 820px; }\n    .ols-figure-card.compact { max-width: 700px; }\n    .ols-figure-image { width: 100%; min-height: 260px; display: flex; align-items: center; justify-content: center; background: #ffffff; padding: 20px; }\n    .ols-figure-image img { max-width: 100%; height: auto; display: block; }\n    .ols-figure-caption { padding: 18px 24px 22px; background: linear-gradient(135deg, #ffffff, #f8fbff); border-top: 1px solid var(--border); }\n    .ols-figure-caption p { margin: 0; color: #5f6b85; font-size: clamp(15px, 1.3vw, 17px); line-height: 1.6; font-weight: 300; font-style: italic; }\n    .ols-zoom-card, .ols-zoom-card * { box-sizing: border-box; }\n    .ols-zoom-card { display: block !important; margin: 26px auto 34px !important; border: 1px solid rgba(28, 36, 75, 0.14) !important; border-radius: 26px !important; background: #ffffff !important; box-shadow: 0 18px 45px rgba(28, 36, 75, 0.10) !important; overflow: visible !important; position: relative !important; z-index: 1 !important; isolation: isolate !important; }\n    .ols-zoom-card.medium { max-width: 820px; }\n    .ols-zoom-card.compact { max-width: 700px; }\n    .ols-zoom-card.wide { max-width: 940px; }\n    .ols-zoom-card.slim { max-width: 600px; }\n    .ols-zoom-card:hover { z-index: 50 !important; }\n    .ols-zoom-card-image { display: flex !important; align-items: center !important; justify-content: center !important; width: 100% !important; min-height: 240px !important; padding: 20px !important; background: #ffffff !important; overflow: visible !important; border-top-left-radius: 26px !important; border-top-right-radius: 26px !important; position: relative !important; z-index: 2 !important; }\n    .ols-zoom-card img.ols-zoomable-img { display: block !important; max-width: 100% !important; height: auto !important; border-radius: 18px !important; cursor: zoom-in !important; pointer-events: auto !important; user-select: none !important; -webkit-user-drag: none !important; transform: translateZ(0) scale(1) !important; transform-origin: center center !important; transition: transform 0.32s ease, box-shadow 0.32s ease, filter 0.32s ease !important; position: relative !important; z-index: 2 !important; }\n    @media (hover: hover) and (pointer: fine) { .ols-zoom-card img.ols-zoomable-img:hover { transform: translateZ(0) scale(1.35) !important; box-shadow: 0 28px 70px rgba(28, 36, 75, 0.34) !important; filter: saturate(1.02) contrast(1.01) !important; z-index: 100 !important; } }\n    .ols-zoom-card-caption { padding: 18px 22px 20px !important; background: linear-gradient(135deg, #ffffff, #f8fbff) !important; border-bottom-left-radius: 26px !important; border-bottom-right-radius: 26px !important; position: relative !important; z-index: 1 !important; }\n    .ols-zoom-card-caption p { margin: 0 !important; color: #5f6b85 !important; font-size: 15px !important; line-height: 1.65 !important; font-weight: 300 !important; font-style: italic !important; font-family: Poppins, Arial, sans-serif !important; }\n    .ols-image-lightbox { position: fixed; inset: 0; z-index: 999999; display: none; align-items: center; justify-content: center; padding: 34px; background: rgba(10, 15, 35, 0.86); backdrop-filter: blur(8px); -webkit-backdrop-filter: blur(8px); }\n    .ols-image-lightbox.is-open { display: flex; }\n    .ols-image-lightbox-inner { position: relative; width: min(96vw, 1500px); max-height: 92vh; display: flex; align-items: center; justify-content: center; }\n    .ols-image-lightbox-img { display: block; max-width: 100%; max-height: 92vh; height: auto; width: auto; border-radius: 22px; background: #ffffff; box-shadow: 