{"id":10739,"date":"2026-09-26T13:55:59","date_gmt":"2026-09-26T12:55:59","guid":{"rendered":"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-5-kinetics\/maxwell-boltzmann-distribution\/"},"modified":"2026-10-03T11:33:11","modified_gmt":"2026-10-03T10:33:11","slug":"maxwell-boltzmann-distribution","status":"publish","type":"page","link":"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-5-kinetics\/maxwell-boltzmann-distribution\/","title":{"rendered":"The Maxwell\u2013Boltzmann Distribution"},"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, 0.14);\n      --shadow: 0 18px 45px rgba(28, 36, 75, 0.10);\n      --inner-shadow: 0 10px 26px rgba(28, 36, 75, 0.08);\n      font-family: Poppins, Arial, sans-serif;\n      color: var(--navy);\n      background: #ffffff;\n    }\n\n    .ols-revision-page * { box-sizing: border-box; }\n    .ols-main { min-width: 0; max-width: 970px; }\n    .ols-breadcrumbs { display: flex; flex-wrap: wrap; gap: 8px; margin: 10px 0 22px; font-size: 15px; color: var(--grey-text); }\n    .ols-breadcrumbs a, .ols-breadcrumbs span { color: var(--grey-text); text-decoration: none; font-weight: 600; }\n    .ols-breadcrumbs a:hover { color: var(--blue); text-decoration: underline; text-underline-offset: 3px; }\n    .ols-title-card, .ols-note-card, .ols-h5p-card, .ols-related-card, .ols-faq-card { background: #ffffff; border: 1px solid var(--border); border-radius: 28px; box-shadow: var(--shadow); padding: 34px; margin-bottom: 24px; overflow: hidden; }\n    .ols-title-card { background: linear-gradient(135deg, #ffffff 0%, #f8fbff 100%); }\n    .ols-title-card h1 { margin: 0 0 18px; font-size: clamp(36px, 5vw, 58px); line-height: 1.08; font-weight: 800; letter-spacing: -0.04em; color: #111827; }\n    .ols-page-intro { font-size: 19px; line-height: 1.7; font-weight: 300; color: var(--body-text); margin: 0 0 22px; }\n    .ols-badges { display: flex; flex-direction: column; align-items: flex-start; gap: 12px; margin-bottom: 22px; }\n    .ols-badge { display: inline-flex; align-items: center; padding: 9px 14px; border-radius: 999px; background: #ffffff; border: 1px solid var(--border); font-size: 15px; font-weight: 600; color: var(--navy); }\n    .ols-author { display: flex; align-items: center; gap: 20px; padding: 28px; border-radius: 28px; background: linear-gradient(135deg, #ffffff 0%, #f8fbff 100%); border: 1px solid rgba(28,36,75,0.12); box-shadow: 0 18px 45px rgba(28,36,75,0.10); margin-top: 22px; }\n    .ols-author-avatar-img { width: 92px; height: 92px; border-radius: 50%; object-fit: 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; letter-spacing: 0.01em; box-shadow: 0 10px 22px rgba(10,102,194,0.24); position: relative; overflow: hidden; transition: transform 0.22s ease, box-shadow 0.22s ease; }\n    .ols-linkedin-pill::before { content: \"\"; position: absolute; top: 0; left: -120%; width: 100%; height: 100%; background: linear-gradient(120deg, rgba(255,255,255,0) 0%, rgba(255,255,255,0.28) 50%, rgba(255,255,255,0) 100%); transition: left 0.7s ease; }\n    .ols-linkedin-pill:hover { transform: translateY(-3px) scale(1.03); box-shadow: 0 16px 34px rgba(10,102,194,0.34), 0 0 0 6px rgba(10,102,194,0.10); color: #ffffff; }\n    .ols-linkedin-pill:hover::before { left: 120%; }\n    .ols-linkedin-icon { width: 18px; height: 18px; display: block; flex-shrink: 0; }\n\n    .ols-note-card.soft { background: linear-gradient(135deg, #ffffff 0%, var(--soft-red) 100%); }\n    .ols-note-card.purple { background: linear-gradient(135deg, #ffffff 0%, var(--soft-purple) 100%); }\n    .ols-note-card.orange { background: 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      gap: 28px;\n      align-items: center;\n      margin-bottom: 24px;\n    }\n    .ols-course-cta-image-link { display: block; text-decoration: