{"id":236285,"date":"2025-06-16T07:08:47","date_gmt":"2025-06-16T07:08:47","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=236285"},"modified":"2025-06-16T07:08:49","modified_gmt":"2025-06-16T07:08:49","slug":"aspartame-has-the-chemical-formula-c14h18n2o5-and-undergoes-combustion-by-the-following-unbalanced-reaction","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/16\/aspartame-has-the-chemical-formula-c14h18n2o5-and-undergoes-combustion-by-the-following-unbalanced-reaction\/","title":{"rendered":"Aspartame has the chemical formula C14H18N2O5 and undergoes combustion by the following unbalanced reaction"},"content":{"rendered":"\n<p>Aspartame has the chemical formula C14H18N2O5 and undergoes combustion by the following unbalanced reaction: C14H18N2O5 + O2 \u00e2\u2020\u2019 CO2 + H2O + N2. Using bond dissociation energies, calculate the amount of energy released upon combustion of 35 pounds of aspartame: C14H18N2O5 + 1.5O2 \u00e2\u2020\u2019 4CO2 + 5H2O + N2. C-C = 347 kJ\/mol, C-H = 413 kJ\/mol, C-N = 305 kJ\/mol, N-N = 163 kJ\/mol, C=O = 799 kJ\/mol, O-H = 463 kJ\/mol, N-H = 391 kJ\/mol. Given that aspartame is often used as a substitute for sucrose (C12H22O11), determine the heat of combustion for 35 pounds of sucrose. Compare the two values and decide which one has the higher caloric content (1 kcal = 4.184 kJ).<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-ast-global-color-1-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To compare the energy released by the combustion of <strong>35 pounds of aspartame<\/strong> versus <strong>35 pounds of sucrose<\/strong>, first calculate the combustion energy using <strong>bond dissociation energies (BDEs)<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Molar Masses<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Aspartame (C\u2081\u2084H\u2081\u2088N\u2082O\u2085)<\/strong><br>= 14(12.01) + 18(1.008) + 2(14.01) + 5(16.00) = <strong>294.30 g\/mol<\/strong><\/li>\n\n\n\n<li><strong>Sucrose (C\u2081\u2082H\u2082\u2082O\u2081\u2081)<\/strong><br>= 12(12.01) + 22(1.008) + 11(16.00) = <strong>342.30 g\/mol<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Mass in grams<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>35 pounds = 35 \u00d7 453.592 = <strong>15,875.72 grams<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Moles of each substance<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Aspartame: 15,875.72 \/ 294.30 \u2248 <strong>53.94 mol<\/strong><\/li>\n\n\n\n<li>Sucrose: 15,875.72 \/ 342.30 \u2248 <strong>46.38 mol<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Energy per mole via bond energies (approximate estimate)<\/h3>\n\n\n\n<h4 class=\"wp-block-heading\">Bonds broken (in reactants, per mole of Aspartame):<\/h4>\n\n\n\n<p>Let\u2019s estimate approximately:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>14 C\u2013H: 14 \u00d7 413 = 5782<\/li>\n\n\n\n<li>6 C\u2013C: 6 \u00d7 347 = 2082<\/li>\n\n\n\n<li>4 C\u2013N: 4 \u00d7 305 = 1220<\/li>\n\n\n\n<li>4 N\u2013H: 4 \u00d7 391 = 1564<\/li>\n\n\n\n<li>5 C=O: 5 \u00d7 799 = 3995<\/li>\n\n\n\n<li>5 O\u2013H: 5 \u00d7 463 = 2315<\/li>\n\n\n\n<li><strong>Total bonds broken (energy input)<\/strong> \u2248 <strong>16,958 kJ\/mol<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Bonds formed (products):<\/h4>\n\n\n\n<ul class=\"wp-block-list\">\n<li>14 CO\u2082 (C=O): 28 C=O \u00d7 799 = 22,372<\/li>\n\n\n\n<li>9 H\u2082O: 18 O\u2013H \u00d7 463 = 8,334<\/li>\n\n\n\n<li>1 N\u2082 (N\u2261N): 1 \u00d7 946 = 946<\/li>\n\n\n\n<li><strong>Total bonds formed (energy released)<\/strong> \u2248 <strong>31,652 kJ\/mol<\/strong><\/li>\n<\/ul>\n\n\n\n<h4 class=\"wp-block-heading\">Net energy released per mole:<\/h4>\n\n\n\n<p>31,652 \u2212 16,958 = <strong>14,694 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\">Step 5: Total energy for 53.94 mol Aspartame<\/h3>\n\n\n\n<p>= 53.94 \u00d7 14,694 \u2248 <strong>792,492 kJ<\/strong><br>= 792,492 \u00f7 4.184 \u2248 <strong>189,414 kcal<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 6: Heat of combustion for sucrose (known)<\/h3>\n\n\n\n<p>Standard enthalpy of combustion for sucrose \u2248 <strong>\u22125645 kJ\/mol<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total energy = 46.38 \u00d7 5645 \u2248 <strong>261,773 kJ<\/strong><\/li>\n\n\n\n<li>In kcal = 261,773 \u00f7 4.184 \u2248 <strong>62,545 kcal<\/strong><\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Conclusion:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Aspartame (35 lb):<\/strong> ~189,414 kcal<\/li>\n\n\n\n<li><strong>Sucrose (35 lb):<\/strong> ~62,545 kcal<\/li>\n<\/ul>\n\n\n\n<p><strong>Aspartame<\/strong> releases significantly more energy per 35 pounds than sucrose, showing a higher caloric content by mass.<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner10-161.jpeg\" alt=\"\" class=\"wp-image-236286\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Aspartame has the chemical formula C14H18N2O5 and undergoes combustion by the following unbalanced reaction: C14H18N2O5 + O2 \u00e2\u2020\u2019 CO2 + H2O + N2. Using bond dissociation energies, calculate the amount of energy released upon combustion of 35 pounds of aspartame: C14H18N2O5 + 1.5O2 \u00e2\u2020\u2019 4CO2 + 5H2O + N2. C-C = 347 kJ\/mol, C-H = [&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-236285","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236285","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=236285"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/236285\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=236285"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=236285"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=236285"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}