0 32px 90px rgba(0, 0, 0, 0.45); object-fit: contain; }\n    .ols-image-lightbox-close { position: absolute; top: -18px; right: -18px; width: 46px; height: 46px; border: 0; border-radius: 50%; background: #ffffff; color: var(--navy); font-family: Poppins, Arial, sans-serif; font-size: 28px; line-height: 1; font-weight: 700; cursor: pointer; box-shadow: 0 16px 34px rgba(0, 0, 0, 0.28); display: flex; align-items: center; justify-content: center; transition: transform 0.2s ease, background 0.2s ease, color 0.2s ease; }\n    .ols-image-lightbox-close:hover { transform: scale(1.08); background: var(--blue); color: #ffffff; }\n    @media (max-width: 760px) { .ols-zoom-card { border-radius: 22px !important; overflow: hidden !important; } .ols-zoom-card-image { min-height: auto !important; padding: 12px !important; overflow: hidden !important; border-top-left-radius: 22px !important; border-top-right-radius: 22px !important; } .ols-zoom-card img.ols-zoomable-img, .ols-zoom-card img.ols-zoomable-img:hover { transform: none !important; box-shadow: none !important; } .ols-zoom-card-caption { border-bottom-left-radius: 22px !important; border-bottom-right-radius: 22px !important; } .ols-image-lightbox { padding: 16px; } .ols-image-lightbox-inner { width: 100%; max-height: 88vh; } .ols-image-lightbox-img { max-height: 88vh; border-radius: 16px; } .ols-image-lightbox-close { top: 10px; right: 10px; width: 42px; height: 42px; font-size: 26px; } }\n\n\n    .ols-table-wrap { overflow: hidden; border-radius: 22px; border: 1px solid var(--border); background: #ffffff; margin-top: 18px; }\n    .ols-table { width: 100%; border-collapse: collapse; table-layout: fixed; }\n    .ols-table th { background: var(--navy); color: #ffffff; padding: 16px; text-align: left; font-size: clamp(14px, 1.2vw, 17px); font-weight: 600; overflow-wrap: anywhere; }\n    .ols-table td { padding: 16px; border-bottom: 1px solid var(--border); font-size: clamp(14px, 1.15vw, 16px); line-height: 1.45; color: var(--body-text); vertical-align: top; overflow-wrap: anywhere; }\n    .ols-table tr:last-child td { border-bottom: none; }\n\n    .ols-h5p-card { background: linear-gradient(135deg, #ffffff 0%, #f7f0ff 100%); }\n    .ols-h5p-frame { margin-top: 22px; padding: 18px; border-radius: 24px; background: #ffffff; border: 1px solid var(--border); box-shadow: inset 0 0 0 1px rgba(28, 36, 75, 0.03); }\n\n    .ols-faq-list { display: grid; gap: 14px; margin-top: 18px; }\n    .ols-faq-item { background: #ffffff; border: 1px solid var(--border); border-radius: 18px; padding: 18px 20px; box-shadow: var(--inner-shadow); }\n    .ols-faq-item h3 { margin: 0 0 8px; font-size: 20px; line-height: 1.3; color: var(--navy); }\n    .ols-faq-item p { margin: 0; font-size: 16px; line-height: 1.65; color: var(--body-text); }\n\n    .ols-related-grid { display: grid; grid-template-columns: repeat(3, minmax(0, 1fr)); gap: 16px; margin-top: 18px; }\n    .ols-related-item { border: 1px solid var(--border); border-radius: 18px; padding: 18px; background: #ffffff; color: var(--navy); text-decoration: none; font-weight: 600; line-height: 1.5; transition: transform 0.2s ease, box-shadow 0.2s ease; }\n    .ols-related-item:hover { transform: translateY(-2px); box-shadow: 0 10px 22px rgba(28, 36, 75, 0.08); }\n\n    .ols-course-cta-covalent {\n      width: 100%;\n      margin: 30px 0 24px;\n      font-family: Poppins, Arial, sans-serif;\n    }\n    .ols-course-cta-covalent, .ols-course-cta-covalent * { box-sizing: border-box; }\n    .ols-course-cta-card {\n      overflow: hidden;\n      border-radius: 30px;\n      border: 1px