{"id":234369,"date":"2025-06-14T05:07:30","date_gmt":"2025-06-14T05:07:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=234369"},"modified":"2025-06-14T05:07:33","modified_gmt":"2025-06-14T05:07:33","slug":"the-two-alternative-chair-conformations-of-cis-1-bromo-2-methylcyclohexane-differ-in-their-gibbs-free-energy","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/14\/the-two-alternative-chair-conformations-of-cis-1-bromo-2-methylcyclohexane-differ-in-their-gibbs-free-energy\/","title":{"rendered":"The two alternative chair conformations of cis-1-bromo-2-methylcyclohexane differ in their Gibbs free energy."},"content":{"rendered":"\n

The two alternative chair conformations of cis-1-bromo-2-methylcyclohexane differ in their Gibbs free energy. Using the data for 4G (Axial-Equatorial) for monosubstituted cyclohexanes at room temperature (25\u00c2\u00b0C): Axial Equatorial Group AGo (kJ\/mol) Group 46\u00c2\u00b0 (kJ\/mol) C=N -0.8 NH2 CH3 5.9 22.4 -73 OH -3.9 L.2-gauche 3.8 Calculate the absolute value of the difference in the Gibbs free energy between the alternative chair conformations: kJ\/mol. Which group in this compound is in the axial position in the energetically preferred chair conformation? Methyl. Submlt Answer Try Another Item attempts remaining amino<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Here are the correct answers and a detailed explanation.<\/p>\n\n\n\n

Part a:<\/strong> The absolute value of the difference in the Gibbs free energy between the alternative chair conformations is 4.9<\/strong> kJ\/mol.<\/p>\n\n\n\n

Part b:<\/strong> The Br<\/strong> group in this compound is in the axial position in the energetically preferred chair conformation.<\/p>\n\n\n\n

\n\n\n\n

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

1. Understanding the Conformations of cis<\/em>-1-bromo-2-methylcyclohexane<\/strong><\/p>\n\n\n\n

The compound is cis<\/em>-1-bromo-2-methylcyclohexane. In a cyclohexane ring, a cis<\/em>-1,2 relationship means that both substituents are on the same side of the ring. For this to occur in a chair conformation, one substituent must be in an axial position and the other in an equatorial position. The molecule exists as an equilibrium between two chair conformations that interconvert via a “ring flip”.<\/p>\n\n\n\n

    \n
  • Conformation A:<\/strong>\u00a0The bromo (Br) group is axial and the methyl (CH\u2083) group is equatorial.<\/li>\n\n\n\n
  • Conformation B:<\/strong>\u00a0After a ring flip, the bromo (Br) group becomes equatorial and the methyl (CH\u2083) group becomes axial.<\/li>\n<\/ul>\n\n\n\n

    2. Analyzing Steric Strain using A-values<\/strong><\/p>\n\n\n\n

    The stability of a substituted cyclohexane conformation depends on the steric strain, primarily the 1,3-diaxial interactions experienced by axial substituents. The provided \u0394G\u00b0 values, often called A-values<\/strong>, quantify this strain. They represent the energy cost of having a group in the axial position versus the more stable equatorial position.<\/p>\n\n\n\n

    From the table:<\/p>\n\n\n\n

      \n
    • A-value for Br:<\/strong>\u00a0The energy cost for an axial Br is\u00a02.4 kJ\/mol<\/strong>. (\u0394G\u00b0 for Axial \u2192 Equatorial is -2.4 kJ\/mol, so the axial state is 2.4 kJ\/mol higher in energy).<\/li>\n\n\n\n
    • A-value for CH\u2083:<\/strong>\u00a0The energy cost for an axial CH\u2083 is\u00a07.3 kJ\/mol<\/strong>. (\u0394G\u00b0 for Axial \u2192 Equatorial is -7.3 kJ\/mol, so the axial state is 7.3 kJ\/mol higher in energy).<\/li>\n<\/ul>\n\n\n\n

      The 1,2-gauche interaction (3.8 kJ\/mol) exists between the two substituents in both conformations (axial-equatorial is a gauche relationship), so it cancels out when we calculate the difference in energy between them.<\/p>\n\n\n\n

      3. Calculating the Energy of Each Conformation<\/strong><\/p>\n\n\n\n

      We can estimate the relative energy of each conformation by summing the A-values for the axial substituents.<\/p>\n\n\n\n

        \n
      • Energy of Conformation A (axial Br, equatorial CH\u2083):<\/strong>\u00a0The only axial substituent is Br.\n
          \n
        • Strain = A-value (Br) =\u00a02.4 kJ\/mol<\/strong><\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Energy of Conformation B (equatorial Br, axial CH\u2083):<\/strong>\u00a0The only axial substituent is CH\u2083.\n
            \n
          • Strain = A-value (CH\u2083) =\u00a07.3 kJ\/mol<\/strong><\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n

            4. Solving Part a: Difference in Gibbs Free Energy<\/strong><\/p>\n\n\n\n

            The difference in Gibbs free energy (\u0394\u0394G\u00b0) between the two conformations is the difference in their total strain energies.<\/p>\n\n\n\n

              \n
            • \u0394\u0394G\u00b0 = Energy(Conformation B) – Energy(Conformation A)<\/li>\n\n\n\n
            • \u0394\u0394G\u00b0 = 7.3 kJ\/mol – 2.4 kJ\/mol = 4.9 kJ\/mol<\/li>\n<\/ul>\n\n\n\n

              The absolute value of this difference is 4.9 kJ\/mol<\/strong>.<\/p>\n\n\n\n

              5. Solving Part b: The Preferred Conformation<\/strong><\/p>\n\n\n\n

              The energetically preferred (most stable) conformation is the one with the lowest Gibbs free energy (i.e., the least steric strain).<\/p>\n\n\n\n

                \n
              • Energy of Conformation A = 2.4 kJ\/mol<\/li>\n\n\n\n
              • Energy of Conformation B = 7.3 kJ\/mol<\/li>\n<\/ul>\n\n\n\n

                Since 2.4 kJ\/mol < 7.3 kJ\/mol, Conformation A is the preferred conformation<\/strong>. This follows the general principle that the larger, bulkier group (the one with the higher A-value, in this case, methyl) will preferentially occupy the less crowded equatorial position to minimize steric strain.<\/p>\n\n\n\n

                In the preferred conformation (Conformation A), the methyl group is equatorial, and the bromo (Br) group is in the axial position<\/strong>.<\/p>\n\n\n\n

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

                The two alternative chair conformations of cis-1-bromo-2-methylcyclohexane differ in their Gibbs free energy. Using the data for 4G (Axial-Equatorial) for monosubstituted cyclohexanes at room temperature (25\u00c2\u00b0C): Axial Equatorial Group AGo (kJ\/mol) Group 46\u00c2\u00b0 (kJ\/mol) C=N -0.8 NH2 CH3 5.9 22.4 -73 OH -3.9 L.2-gauche 3.8 Calculate the absolute value of the difference in the Gibbs […]<\/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-234369","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234369","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=234369"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/234369\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=234369"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=234369"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=234369"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}