{"id":198000,"date":"2025-03-08T07:50:45","date_gmt":"2025-03-08T07:50:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=198000"},"modified":"2025-03-08T07:50:48","modified_gmt":"2025-03-08T07:50:48","slug":"the-change-in-internal-energy-of-the-combustion-of-solid-naphthalene-c10h8-was-determined-to-be-equal-to-5151-kj-mol","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/03\/08\/the-change-in-internal-energy-of-the-combustion-of-solid-naphthalene-c10h8-was-determined-to-be-equal-to-5151-kj-mol\/","title":{"rendered":"The change in internal energy of the combustion of solid naphthalene (C10H8) was determined to be equal to -5151 kJ\/mol"},"content":{"rendered":"\n<p>The change in internal energy of the combustion of solid naphthalene (C10H8) was determined to be equal to -5151 kJ\/mol. Calculate its enthalpy of combustion.<\/p>\n\n\n\n<p> What is the change in internal energy of a system if the system evolves 525 J of heat and has 1.25 kJ of work done on it<\/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<h3 class=\"wp-block-heading\">1. Enthalpy of Combustion of Naphthalene (C\u2081\u2080H\u2088)<\/h3>\n\n\n\n<p>The change in internal energy (\u0394U) for the combustion of solid naphthalene (C\u2081\u2080H\u2088) is given as -5151 kJ\/mol. The relationship between internal energy (\u0394U) and enthalpy (\u0394H) is given by the following equation:<\/p>\n\n\n\n<p>[<br>\\Delta H = \\Delta U + \\Delta n \\cdot R \\cdot T<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0394H is the enthalpy change<\/li>\n\n\n\n<li>\u0394U is the internal energy change<\/li>\n\n\n\n<li>\u0394n is the change in the number of moles of gas (products minus reactants)<\/li>\n\n\n\n<li>R is the universal gas constant (8.314 J\/mol\u00b7K)<\/li>\n\n\n\n<li>T is the temperature (assumed to be 298 K for standard conditions)<\/li>\n<\/ul>\n\n\n\n<p>For combustion reactions involving solid naphthalene, the combustion products are gaseous CO\u2082 and H\u2082O. The combustion equation for naphthalene is:<\/p>\n\n\n\n<p>[<br>C_{10}H_8 (s) + 12 O_2 (g) \\rightarrow 10 CO_2 (g) + 4 H_2O (g)<br>]<\/p>\n\n\n\n<p>Now, let&#8217;s determine \u0394n (change in moles of gas):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>On the left side, we have 12 moles of O\u2082 (gas).<\/li>\n\n\n\n<li>On the right side, we have 10 moles of CO\u2082 (gas) and 4 moles of H\u2082O (gas).<br>Thus, \u0394n = (10 + 4) &#8211; 12 = 2.<\/li>\n<\/ul>\n\n\n\n<p>Now, applying the equation to calculate \u0394H:<br>[<br>\\Delta H = \\Delta U + \\Delta n \\cdot R \\cdot T = -5151 \\, \\text{kJ\/mol} + (2) \\cdot (8.314 \\, \\text{J\/mol\u00b7K}) \\cdot (298 \\, \\text{K})<br>]<\/p>\n\n\n\n<p>First, convert the gas constant to kJ for consistency with the units of \u0394U:<br>[<br>\\Delta H = -5151 \\, \\text{kJ\/mol} + (2 \\cdot 8.314 \\cdot 298) \/ 1000<br>]<br>[<br>\\Delta H = -5151 \\, \\text{kJ\/mol} + 4.95 \\, \\text{kJ\/mol}<br>]<br>[<br>\\Delta H = -5146.05 \\, \\text{kJ\/mol}<br>]<\/p>\n\n\n\n<p>Thus, the enthalpy of combustion of solid naphthalene is approximately <strong>-5146.05 kJ\/mol<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">2. Change in Internal Energy of a System<\/h3>\n\n\n\n<p>The change in internal energy of a system can be determined using the following equation:<\/p>\n\n\n\n<p>[<br>\\Delta U = Q &#8211; W<br>]<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0394U is the change in internal energy<\/li>\n\n\n\n<li>Q is the heat evolved (or absorbed) by the system<\/li>\n\n\n\n<li>W is the work done by or on the system<\/li>\n<\/ul>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Q = 525 J (heat evolved by the system)<\/li>\n\n\n\n<li>W = 1.25 kJ = 1250 J (work done on the system)<\/li>\n<\/ul>\n\n\n\n<p>Now, substitute these values into the equation:<\/p>\n\n\n\n<p>[<br>\\Delta U = 525 \\, \\text{J} &#8211; 1250 \\, \\text{J}<br>]<br>[<br>\\Delta U = -725 \\, \\text{J}<br>]<\/p>\n\n\n\n<p>Thus, the change in internal energy of the system is <strong>-725 J<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Enthalpy of Combustion of Naphthalene<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The combustion reaction of solid naphthalene involves the conversion of a solid to gaseous products (CO\u2082 and H\u2082O), leading to a release of heat. The internal energy change (\u0394U) is given as -5151 kJ\/mol, which reflects the heat released during combustion.<\/li>\n\n\n\n<li>The difference between enthalpy (\u0394H) and internal energy (\u0394U) is accounted for by the change in the number of moles of gas produced in the reaction, which is why we apply the equation \u0394H = \u0394U + \u0394nRT.<\/li>\n<\/ul>\n\n\n\n<ol class=\"wp-block-list\">\n<li><strong>Change in Internal Energy of a System<\/strong>:<\/li>\n<\/ol>\n\n\n\n<ul class=\"wp-block-list\">\n<li>In the second part, the system undergoes a process where heat is released (525 J) and work is done on it (1.25 kJ). Since heat is released (positive Q), and work is done on the system (positive W), the internal energy decreases because the work done on the system is greater than the heat released. Therefore, the internal energy change is negative, -725 J.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-large\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/03\/image-590-1024x766.png\" alt=\"\" class=\"wp-image-198001\"\/><\/figure>\n\n\n\n<p>Here is a visual representation of the change in internal energy of the system:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The first bar shows the heat evolved (525 J).<\/li>\n\n\n\n<li>The second bar represents the work done on the system (1.25 kJ or 1250 J).<\/li>\n\n\n\n<li>The third bar shows the total change in internal energy (\u0394U), which is -725 J.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>The change in internal energy of the combustion of solid naphthalene (C10H8) was determined to be equal to -5151 kJ\/mol. Calculate its enthalpy of combustion. What is the change in internal energy of a system if the system evolves 525 J of heat and has 1.25 kJ of work done on it The correct answer [&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-198000","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198000","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=198000"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/198000\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=198000"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=198000"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=198000"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}