{"id":184203,"date":"2025-01-19T12:51:30","date_gmt":"2025-01-19T12:51:30","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=184203"},"modified":"2025-01-19T12:51:33","modified_gmt":"2025-01-19T12:51:33","slug":"how-do-they-get-rid-of-the-ln-in-the-second-to-last-step-to-get-the-keq","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/19\/how-do-they-get-rid-of-the-ln-in-the-second-to-last-step-to-get-the-keq\/","title":{"rendered":"How do they get rid of the &#8220;ln&#8221; in the second to last step to get the K&#8217;eq"},"content":{"rendered":"\n<p>How do they get rid of the &#8220;ln&#8221; in the second to last step to get the K&amp;#39;eq?<\/p>\n\n\n\n<p>I tried to divide the 5.56 by the ln (5.56\/ln) but it didn&amp;#39;t give me the 260 like they got.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-6-color\">The correct answer and explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>The confusion arises because &#8220;ln&#8221; refers to the natural logarithm, which is the inverse of the exponential function. To clarify the process for obtaining KeqK_{\\text{eq}}, let&#8217;s break it down step by step:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Equation Setup<\/strong>: From the second-to-last step, we have: \u0394G\u2218=\u2212RTln\u2061Keq\\Delta G^\\circ = -RT \\ln K_{\\text{eq}} where:\n<ul class=\"wp-block-list\">\n<li>\u0394G\u2218=\u22123.2\u2009kJ\/mol=\u22123200\u2009J\/mol\\Delta G^\\circ = -3.2 \\, \\text{kJ\/mol} = -3200 \\, \\text{J\/mol},<\/li>\n\n\n\n<li>R=8.314\u2009J\/(mol\\cdotpK)R = 8.314 \\, \\text{J\/(mol\u00b7K)},<\/li>\n\n\n\n<li>T=298\u2009KT = 298 \\, \\text{K}.<\/li>\n<\/ul>\n<\/li>\n\n\n\n<li><strong>Rearrange for KeqK_{\\text{eq}}<\/strong>: ln\u2061Keq=\u2212\u0394G\u2218RT\\ln K_{\\text{eq}} = -\\frac{\\Delta G^\\circ}{RT}<\/li>\n\n\n\n<li><strong>Calculate ln\u2061Keq\\ln K_{\\text{eq}}<\/strong>: Substitute the values: ln\u2061Keq=\u2212\u221232008.314\u00d7298\\ln K_{\\text{eq}} = -\\frac{-3200}{8.314 \\times 298} Simplify: ln\u2061Keq=32002478.572\u22481.29\\ln K_{\\text{eq}} = \\frac{3200}{2478.572} \\approx 1.29<\/li>\n\n\n\n<li><strong>Solve for KeqK_{\\text{eq}}<\/strong>: To find KeqK_{\\text{eq}}, take the exponential of both sides: Keq=eln\u2061Keq=e1.29K_{\\text{eq}} = e^{\\ln K_{\\text{eq}}} = e^{1.29} Use a calculator: Keq\u2248e1.29\u22483.64K_{\\text{eq}} \\approx e^{1.29} \\approx 3.64<\/li>\n<\/ol>\n\n\n\n<p>If you provide the exact details from your question or the original \u0394G\u2218\\Delta G^\\circ and parameters, I can confirm or refine this explanation further. The value you&#8217;re trying to get\u2014like 260\u2014might arise from different parameter values or units.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>How do they get rid of the &#8220;ln&#8221; in the second to last step to get the K&amp;#39;eq? I tried to divide the 5.56 by the ln (5.56\/ln) but it didn&amp;#39;t give me the 260 like they got. The correct answer and explanation is: The confusion arises because &#8220;ln&#8221; refers to the natural logarithm, which [&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-184203","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184203","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=184203"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/184203\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=184203"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=184203"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=184203"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}