solid var(--border);\n      background: radial-gradient(circle at top left, rgba(37, 99, 235, 0.16), transparent 34%), linear-gradient(135deg, #ffffff 0%, #f8fbff 100%);\n      box-shadow: var(--shadow);\n      padding: 30px;\n    }\n    .ols-course-cta-top {\n      display: grid;\n      grid-template-columns: minmax(260px, 0.9fr) minmax(0, 1.1fr);\n  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}\n    .ols-course-cta-kicker { display: inline-flex; align-items: center; padding: 8px 14px; border-radius: 999px; background: #ffffff; border: 1px solid rgba(37, 99, 235, 0.18); color: var(--blue); font-size: 14px; line-height: 1.2; font-weight: 700; box-shadow: var(--inner-shadow); }\n    .ols-course-cta-covalent h2 { margin: 0 0 14px; font-size: clamp(28px, 3.5vw, 42px); line-height: 1.15; font-weight: 800; letter-spacing: -0.03em; color: #111827; }\n    .ols-course-cta-intro { margin: 0 0 24px; color: var(--body-text); font-size: clamp(16px, 1.4vw, 18px); line-height: 1.7; font-weight: 300; }\n    .ols-course-cta-features { display: grid; grid-template-columns: repeat(2, minmax(0, 1fr)); gap: 14px; margin: 0 0 30px; }\n    .ols-course-feature { background: rgba(255, 255, 255, 0.78); border: 1px solid var(--border); border-radius: 18px; padding: 16px 18px; }\n    .ols-course-feature h3 { margin: 0 0 6px; color: var(--navy); font-size: 18px; line-height: 1.3; font-weight: 800; }\n   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0.14);\n      border-radius: 28px;\n      box-shadow: 0 18px 45px rgba(28, 36, 75, 0.10);\n      padding: 34px;\n      margin-bottom: 24px;\n      overflow: hidden;\n      font-family: Poppins, Arial, sans-serif;\n      box-sizing: border-box;\n    }\n    .ols-attribution-card, .ols-attribution-card * { box-sizing: border-box; }\n    .ols-attribution-card p { margin: 0; font-size: 14px; line-height: 1.65; font-weight: 300; color: #667085; }\n    .ols-attribution-card strong { font-weight: 700; color: #1C244B; }\n\n    @media (max-width: 1050px) {\n      .ols-main { max-width: none; }\n      .ols-related-grid { grid-template-columns: repeat(2, minmax(0, 1fr)); }\n      .ols-course-cta-top { grid-template-columns: 1fr; }\n      .ols-course-cta-image-link { max-width: 520px; margin: 0 auto; }\n    }\n\n    @media (max-width: 760px) {\n      .ols-title-card, .ols-note-card, .ols-h5p-card, .ols-related-card, .ols-faq-card, .ols-attribution-card { padding: 24px 18px; border-radius: 22px; }\n 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760px) { .ols-h5p-card.ols-h5p-inline { padding: 20px 16px; } }\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>3.1.8 Thermodynamics<\/h4>\n\n    <ul class=\"ols-topic-list\">\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/\">3.1.8 Thermodynamics Overview<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/lattice-energy-and-born-haber-cycles\/\">Lattice Enthalpy and Born\u2013Haber Cycles<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/lattice-energy-trends-and-covalent-character\/\">Lattice Enthalpy Trends and Covalent Character<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/enthalpy-of-solution-and-hydration\/\">Enthalpy of Solution and Hydration<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/entropy-and-the-direction-of-change\/\">Entropy and the Direction of Change<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/calculating-entropy-changes\/\">Calculating Entropy Changes<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/feasibility-gibbs-energy-and-temperature\/\">Feasibility, Gibbs Energy and