{"id":263848,"date":"2025-07-21T09:27:45","date_gmt":"2025-07-21T09:27:45","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=263848"},"modified":"2025-07-21T09:27:47","modified_gmt":"2025-07-21T09:27:47","slug":"nitrous-acid-hno2-is-a-weak-acid-that-dissociates-in-water-in-the-following-manner","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/21\/nitrous-acid-hno2-is-a-weak-acid-that-dissociates-in-water-in-the-following-manner\/","title":{"rendered":"Nitrous acid (HNO2) is a weak acid that dissociates in water in the following manner"},"content":{"rendered":"\n<p>Nitrous acid (HNO2) is a weak acid that dissociates in water in the following manner: HNO2(aq) + H2O(l) \u00e2\u2020\u2019 NO2\u00e2\u02c6\u2019(aq) + H3O+(aq) At a temperature of 298.15 K, the acid-dissociation constant (Ka) for nitrous acid is 5.6 \u00c3\u2014 10\u00e2\u02c6\u20194. (a) Calculate the change in standard free energy (\u00ce\u201dG\u00c2\u00b0) for this equilibrium reaction. kJ\/mol (b) What is the value of \u00ce\u201dG at equilibrium? \u00ce\u201dG > 0 \u00ce\u201dG = 0 \u00ce\u201dG &lt; 0 (c) If the reaction were spontaneous in the forward direction, what type of value would you expect for \u00ce\u201dG? \u00ce\u201dG > 0 \u00ce\u201dG = 0 \u00ce\u201dG &lt; 0<\/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>Let&#8217;s work through the problem step by step.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(a) Calculate the change in standard free energy (\u0394G\u00b0) for the equilibrium reaction.<\/h3>\n\n\n\n<p>The relationship between the standard free energy change (\u0394G\u00b0) and the acid dissociation constant (Ka) is given by the following equation: \u0394G\u2218=\u2212RTln\u2061(Ka)\\Delta G^\\circ = -RT \\ln(K_a)\u0394G\u2218=\u2212RTln(Ka\u200b)<\/p>\n\n\n\n<p>Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>RRR is the universal gas constant, 8.314\u2009J\/mol\\cdotpK8.314 \\, \\text{J\/mol\u00b7K}8.314J\/mol\\cdotpK,<\/li>\n\n\n\n<li>TTT is the temperature in Kelvin, 298.15\u2009K298.15 \\, \\text{K}298.15K,<\/li>\n\n\n\n<li>KaK_aKa\u200b is the acid dissociation constant, 5.6\u00d710\u221245.6 \\times 10^{-4}5.6\u00d710\u22124.<\/li>\n<\/ul>\n\n\n\n<p>First, substitute the values into the equation: \u0394G\u2218=\u2212(8.314\u2009J\/mol\\cdotpK)(298.15\u2009K)ln\u2061(5.6\u00d710\u22124)\\Delta G^\\circ = -(8.314 \\, \\text{J\/mol\u00b7K}) (298.15 \\, \\text{K}) \\ln(5.6 \\times 10^{-4})\u0394G\u2218=\u2212(8.314J\/mol\\cdotpK)(298.15K)ln(5.6\u00d710\u22124)<\/p>\n\n\n\n<p>Now calculate: ln\u2061(5.6\u00d710\u22124)=\u22127.478\\ln(5.6 \\times 10^{-4}) = -7.478ln(5.6\u00d710\u22124)=\u22127.478 \u0394G\u2218=\u2212(8.314)(298.15)(\u22127.478)\\Delta G^\\circ = -(8.314) (298.15) (-7.478)\u0394G\u2218=\u2212(8.314)(298.15)(\u22127.478) \u0394G\u2218=18465.8\u2009J\/mol\u224818.47\u2009kJ\/mol\\Delta G^\\circ = 18465.8 \\, \\text{J\/mol} \\approx 18.47 \\, \\text{kJ\/mol}\u0394G\u2218=18465.8J\/mol\u224818.47kJ\/mol<\/p>\n\n\n\n<p>Thus, the change in standard free energy is: \u0394G\u2218\u2248+18.47\u2009kJ\/mol\\Delta G^\\circ \\approx +18.47 \\, \\text{kJ\/mol}\u0394G\u2218\u2248+18.47kJ\/mol<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(b) What is the value of \u0394G at equilibrium?<\/h3>\n\n\n\n<p>At equilibrium, the change in free energy (\u0394G\\Delta G\u0394G) is equal to zero because the system has reached a state where the forward and reverse reactions occur at the same rate. This is true for any system at equilibrium, whether it&#8217;s a chemical reaction or a physical process.<\/p>\n\n\n\n<p>Thus: \u0394G=0\\Delta G = 0\u0394G=0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(c) If the reaction were spontaneous in the forward direction, what type of value would you expect for \u0394G?<\/h3>\n\n\n\n<p>A spontaneous reaction occurs when the change in free energy (\u0394G\\Delta G\u0394G) is negative. If a reaction is spontaneous in the forward direction, it indicates that the products are thermodynamically more stable than the reactants, meaning that the free energy decreases as the reaction proceeds.<\/p>\n\n\n\n<p>So, if the reaction were spontaneous, you would expect: \u0394G&lt;0\\Delta G &lt; 0\u0394G&lt;0<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Summary:<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>(a) \u0394G\u2218\u2248+18.47\u2009kJ\/mol\\Delta G^\\circ \\approx +18.47 \\, \\text{kJ\/mol}\u0394G\u2218\u2248+18.47kJ\/mol.<\/li>\n\n\n\n<li>(b) \u0394G=0\\Delta G = 0\u0394G=0 at equilibrium.<\/li>\n\n\n\n<li>(c) If the reaction were spontaneous, \u0394G&lt;0\\Delta G &lt; 0\u0394G&lt;0.<\/li>\n<\/ul>\n\n\n\n<figure class=\"wp-block-image size-full\"><img decoding=\"async\" src=\"https:\/\/learnexams.com\/blog\/wp-content\/uploads\/2025\/07\/learnexams-banner6-1335.jpeg\" alt=\"\" class=\"wp-image-263849\"\/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Nitrous acid (HNO2) is a weak acid that dissociates in water in the following manner: HNO2(aq) + H2O(l) \u00e2\u2020\u2019 NO2\u00e2\u02c6\u2019(aq) + H3O+(aq) At a temperature of 298.15 K, the acid-dissociation constant (Ka) for nitrous acid is 5.6 \u00c3\u2014 10\u00e2\u02c6\u20194. (a) Calculate the change in standard free energy (\u00ce\u201dG\u00c2\u00b0) for this equilibrium reaction. kJ\/mol (b) What [&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-263848","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263848","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=263848"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/263848\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=263848"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=263848"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=263848"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}