{"id":149238,"date":"2024-10-07T06:40:55","date_gmt":"2024-10-07T06:40:55","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=149238"},"modified":"2024-10-07T06:40:58","modified_gmt":"2024-10-07T06:40:58","slug":"acetylene-c2h2-can-be-converted-to-ethane","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/07\/acetylene-c2h2-can-be-converted-to-ethane\/","title":{"rendered":"Acetylene, C2H2, can be converted to ethane"},"content":{"rendered":"\n<p>Acetylene, C2H2, can be converted to ethane, C2H6, by a process known as hydrogenation. The reaction is C2H2(g)+2H2(g)?C2H6(g)<br>Given the following data, what is the value of Kp for this reaction?<\/p>\n\n\n\n<p>Substance ?G?f<br>(kJ\/mol)<br>C2H2(g) 209.2<br>H2(g) 0<br>C2H6(g) ?32.89<\/p>\n\n\n\n<p><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\"><strong>The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n<p>To calculate the equilibrium constant ( K_p ) for the hydrogenation of acetylene to ethane, we can use the Gibbs free energy change (( \\Delta G )) of the reaction. The equation for the reaction is:<\/p>\n\n\n\n<p>[<br>\\text{C}_2\\text{H}_2(g) + 2\\text{H}_2(g) \\rightleftharpoons \\text{C}_2\\text{H}_6(g)<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Calculate the Gibbs Free Energy Change (( \\Delta G ))<\/h3>\n\n\n\n<p>The standard Gibbs free energy change for a reaction can be calculated using the following equation:<\/p>\n\n\n\n<p>[<br>\\Delta G^\\circ = \\sum \\Delta G_f^\\circ \\text{(products)} &#8211; \\sum \\Delta G_f^\\circ \\text{(reactants)}<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\Delta G_f^\\circ ) is the standard Gibbs free energy of formation.<\/li>\n<\/ul>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( \\Delta G_f^\\circ ) for C\u2082H\u2082(g) = 209.2 kJ\/mol<\/li>\n\n\n\n<li>( \\Delta G_f^\\circ ) for H\u2082(g) = 0 kJ\/mol (as it&#8217;s an element in its standard state)<\/li>\n\n\n\n<li>( \\Delta G_f^\\circ ) for C\u2082H\u2086(g) = -32.89 kJ\/mol<\/li>\n<\/ul>\n\n\n\n<p>Plugging these values into the equation gives:<\/p>\n\n\n\n<p>[<br>\\Delta G^\\circ = \\Delta G_f^\\circ \\text{(C}_2\\text{H}_6\\text{)} &#8211; \\left[ \\Delta G_f^\\circ \\text{(C}_2\\text{H}_2\\text{)} + 2 \\cdot \\Delta G_f^\\circ \\text{(H}_2\\text{)} \\right]<br>]<\/p>\n\n\n\n<p>[<br>\\Delta G^\\circ = (-32.89 \\, \\text{kJ\/mol}) &#8211; \\left[ 209.2 \\, \\text{kJ\/mol} + 2 \\cdot 0 \\, \\text{kJ\/mol} \\right]<br>]<\/p>\n\n\n\n<p>[<br>\\Delta G^\\circ = -32.89 \\, \\text{kJ\/mol} &#8211; 209.2 \\, \\text{kJ\/mol} = -242.09 \\, \\text{kJ\/mol}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate the Equilibrium Constant (( K_p ))<\/h3>\n\n\n\n<p>The relationship between the Gibbs free energy change and the equilibrium constant is given by the equation:<\/p>\n\n\n\n<p>[<br>\\Delta G^\\circ = -RT \\ln K_p<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>( R ) is the universal gas constant ( (8.314 \\, \\text{J\/mol\u00b7K}) )<\/li>\n\n\n\n<li>( T ) is the temperature in Kelvin (assuming standard conditions, ( T = 298 \\, \\text{K} ))<\/li>\n<\/ul>\n\n\n\n<p>First, convert ( \\Delta G^\\circ ) to Joules:<\/p>\n\n\n\n<p>[<br>\\Delta G^\\circ = -242.09 \\, \\text{kJ\/mol} \\times 1000 \\, \\text{J\/kJ} = -242090 \\, \\text{J\/mol}<br>]<\/p>\n\n\n\n<p>Now, rearranging the equation to solve for ( K_p ):<\/p>\n\n\n\n<p>[<br>K_p = e^{-\\Delta G^\\circ \/ RT}<br>]<\/p>\n\n\n\n<p>Substituting the values:<\/p>\n\n\n\n<p>[<br>K_p = e^{242090 \\, \\text{J\/mol} \/ (8.314 \\, \\text{J\/mol\u00b7K} \\cdot 298 \\, \\text{K})}<br>]<\/p>\n\n\n\n<p>Calculating:<\/p>\n\n\n\n<p>[<br>K_p = e^{242090 \/ 2478.572} = e^{97.685}<br>]<\/p>\n\n\n\n<p>Calculating ( e^{97.685} ):<\/p>\n\n\n\n<p>[<br>K_p \\approx 1.305 \\times 10^{42}<br>]<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Conclusion<\/h3>\n\n\n\n<p>The equilibrium constant ( K_p ) for the hydrogenation of acetylene to ethane at standard conditions is approximately ( 1.305 \\times 10^{42} ). This indicates that the reaction strongly favors the formation of ethane from acetylene and hydrogen, demonstrating the stability of ethane compared to the reactants under standard conditions.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>Acetylene, C2H2, can be converted to ethane, C2H6, by a process known as hydrogenation. The reaction is C2H2(g)+2H2(g)?C2H6(g)Given the following data, what is the value of Kp for this reaction? Substance ?G?f(kJ\/mol)C2H2(g) 209.2H2(g) 0C2H6(g) ?32.89 The Correct Answer and Explanation is : To calculate the equilibrium constant ( K_p ) for the hydrogenation of acetylene [&hellip;]<\/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-149238","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149238","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=149238"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/149238\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=149238"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=149238"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=149238"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}