Temperature<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/thermodynamic-and-kinetic-stability\/\">Thermodynamic and Kinetic Stability<\/a>\n      <\/li>\n    <\/ul>\n  <\/div>\n\n  <div class=\"ols-topic-group\">\n    <h4>Other Sections<\/h4>\n\n    <ul class=\"ols-topic-list\">\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-4-energetics\/\">3.1.4 Energetics<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-9-rate-equations\/\">3.1.9 Rate Equations<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-2-2-group-2-the-alkaline-earth-metals\/\">3.2.2 Group 2<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/required-practicals\/\">Required Practicals<\/a>\n      <\/li>\n    <\/ul>\n  <\/div>\n<\/aside>\n\n<script>\r\n(function() {\r\n  function normalisePath(path) {\r\n    return String(path || '')\r\n      .split('?')[0]\r\n      .split('#')[0]\r\n      .replace(\/\\\/+$\/, '')\r\n      .toLowerCase();\r\n  }\r\n\r\n  function highlightActive() {\r\n    var sidebar = document.querySelector('.ols-sidebar');\r\n    if (!sidebar) return false;\r\n\r\n    var currentPath = normalisePath(window.location.pathname);\r\n    var links = sidebar.querySelectorAll('a[href]');\r\n    var matched = null;\r\n    var matchedLength = 0;\r\n\r\n    sidebar.querySelectorAll('.active, .active-main, .parent-active').forEach(function(item) {\r\n      item.classList.remove('active', 'active-main', 'parent-active');\r\n    });\r\n\r\n    sidebar.querySelectorAll('a[data-ols-disabled-parent=\"1\"], 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true;\r\n  }\r\n\r\n  if (!highlightActive()) {\r\n    document.addEventListener('DOMContentLoaded', highlightActive);\r\n  }\r\n})();\r\n<\/script>\n\n  <main class=\"ols-main\">\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\/aqa\/\">AQA<\/a> \/\n<a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/\">3.1.8 Thermodynamics<\/a> \/\n<span>Calculating Entropy Changes<\/span>\n<\/nav>\n\n      <header class=\"ols-title-card\">\n        <h1>Calculating Entropy Changes<\/h1>\n        <p class=\"ols-page-intro\">A concise revision guide to calculating the entropy change of a reaction from standard entropies, with the units, the signs and the common slips.<\/p>\n\n        <div class=\"ols-badges\">\n<div class=\"ols-badge\">Paper 1 AQA<\/div>\n<div class=\"ols-badge\">3.1.8 Thermodynamics<\/div>\n<div class=\"ols-badge\">7405\/1<\/div>\n<\/div>\n\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:<br><span>Dr. Mohammed Al-Fatah<\/span>\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>\u0394S of the System From Standard Entropies<\/h2>\n<\/div>\n<p>The <strong>entropy change of the system<\/strong>, \u0394S, is the difference between the entropies of the products and the reactants.<\/p>\n<p>It is found from tabulated standard entropies, in the same way that an enthalpy change is found from enthalpies of formation:<\/p>\n<p>\u0394S = \u03a3S\u29b5(products) \u2212 \u03a3S\u29b5(reactants)<\/p>\n<ul class=\"ols-list\">\n<li>Each entropy is multiplied by the number of moles of that substance in the equation.<\/li>\n<li>The answer has the same units as the data, <strong>J K\u207b\u00b9 mol\u207b\u00b9<\/strong>.<\/li>\n<li>There is one difference from enthalpy calculations: elements have non-zero entropies, so an element in the equation must be included with its tabulated value, not treated as zero.<\/li>\n<\/ul>\n<h3>Worked example 1: a gas is made<\/h3>\n<p>The thermal decomposition of calcium carbonate is CaCO\u2083(s) \u2192 CaO(s) + CO\u2082(g).