{"id":41945,"date":"2025-06-28T12:15:42","date_gmt":"2025-06-28T12:15:42","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=41945"},"modified":"2025-06-28T12:15:44","modified_gmt":"2025-06-28T12:15:44","slug":"consider-an-aqueous-solution-which-is-saturated-with-ag2so4","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/consider-an-aqueous-solution-which-is-saturated-with-ag2so4\/","title":{"rendered":"Consider an aqueous solution which is saturated with Ag2SO4."},"content":{"rendered":"\n<p>Consider an aqueous solution which is saturated with Ag2SO4. Given that Ksp of Ag2SO4 = 1.4 \u00d7 10\u20135. (a) Calculate [Ag+] in this saturated solution. Show your calculation. (b) What mass of Na2SO4 must be added to 0.500 L of the solution to decrease [Ag+] to 4.0 \u00d7 10\u20133 M? Show your calculation.<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(a) Calculation of [Ag+] in Saturated Solution<\/h3>\n\n\n\n<p>We are given that Ag2SO4 is saturated in an aqueous solution, and the solubility product (Ksp) of Ag2SO4 is:Ksp=1.4\u00d710\u22125K_{\\text{sp}} = 1.4 \\times 10^{-5}Ksp\u200b=1.4\u00d710\u22125<\/p>\n\n\n\n<p>The dissociation of Ag2SO4 in water can be represented as:Ag2SO4(s)\u21cc2Ag+(aq)+SO42\u2212(aq)\\text{Ag}_2\\text{SO}_4 (s) \\rightleftharpoons 2\\text{Ag}^+ (aq) + \\text{SO}_4^{2-} (aq)Ag2\u200bSO4\u200b(s)\u21cc2Ag+(aq)+SO42\u2212\u200b(aq)<\/p>\n\n\n\n<p>Let the solubility of Ag2SO4 be denoted as sss mol\/L. From the stoichiometry of the dissociation, we know that:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>The concentration of Ag+\\text{Ag}^+Ag+ ions will be 2s2s2s mol\/L (since 2 moles of Ag+ are produced for every mole of Ag2SO4 that dissolves).<\/li>\n\n\n\n<li>The concentration of SO42\u2212\\text{SO}_4^{2-}SO42\u2212\u200b ions will be sss mol\/L.<\/li>\n<\/ul>\n\n\n\n<p>Now, we write the expression for the solubility product (Ksp):Ksp=[Ag+]2[SO42\u2212]K_{\\text{sp}} = [\\text{Ag}^+]^2 [\\text{SO}_4^{2-}]Ksp\u200b=[Ag+]2[SO42\u2212\u200b]<\/p>\n\n\n\n<p>Substitute the values for [Ag+]=2s[\\text{Ag}^+] = 2s[Ag+]=2s and [SO42\u2212]=s[\\text{SO}_4^{2-}] = s[SO42\u2212\u200b]=s:1.4\u00d710\u22125=(2s)2\u22c5s1.4 \\times 10^{-5} = (2s)^2 \\cdot s1.4\u00d710\u22125=(2s)2\u22c5s<\/p>\n\n\n\n<p>Simplifying:1.4\u00d710\u22125=4s31.4 \\times 10^{-5} = 4s^31.4\u00d710\u22125=4s3<\/p>\n\n\n\n<p>Solve for sss:s3=1.4\u00d710\u221254=3.5\u00d710\u22126s^3 = \\frac{1.4 \\times 10^{-5}}{4} = 3.5 \\times 10^{-6}s3=41.4\u00d710\u22125\u200b=3.5\u00d710\u22126s=3.5\u00d710\u221263=1.52\u00d710\u22122\u2009Ms = \\sqrt[3]{3.5 \\times 10^{-6}} = 1.52 \\times 10^{-2} \\, \\text{M}s=33.5\u00d710\u22126\u200b=1.52\u00d710\u22122M<\/p>\n\n\n\n<p>Thus, the concentration of Ag+ ions in the saturated solution is:[Ag+]=2s=2\u00d71.52\u00d710\u22122=3.04\u00d710\u22122\u2009M[\\text{Ag}^+] = 2s = 2 \\times 1.52 \\times 10^{-2} = 3.04 \\times 10^{-2} \\, \\text{M}[Ag+]=2s=2\u00d71.52\u00d710\u22122=3.04\u00d710\u22122M<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">(b) Mass of Na2SO4 to Decrease [Ag+] to 4.0 \u00d7 10\u20133 M<\/h3>\n\n\n\n<p>We are tasked with reducing the concentration of Ag+\\text{Ag}^+Ag+ to 4.0\u00d710\u221234.0 \\times 10^{-3}4.0\u00d710\u22123 M by adding Na2SO4. The addition of Na2SO4 will provide SO42\u2212\\text{SO}_4^{2-}SO42\u2212\u200b ions, which will cause some of the Ag+\\text{Ag}^+Ag+ ions to precipitate as Ag2SO4. The relationship between the concentrations of ions and the solubility product remains:Ksp=[Ag+]2[SO42\u2212]K_{\\text{sp}} = [\\text{Ag}^+]^2 [\\text{SO}_4^{2-}]Ksp\u200b=[Ag+]2[SO42\u2212\u200b]<\/p>\n\n\n\n<p>We want to reduce [Ag+][\\text{Ag}^+][Ag+] to 4.0 \u00d7 10\u20133 M. Let\u2019s assume the concentration of SO42\u2212\\text{SO}_4^{2-}SO42\u2212\u200b added from Na2SO4 is xxx M.