none; border-radius: 24px; }\n    .ols-course-cta-image {\n      width: 100%;\n      border-radius: 24px;\n      overflow: hidden;\n      border: 1px solid var(--border);\n      background: #ffffff;\n      box-shadow: var(--inner-shadow);\n      transition: transform 0.35s ease, box-shadow 0.35s ease;\n    }\n    .ols-course-cta-image img { width: 100%; height: auto; display: block; transition: transform 0.45s ease; }\n    .ols-course-cta-image-link:hover .ols-course-cta-image { transform: translateY(-8px) scale(1.015); box-shadow: 0 26px 60px rgba(28, 36, 75, 0.18), 0 0 0 1px rgba(37, 99, 235, 0.12); }\n    .ols-course-cta-image-link:hover .ols-course-cta-image img { transform: scale(1.03); }\n    .ols-course-cta-header-row { display: flex; flex-wrap: wrap; align-items: center; justify-content: space-between; gap: 14px; margin-bottom: 18px; }\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    .ols-course-feature p { margin: 0; color: var(--body-text); font-size: 15px; line-height: 1.6; font-weight: 300; }\n    .ols-course-cta-bottom { display: flex; justify-content: center; padding-top: 22px; border-top: 1px solid var(--border); }\n    .ols-course-button { display: inline-flex; align-items: center; justify-content: center; padding: 15px 28px; border-radius: 999px; background: var(--navy); color: #ffffff; text-decoration: none; font-size: 16px; line-height: 1.2; font-weight: 800; box-shadow: 0 12px 26px rgba(28, 36, 75, 0.18); transition: transform 0.2s ease, background 0.2s ease, box-shadow 0.2s ease; }\n    .ols-course-button:hover { transform: translateY(-2px); background: var(--blue); color: #ffffff; box-shadow: 0 16px 32px rgba(37, 99, 235, 0.24); }\n    .ols-course-button-top { flex-shrink: 0; padding: 12px 22px; font-size: 15px; }\n\n    .ols-attribution-card {\n      background: linear-gradient(135deg, #ffffff, #f8fbff);\n      border: 1px solid rgba(28, 36, 75, 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      .ols-note-title { align-items: flex-start; }\n      .ols-related-grid, .ols-course-cta-features { grid-template-columns: 1fr; }\n      .ols-figure-card { border-radius: 22px; }\n      .ols-figure-image { min-height: 210px; padding: 14px; }\n      .ols-figure-caption { padding: 16px; }\n      .ols-table-wrap { border: none; background: transparent; }\n      .ols-table, .ols-table thead, .ols-table tbody, .ols-table th, .ols-table td, .ols-table tr { display: block; width: 100%; }\n      .ols-table { border-collapse: separate; border-spacing: 0; }\n      .ols-table thead { display: none; }\n      .ols-table tr { margin-bottom: 14px; border: 1px solid var(--border); border-radius: 18px; overflow: hidden; background: #ffffff; box-shadow: var(--inner-shadow); }\n      .ols-table td { border-bottom: 1px solid var(--border); padding: 14px 16px; overflow-wrap: anywhere; }\n      .ols-table td:last-child { border-bottom: none; }\n      .ols-table td::before { content: attr(data-label); display: block; margin-bottom: 6px; font-size: 13px; font-weight: 700; color: var(--blue); }\n      .ols-author { align-items: flex-start; padding: 22px 18px; border-radius: 22px; }\n      .ols-author-avatar-img { width: 72px; height: 72px; }\n      .ols-author-title { font-size: 24px; }\n      .ols-author-description { font-size: 15px; }\n      .ols-course-cta-card { padding: 20px; border-radius: 24px; }\n      .ols-course-cta-header-row { align-items: stretch; }\n      .ols-course-button-top, .ols-course-button { width: 100%; }\n    }\n  \n    .ols-figure-placeholder .ols-placeholder-box { border: 2px dashed #c9973a; background: #fffaf0; border-radius: 16px; padding: 26px 22px; font-weight: 700; color: #7a4b12; text-align: center; line-height: 1.6; }\n    .ols-figure-placeholder .ols-figure-image { background: transparent; }\n    .ols-figure-placeholder { background: #ffffff; border: 1px solid rgba(28, 36, 75, 0.12); border-radius: 22px; padding: 14px; margin: 18px 0 6px; }\n    .ols-figure-placeholder .ols-figure-caption p { margin: 10px 0 0; font-size: 14px; color: #667085; text-align: center; }\n\n    \/* inline checks (H5P re-flow, Sep 2026) *\/\n    .ols-h5p-card.ols-h5p-inline { padding: 26px 28px; border-left: 6px solid #7c3aed; }\n    .ols-h5p-card.ols-h5p-inline h2 { font-size: clamp(20px, 2.2vw, 27px); letter-spacing: -0.02em; }\n    .ols-h5p-card.ols-h5p-inline > p { margin: 8px 0 0; }\n    .ols-h5p-card.ols-h5p-inline .ols-h5p-frame { margin-top: 16px; padding: 14px; border-radius: 20px; }\n    .ols-h5p-kicker { display: inline-block; margin-bottom: 10px; padding: 5px 12px; border-radius: 999px; background: #ede9fe; color: #5b21b6; font-size: 12px; font-weight: 700; letter-spacing: 0.06em; text-transform: uppercase; }\n    .ols-h5p-card.ols-h5p-recap { border-left-color: #c9973a; background: linear-gradient(135deg, #ffffff 0%, #fff8e8 100%); }\n    .ols-h5p-recap .ols-h5p-kicker { background: #fdf0d2; color: #8a5a00; }\n    @media (max-width: 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>3.1.5 Kinetics<\/h4>\n\n    <ul class=\"ols-topic-list\">\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-5-kinetics\/\">3.1.5 Overview<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-5-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\/aqa\/3-1-5-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\/aqa\/3-1-5-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\/aqa\/3-1-5-kinetics\/catalysts-and-reaction-profiles\/\">Catalysts and Reaction Profiles<\/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\/3-1-6-chemical-equilibria-le-chateliers-principle-and-kc\/\">3.1.6 Chemical Equilibria<\/a>\n      <\/li>\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\/3-1-2-amount-of-substance\/\">3.1.2 Amount of Substance<\/a>\n      <\/li>\n      <li>\n        <a href=\"https:\/\/www.onlinelearningsystem.net\/xyz\/revision-notes\/a-level-chemistry\/aqa\/3-1-7-oxidation-reduction-and-redox-equations\/\">3.1.7 Oxidation, Reduction and Redox<\/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, 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  <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\n        <div class=\"ols-badges\">\n<div class=\"ols-badge\">Paper 2 AQA<\/div>\n<div class=\"ols-badge\">3.1.5 Kinetics<\/div>\n<div class=\"ols-badge\">7405\/2<\/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>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-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\/t9x-tempchain.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\/t9x-tempchain.jpg\" alt=\"Cause-and-effect chain for the effect of temperature on rate, with distribution changes and a temperature versus catalyst table.\">\n<\/a>\n<\/div>\n<div class=\"ols-zoom-card-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-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\/kinetics-equilibria-boltzmann-temperature-catalyst.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\/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\">\n<\/a>\n<\/div>\n<div class=\"ols-zoom-card-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 3.1.5 Kinetics Pages<\/h2>\n<p>Use these pages to connect the ideas across 3.1.5 Kinetics 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\/3-1-5-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\/aqa\/3-1-5-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\/aqa\/3-1-5-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\/aqa\/3-1-5-kinetics\/\">3.1.5 Kinetics 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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