<\/p>\n<div class=\"ols-table-wrap\">\n<table class=\"ols-table\">\n<thead>\n<tr><th>Substance<\/th><th>S\u29b5 \/ J K\u207b\u00b9 mol\u207b\u00b9<\/th><\/tr>\n<\/thead>\n<tbody>\n<tr><td><strong>CaCO\u2083(s)<\/strong><\/td><td>92.9<\/td><\/tr>\n<tr><td><strong>CaO(s)<\/strong><\/td><td>39.7<\/td><\/tr>\n<tr><td><strong>CO\u2082(g)<\/strong><\/td><td>213.6<\/td><\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n<p><strong>Step 1.<\/strong> Add the entropies of the products: 39.7 + 213.6 = 253.3 J K\u207b\u00b9 mol\u207b\u00b9.<\/p>\n<p><strong>Step 2.<\/strong> Subtract the entropy of the reactant: \u0394S = (39.7 + 213.6) \u2212 92.9.<\/p>\n<p><strong>Answer.<\/strong> \u0394S = <strong>+160.4 J K\u207b\u00b9 mol\u207b\u00b9<\/strong>.<\/p>\n<ul class=\"ols-list\">\n<li>The sign is positive, as page 1 predicted for a reaction that makes a gas from a solid.<\/li>\n<li>The size is typical of a reaction that produces one mole of gas: roughly 150 to 200 J K\u207b\u00b9 mol\u207b\u00b9 per mole of gas gained.<\/li>\n<\/ul>\n<h3>Worked example 2: gas moles fall<\/h3>\n<p>For N\u2082(g) + 3H\u2082(g) \u2192 2NH\u2083(g), S\u29b5 = 192 (N\u2082), 131 (H\u2082) and 193 (NH\u2083) J K\u207b\u00b9 mol\u207b\u00b9.<\/p>\n<p><strong>Step 1.<\/strong> Products: 2 \u00d7 193 = 386 J K\u207b\u00b9 mol\u207b\u00b9.<\/p>\n<p><strong>Step 2.<\/strong> Reactants: 192 + (3 \u00d7 131) = 585 J K\u207b\u00b9 mol\u207b\u00b9.<\/p>\n<p><strong>Answer.<\/strong> \u0394S = 386 \u2212 585 = \u2212199 J K\u207b\u00b9 mol\u207b\u00b9. Four moles of gas become two, so the entropy of the system falls.<\/p>\n<div class=\"ols-zoom-card\">\n<div class=\"ols-zoom-card-image\">\n<a class=\"ols-lightbox-link\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/entropy-t12-03-scalc.jpg\" aria-label=\"Open image full screen\">\n<img decoding=\"async\" class=\"ols-zoomable-img ols-lightbox-target\" src=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/entropy-t12-03-scalc.jpg\" alt=\"Worked card calculating \u0394S of the system for the thermal decomposition of calcium car\">\n<\/a>\n<\/div>\n<div class=\"ols-zoom-card-caption\"><p>The calcium carbonate calculation laid out in full: standard entropies, \u0394S of the system, then the surroundings and total entropy at 298 K and at 1200 K.<\/p><\/div>\n<\/div>\n<div class=\"ols-key-box\">\n<p><strong>Worked example:<\/strong> CaCO\u2083(s) \u2192 CaO(s) + CO\u2082(g): \u0394S = \u03a3S(products) \u2212 \u03a3S(reactants) = (39.7 + 213.6) \u2212 92.9 = +160.4 J K\u207b\u00b9 mol\u207b\u00b9. Multiply each S by its balancing number, and include the elements.<\/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: \u0394S From Standard Entropies<\/h2>\n<p>Calculate the entropy change of the system with its sign and units for reactions not used on this page.<\/p>\n<div class=\"ols-h5p-frame\"><div class=\"h5p-content\" data-content-id=\"1102\"><\/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>Why the Surroundings Matter<\/h2>\n<\/div>\n<p>A reaction does not only change the entropy of the substances taking part.<\/p>\n<ul class=\"ols-list\">\n<li>An exothermic reaction gives out heat to its surroundings. That heat spreads among the surrounding particles, and their entropy rises.<\/li>\n<li>An endothermic reaction takes heat in and lowers the entropy of the surroundings.<\/li>\n<li>The size of that change is the heat transferred divided by the temperature.<\/li>\n<li>So an exothermic reaction with enthalpy change \u0394H raises the entropy of the surroundings by \u2212\u0394H \u00f7 T, with T in kelvin.<\/li>\n<li>Because T is in the denominator, the effect is large at low temperatures and shrinks as the temperature rises.