<\/p>\n\n\n\n<p>At equilibrium, we know:1.4\u00d710\u22125=(4.0\u00d710\u22123)2\u22c5x1.4 \\times 10^{-5} = (4.0 \\times 10^{-3})^2 \\cdot x1.4\u00d710\u22125=(4.0\u00d710\u22123)2\u22c5x<\/p>\n\n\n\n<p>Solve for xxx:1.4\u00d710\u22125=1.6\u00d710\u22125\u22c5x1.4 \\times 10^{-5} = 1.6 \\times 10^{-5} \\cdot x1.4\u00d710\u22125=1.6\u00d710\u22125\u22c5xx=1.4\u00d710\u221251.6\u00d710\u22125=0.875\u2009Mx = \\frac{1.4 \\times 10^{-5}}{1.6 \\times 10^{-5}} = 0.875 \\, \\text{M}x=1.6\u00d710\u221251.4\u00d710\u22125\u200b=0.875M<\/p>\n\n\n\n<p>Now, we need to find the mass of Na2SO4 required to achieve this concentration of SO42\u2212\\text{SO}_4^{2-}SO42\u2212\u200b in 0.500 L of solution. The number of moles of Na2SO4 required is:moles&nbsp;of&nbsp;Na2SO4=x\u00d7V=0.875\u2009mol\/L\u00d70.500\u2009L=0.4375\u2009mol\\text{moles of Na}_2\\text{SO}_4 = x \\times V = 0.875 \\, \\text{mol\/L} \\times 0.500 \\, \\text{L} = 0.4375 \\, \\text{mol}moles&nbsp;of&nbsp;Na2\u200bSO4\u200b=x\u00d7V=0.875mol\/L\u00d70.500L=0.4375mol<\/p>\n\n\n\n<p>The molar mass of Na2SO4 is:Molar&nbsp;mass&nbsp;of&nbsp;Na2SO4=(2\u00d723)+32+(4\u00d716)=142\u2009g\/mol\\text{Molar mass of Na}_2\\text{SO}_4 = (2 \\times 23) + 32 + (4 \\times 16) = 142 \\, \\text{g\/mol}Molar&nbsp;mass&nbsp;of&nbsp;Na2\u200bSO4\u200b=(2\u00d723)+32+(4\u00d716)=142g\/mol<\/p>\n\n\n\n<p>The mass of Na2SO4 required is:mass=moles\u00d7molar&nbsp;mass=0.4375\u2009mol\u00d7142\u2009g\/mol=62.125\u2009g\\text{mass} = \\text{moles} \\times \\text{molar mass} = 0.4375 \\, \\text{mol} \\times 142 \\, \\text{g\/mol} = 62.125 \\, \\text{g}mass=moles\u00d7molar&nbsp;mass=0.4375mol\u00d7142g\/mol=62.125g<\/p>\n\n\n\n<p>Thus, the mass of Na2SO4 that must be added is approximately:62.1\u2009g\\boxed{62.1 \\, \\text{g}}62.1g\u200b<\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1366.jpeg\" alt=\"\" class=\"wp-image-41946\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1366.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1366-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-1366-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>Consider an aqueous solution which is saturated with Ag2SO4. Given that Ksp of Ag2SO4 = 1.4 \u00d7 10\u20135. (a) Calculate [Ag+] in this saturated solution. Show your calculation. (b) What mass of Na2SO4 must be added to 0.500 L of the solution to decrease [Ag+] to 4.0 \u00d7 10\u20133 M? Show your calculation. The Correct [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-41945","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41945","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=41945"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41945\/revisions"}],"predecessor-version":[{"id":41947,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/41945\/revisions\/41947"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=41945"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=41945"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=41945"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}