{"id":233397,"date":"2025-06-13T05:55:47","date_gmt":"2025-06-13T05:55:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=233397"},"modified":"2025-06-13T05:55:49","modified_gmt":"2025-06-13T05:55:49","slug":"using-the-following-data-estimate-the-boiling-point-of-carbon-disulfide-cs2-cs2-l-%e2%86%92-cs2-g-%ce%b4h-27-2-kj-mol-%ce%b4s-86-66-j-k%c2%b7mol","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/13\/using-the-following-data-estimate-the-boiling-point-of-carbon-disulfide-cs2-cs2-l-%e2%86%92-cs2-g-%ce%b4h-27-2-kj-mol-%ce%b4s-86-66-j-k%c2%b7mol\/","title":{"rendered":"Using the following data, estimate the boiling point of carbon disulfide, CS2: CS2 (l) \u2192 CS2 (g) \u0394H\u00b0 = 27.2 kJ\/mol \u0394S\u00b0 = 86.66 J\/K\u00b7mol"},"content":{"rendered":"\n

Using the following data, estimate the boiling point of carbon disulfide, CS2: CS2 (l) \u2192 CS2 (g) \u0394H\u00b0 = 27.2 kJ\/mol \u0394S\u00b0 = 86.66 J\/K\u00b7mol<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To estimate the boiling point<\/strong> of carbon disulfide (CS\u2082)<\/strong>, we use the Gibbs free energy equation<\/strong> at equilibrium:<\/p>\n\n\n\n

Step 1: Use the Gibbs Free Energy Equation<\/strong><\/h3>\n\n\n\n

\u0394G\u2218=\u0394H\u2218\u2212T\u0394S\u2218\\Delta G^\\circ = \\Delta H^\\circ – T\\Delta S^\\circ\u0394G\u2218=\u0394H\u2218\u2212T\u0394S\u2218<\/p>\n\n\n\n

At the boiling point<\/strong>, the liquid and gas phases are in equilibrium, so:\u0394G\u2218=0\\Delta G^\\circ = 0\u0394G\u2218=0<\/p>\n\n\n\n

Thus:0=\u0394H\u2218\u2212T\u0394S\u2218\u21d2T=\u0394H\u2218\u0394S\u22180 = \\Delta H^\\circ – T\\Delta S^\\circ \\Rightarrow T = \\frac{\\Delta H^\\circ}{\\Delta S^\\circ}0=\u0394H\u2218\u2212T\u0394S\u2218\u21d2T=\u0394S\u2218\u0394H\u2218\u200b<\/p>\n\n\n\n

Step 2: Convert Units<\/strong><\/h3>\n\n\n\n
    \n
  • \u0394H\u00b0 = 27.2 kJ\/mol = 27,200 J\/mol<\/strong><\/li>\n\n\n\n
  • \u0394S\u00b0 = 86.66 J\/mol\u00b7K<\/strong><\/li>\n<\/ul>\n\n\n\n

    Step 3: Plug into the Equation<\/strong><\/h3>\n\n\n\n

    T=27,200 J\/mol86.66 J\/mol\\cdotpK=313.8 KT = \\frac{27,200\\ \\text{J\/mol}}{86.66\\ \\text{J\/mol\u00b7K}} = 313.8\\ \\text{K}T=86.66 J\/mol\\cdotpK27,200 J\/mol\u200b=313.8 K<\/p>\n\n\n\n

    Step 4: Convert to Celsius<\/strong><\/h3>\n\n\n\n

    T(\u00b0C)=313.8 K\u2212273.15=40.65\u2218CT(\u00b0C) = 313.8\\ \\text{K} – 273.15 = \\boxed{40.65^\\circ \\text{C}}T(\u00b0C)=313.8 K\u2212273.15=40.65\u2218C\u200b<\/p>\n\n\n\n

    \n\n\n\n

    Final Answer: The estimated normal boiling point of CS\u2082 is approximately 40.65\u00b0C.<\/strong><\/h3>\n\n\n\n
    \n\n\n\n

    Explanation <\/strong><\/h3>\n\n\n\n

    To determine the normal boiling point of carbon disulfide (CS\u2082), we apply thermodynamic principles involving phase equilibrium. The boiling point is the temperature at which the liquid and gas phases of a substance are in equilibrium at 1 atm pressure. At this point, the Gibbs free energy change (\u0394G\u00b0) for vaporization is zero because there is no net change in energy when the substance moves between liquid and vapor states.<\/p>\n\n\n\n

    We start by using the standard Gibbs free energy equation:\u0394G\u2218=\u0394H\u2218\u2212T\u0394S\u2218\\Delta G^\\circ = \\Delta H^\\circ – T\\Delta S^\\circ\u0394G\u2218=\u0394H\u2218\u2212T\u0394S\u2218<\/p>\n\n\n\n

    At the boiling point, \u0394G\u2218=0\\Delta G^\\circ = 0\u0394G\u2218=0, so the equation simplifies to:T=\u0394H\u2218\u0394S\u2218T = \\frac{\\Delta H^\\circ}{\\Delta S^\\circ}T=\u0394S\u2218\u0394H\u2218\u200b<\/p>\n\n\n\n

    Given values are:<\/p>\n\n\n\n

      \n
    • Enthalpy of vaporization, \u0394H\u2218=27.2\u00a0kJ\/mol=27,200\u00a0J\/mol\\Delta H^\\circ = 27.2\\ \\text{kJ\/mol} = 27,200\\ \\text{J\/mol}\u0394H\u2218=27.2\u00a0kJ\/mol=27,200\u00a0J\/mol<\/li>\n\n\n\n
    • Entropy of vaporization, \u0394S\u2218=86.66\u00a0J\/mol\\cdotpK\\Delta S^\\circ = 86.66\\ \\text{J\/mol\u00b7K}\u0394S\u2218=86.66\u00a0J\/mol\\cdotpK<\/li>\n<\/ul>\n\n\n\n

      Substituting into the equation:T=27,20086.66\u2248313.8 KT = \\frac{27,200}{86.66} \\approx 313.8\\ \\text{K}T=86.6627,200\u200b\u2248313.8 K<\/p>\n\n\n\n

      To convert this to Celsius, subtract 273.15:T(\u00b0C)=313.8\u2212273.15=40.65\u2218CT(\u00b0C) = 313.8 – 273.15 = 40.65^\\circ \\text{C}T(\u00b0C)=313.8\u2212273.15=40.65\u2218C<\/p>\n\n\n\n

      Thus, the estimated normal boiling point of carbon disulfide is approximately 40.65\u00b0C<\/strong>, consistent with its known physical properties. This method provides a useful estimation by applying fundamental thermodynamic relationships.<\/p>\n\n\n\n

      \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

      Using the following data, estimate the boiling point of carbon disulfide, CS2: CS2 (l) \u2192 CS2 (g) \u0394H\u00b0 = 27.2 kJ\/mol \u0394S\u00b0 = 86.66 J\/K\u00b7mol The Correct Answer and Explanation is: To estimate the boiling point of carbon disulfide (CS\u2082), we use the Gibbs free energy equation at equilibrium: Step 1: Use the Gibbs Free […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-233397","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233397","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=233397"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/233397\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=233397"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=233397"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=233397"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}