<\/li>\n<\/ul>\n<h3>Where the Gibbs equation comes from<\/h3>\n<p>A change is feasible when the total entropy, the \u0394S of the system plus this surroundings term, is positive.<\/p>\n<p>Multiplying that condition through by \u2212T gives \u0394H \u2212 T\u0394S < 0, which is the <strong>Gibbs equation<\/strong> that page 3 uses.<\/p>\n<ul class=\"ols-list\">\n<li>The \u2212T\u0394S term is the entropy change of the system in energy units.<\/li>\n<li>\u0394H stands for the entropy change of the surroundings.<\/li>\n<li>The calculation is done in kJ mol\u207b\u00b9 rather than J K\u207b\u00b9 mol\u207b\u00b9.<\/li>\n<\/ul>\n<p>You do not need to calculate the entropy change of the surroundings separately. Knowing where the equation comes from explains why exothermic reactions with a negative \u0394S can still be feasible.<\/p>\n<div class=\"ols-key-box\">\n<p><strong>Key idea:<\/strong> Heat given out to the surroundings raises their entropy by \u2212\u0394H\/T. That is why \u0394H appears in the Gibbs equation alongside \u2212T\u0394S: together they measure the total entropy change in energy units.<\/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: Units and Signs<\/h2>\n<p>Convert between J and kJ, use kelvin temperatures and keep the signs straight in entropy calculations not used on this page.<\/p>\n<div class=\"ols-h5p-frame\"><div class=\"h5p-content\" data-content-id=\"1103\"><\/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>Putting \u0394S and \u0394H Together<\/h2>\n<\/div>\n<p>For the decomposition of calcium carbonate \u0394H = +178 kJ mol\u207b\u00b9 and \u0394S = +160.4 J K\u207b\u00b9 mol\u207b\u00b9.<\/p>\n<p>The enthalpy change is unfavourable and the entropy change favourable, so whether the reaction is feasible depends on the temperature.<\/p>\n<p>The Gibbs energy change, <strong>\u0394G = \u0394H \u2212 T\u0394S<\/strong>, weighs the two against each other. The reaction is feasible when \u0394G is negative.<\/p>\n<h3>Worked example: calcium carbonate at two temperatures<\/h3>\n<p><strong>Step 1.<\/strong> Convert the entropy term to kJ first: 160.4 J K\u207b\u00b9 mol\u207b\u00b9 = 0.1604 kJ K\u207b\u00b9 mol\u207b\u00b9.<\/p>\n<p><strong>Step 2.<\/strong> At 298 K: \u0394G = 178 \u2212 (298 \u00d7 0.1604) = 178 \u2212 47.8 = <strong>+130 kJ mol\u207b\u00b9<\/strong>.<\/p>\n<p><strong>Step 3.<\/strong> At 1200 K: \u0394G = 178 \u2212 (1200 \u00d7 0.1604) = 178 \u2212 192.5 = <strong>\u221215 kJ mol\u207b\u00b9<\/strong>.<\/p>\n<p><strong>Answer.<\/strong> \u0394G is positive at 298 K, so limestone does not decompose at room temperature. \u0394G is negative at 1200 K, so in a lime kiln the reaction goes.<\/p>\n<div class=\"ols-zoom-card\">\n<div class=\"ols-zoom-card-image\">\n<a class=\"ols-lightbox-link\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/entropy-t12-12-smethod.jpg\" aria-label=\"Open image full screen\">\n<img decoding=\"async\" class=\"ols-zoomable-img ols-lightbox-target\" src=\"https:\/\/www.onlinelearningsystem.net\/xyz\/wp-content\/uploads\/2026\/09\/entropy-t12-12-smethod.jpg\" alt=\"Flow chart poster of the method for an entropy calculation: \u0394S of the system from standard entropies, then two routes to the verdict, total entropy using \u2212\u0394H\/T or Gibbs energy using \u0394G = \u0394H \u2212 T\u0394S, with three unit traps flagged and the calcium carbonate numbers showing that both routes agree\">\n<\/a>\n<\/div>\n<div class=\"ols-zoom-card-caption\"><p>The method as a flow chart: \u0394S of the system first, then the total entropy route or the Gibbs energy route, with the unit traps marked and both routes giving the same verdict for calcium carbonate.<\/p><\/div>\n<\/div>\n<ul class=\"ols-list\">\n<li>The T\u0394S term grows with temperature until it outweighs \u0394H.<\/li>\n<li>This is the reason an endothermic reaction with a positive entropy change becomes feasible when hot.<\/li>\n<li>Page 3 deals with the full equation, its sign combinations and the temperature at which \u0394G changes sign.<\/li>\n<\/ul>\n<div class=\"ols-key-box\">\n<p><strong>Worked example:<\/strong> CaCO\u2083(s) \u2192 CaO(s) + CO\u2082(g) at 298 K: \u0394G = \u0394H \u2212 T\u0394S = 178 \u2212 (298 \u00d7 0.1604) = +130 kJ mol\u207b\u00b9, not feasible. At 1200 K: 178 \u2212 (1200 \u00d7 0.1604) = \u221215 kJ mol\u207b\u00b9, feasible.<\/p>\n<\/div>\n<\/article>\n<article class=\"ols-note-card\">\n<div class=\"ols-note-title\">\n<div class=\"ols-note-icon\">4<\/div>\n<h2>Common Exam Points<\/h2>\n<\/div>\n<h3>Say<\/h3>\n<ul class=\"ols-list\">\n<li>&#8220;\u0394S = \u03a3S(products) \u2212 \u03a3S(reactants), including the elements.&#8221;<\/li>\n<li>&#8220;Convert \u0394S to kJ K\u207b\u00b9 mol\u207b\u00b9 before using \u0394G = \u0394H \u2212 T\u0394S.&#8221;<\/li>\n<li>&#8220;\u0394G is negative, so the reaction is feasible.&#8221;<\/li>\n<\/ul>\n<h3>Do not say<\/h3>\n<ul class=\"ols-list\">\n<li>&#8220;Elements have an entropy of zero&#8221; (only their enthalpy of formation is zero).<\/li>\n<li>&#8220;T = 25&#8221; (use kelvin: 298 K).<\/li>\n<li>&#8220;\u0394G = 178 \u2212 298 \u00d7 160.4&#8221; (units mixed: use 0.1604 kJ K\u207b\u00b9 mol\u207b\u00b9).<\/li>\n<\/ul>\n<h3>Watch for<\/h3>\n<ul class=\"ols-list\">\n<li>The most common slip in this topic is <strong>units<\/strong>: entropies are in J K\u207b\u00b9 mol\u207b\u00b9 and enthalpies in kJ mol\u207b\u00b9, so one of them must be converted before they are combined.<\/li>\n<li>Check that the sign of \u0394S matches the change in moles of gas.<\/li>\n<li>Check that a temperature given in \u00b0C has had 273 added.<\/li>\n<\/ul>\n<\/article>\n<section class=\"ols-h5p-card ols-h5p-inline\">\n<span class=\"ols-h5p-kicker\">Check your understanding<\/span>\n<h2>Check: A Full Calculation<\/h2>\n<p>Carry out a complete calculation of \u0394S and then \u0394G and decide whether a reaction not used on this page is feasible.<\/p>\n<div class=\"ols-h5p-frame\"><div class=\"h5p-content\" data-content-id=\"1104\"><\/div><\/div>\n<\/section>\n<section class=\"ols-faq-card\">\n<h2>FAQs<\/h2>\n<p>Use these quick answers to check the entropy calculations.<\/p>\n\n<div class=\"ols-faq-list\">\n<div class=\"ols-faq-item\">\n<h3>Why must I convert J to kJ?<\/h3>\n<p>Because standard entropies are tabulated in J K\u207b\u00b9 mol\u207b\u00b9 while enthalpy changes are in kJ mol\u207b\u00b9. Whenever the two meet in one equation they must share a unit, so either divide the entropy term by 1000 or multiply \u0394H by 1000. Mixing them is the most common reason for an answer that is out by a factor of a thousand.<\/p>\n<\/div>\n\n<div class=\"ols-faq-item\">\n<h3>Why do I have to multiply each standard entropy by the balancing number?<\/h3>\n<p>Because standard entropy is quoted per mole of substance, and the equation may involve two or three moles. In 2H\u2082(g) + O\u2082(g) \u2192 2H\u2082O(l) the hydrogen contributes 2 \u00d7 131 J K\u207b\u00b9 mol\u207b\u00b9 and the water 2 \u00d7 70 J K\u207b\u00b9 mol\u207b\u00b9. Forgetting the multiplier changes both the size and, sometimes, the sign of \u0394S.<\/p>\n<\/div>\n\n<div class=\"ols-faq-item\">\n<h3>Where does the \u2212T\u0394S term come from?<\/h3>\n<p>Heat given out by the reaction raises the entropy of the surroundings by \u2212\u0394H\/T. Adding that to the entropy change of the system and multiplying the whole thing through by \u2212T turns the total entropy change into a quantity in kJ mol\u207b\u00b9, which is \u0394G = \u0394H \u2212 T\u0394S. The \u2212T\u0394S term is therefore the entropy change of the system written in energy units.<\/p>\n<\/div>\n\n<div class=\"ols-faq-item\">\n<h3>Can \u0394S for a reaction be negative and the reaction still happen?<\/h3>\n<p>Yes, provided the reaction is exothermic enough. The condensation of steam and the combustion of hydrogen both lower the entropy of the system, but the heat they release raises the entropy of the surroundings by more, so overall the change is still feasible.<\/p>\n<\/div>\n\n<div class=\"ols-faq-item\">\n<h3>What temperature do I use if the question does not say?<\/h3>\n<p>Standard conditions, which means 298 K. Always convert Celsius to kelvin by adding 273 before substituting; an entropy calculation at 25 K instead of 298 K gives nonsense. If the question sets a different temperature, use that one throughout.<\/p>\n<\/div>\n<\/div>\n<\/section>\n<section class=\"ols-related-card\">\n<h2>Related 3.1.8 Thermodynamics Pages<\/h2>\n<p>Use these pages to connect the ideas across 3.1.8 Thermodynamics and the rest of the course.<\/p>\n<div class=\"ols-related-grid\">\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/lattice-energy-and-born-haber-cycles\/\">Lattice Enthalpy and Born\u2013Haber Cycles<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/lattice-energy-trends-and-covalent-character\/\">Lattice Enthalpy Trends and Covalent Character<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/enthalpy-of-solution-and-hydration\/\">Enthalpy of Solution and Hydration<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/entropy-and-the-direction-of-change\/\">Entropy and the Direction of Change<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/feasibility-gibbs-energy-and-temperature\/\">Feasibility, Gibbs Energy and Temperature<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/thermodynamic-and-kinetic-stability\/\">Thermodynamic and Kinetic Stability<\/a>\n<a class=\"ols-related-item\" href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-8-thermodynamics\/\">3.1.8 Thermodynamics Overview<\/a>\n<\/div>\n<\/section>\n<section class=\"ols-attribution-card\">\n        <p><strong>Copyright and author footprint:<\/strong> This OLS revision page was written for Online Learning System by <strong>Dr. Mohammed Al-Fatah<\/strong>. It is designed for A Level Chemistry revision and should not be copied or redistributed without permission.<\/p>\n      <\/section>\n\n      <div class=\"ols-image-lightbox\" id=\"olsImageLightboxNatureCovalentBonding9ch0\" aria-hidden=\"true\" role=\"dialog\" aria-modal=\"true\" aria-label=\"Expanded revision image\">\n        <div class=\"ols-image-lightbox-inner\">\n          <button class=\"ols-image-lightbox-close\" type=\"button\" aria-label=\"Close enlarged image\">\u00d7<\/button>\n          <img decoding=\"async\" class=\"ols-image-lightbox-img\" src=\"\" alt=\"\">\n        <\/div>\n      <\/div>\n\n      <script>\n        (function(){\n          var page = document.querySelector(\".ols-nature-of-covalent-bonding-9ch0-page\");\n          if (!page) { return; }\n          var lightbox = page.querySelector(\"#olsImageLightboxNatureCovalentBonding9ch0\");\n          if (!lightbox) { return; }\n          var lightboxImage = lightbox.querySelector(\".ols-image-lightbox-img\");\n    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