{"id":16846,"date":"2025-06-11T20:37:01","date_gmt":"2025-06-11T20:37:01","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=16846"},"modified":"2025-06-11T20:37:03","modified_gmt":"2025-06-11T20:37:03","slug":"at-home-she-dissolves-40-0g-of-epsom-salt-mgso4-in-5-0-kg-of-water","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/at-home-she-dissolves-40-0g-of-epsom-salt-mgso4-in-5-0-kg-of-water\/","title":{"rendered":"At home, she dissolves 40.0g of Epsom salt, MgSO4, in 5.0 kg of water"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">At home, she dissolves 40.0g of Epsom salt, MgSO4, in 5.0 kg of water. What is the freezing point of this solution? (Kf water = 1.86 oC\/m)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-cyan-blue-color\"><strong>The correct answer and explanation is:<\/strong><\/mark><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">To calculate the <strong>freezing point<\/strong> of the Epsom salt solution, we use the <strong>freezing point depression formula<\/strong>: \u0394Tf=i\u22c5Kf\u22c5m\\Delta T_f = i \\cdot K_f \\cdot m<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Where:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>\u0394Tf\\Delta T_f = freezing point depression<\/li>\n\n\n\n<li>ii = van &#8216;t Hoff factor (number of particles the solute splits into)<\/li>\n\n\n\n<li>KfK_f = cryoscopic constant (1.86 \u00b0C\u00b7kg\/mol for water)<\/li>\n\n\n\n<li>mm = molality of the solution (mol\/kg)<\/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 1: Calculate moles of MgSO\u2084<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Molar mass of MgSO\u2084: 24.3&nbsp;(Mg)+32.1&nbsp;(S)+4\u00d716.0&nbsp;(O)=120.4&nbsp;g\/mol24.3\\ (\\text{Mg}) + 32.1\\ (\\text{S}) + 4 \\times 16.0\\ (\\text{O}) = 120.4\\ \\text{g\/mol} Moles&nbsp;of&nbsp;MgSO\u2084=40.0&nbsp;g120.4&nbsp;g\/mol\u22480.3323&nbsp;mol\\text{Moles of MgSO\u2084} = \\frac{40.0\\ \\text{g}}{120.4\\ \\text{g\/mol}} \\approx 0.3323\\ \\text{mol}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Calculate molality (m)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Molality=0.3323&nbsp;mol5.0&nbsp;kg&nbsp;water=0.0665&nbsp;mol\/kg\\text{Molality} = \\frac{0.3323\\ \\text{mol}}{5.0\\ \\text{kg water}} = 0.0665\\ \\text{mol\/kg}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Determine van \u2019t Hoff factor (i)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Magnesium sulfate (MgSO\u2084) <strong>dissociates<\/strong> in water: MgSO\u2084\u2192Mg2++SO\u20842\u2212\\text{MgSO\u2084} \\rightarrow \\text{Mg}^{2+} + \\text{SO\u2084}^{2-}<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, i=2i = 2<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Calculate freezing point depression<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u0394Tf=2\u22c51.86&nbsp;\u00b0C\\cdotpkg\/mol\u22c50.0665&nbsp;mol\/kg=0.2477&nbsp;\u00b0C\\Delta T_f = 2 \\cdot 1.86\\ \\text{\u00b0C\u00b7kg\/mol} \\cdot 0.0665\\ \\text{mol\/kg} = 0.2477\\ \\text{\u00b0C}<\/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: Calculate new freezing point<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Freezing&nbsp;point&nbsp;of&nbsp;solution=0.0&nbsp;\u00b0C&nbsp;(pure&nbsp;water)\u22120.2477&nbsp;\u00b0C\u2248\u22120.25&nbsp;\u00b0C\\text{Freezing point of solution} = 0.0\\ \\text{\u00b0C (pure water)} &#8211; 0.2477\\ \\text{\u00b0C} \\approx \\boxed{-0.25\\ \\text{\u00b0C}}<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\">Explanation (300 words)<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Freezing point depression is a colligative property, meaning it depends on the number of solute particles in a solvent rather than the type of particles. In this case, we\u2019re adding 40.0 grams of Epsom salt (magnesium sulfate, MgSO\u2084) to 5.0 kg of water. When MgSO\u2084 dissolves, it dissociates into two ions: Mg\u00b2\u207a and SO\u2084\u00b2\u207b. This dissociation doubles the effective number of solute particles, increasing the freezing point depression.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">First, we calculated the number of moles of MgSO\u2084 by dividing its mass (40.0 g) by its molar mass (120.4 g\/mol), giving 0.3323 mol. Then we determined the molality of the solution by dividing the moles of solute by the mass of water in kilograms, resulting in 0.0665 mol\/kg.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Next, we applied the formula for freezing point depression. The van \u2019t Hoff factor (i) for MgSO\u2084 is 2 because it splits into two particles. The freezing point depression constant (Kf) for water is 1.86 \u00b0C\u00b7kg\/mol. Multiplying these together with the molality gives a freezing point depression of 0.2477 \u00b0C.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Finally, we subtract this value from the normal freezing point of water (0.0 \u00b0C) to get the new freezing point of the solution, which is approximately <strong>\u20130.25 \u00b0C<\/strong>. This means the water will now freeze at a slightly lower temperature due to the presence of dissolved ions, which disrupt the formation of the solid ice lattice.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This principle is also used in real life\u2014for example, in salting icy roads or using antifreeze in car engines.<\/p>\n","protected":false},"excerpt":{"rendered":"<p>At home, she dissolves 40.0g of Epsom salt, MgSO4, in 5.0 kg of water. What is the freezing point of this solution? (Kf water = 1.86 oC\/m) The correct answer and explanation is: To calculate the freezing point of the Epsom salt solution, we use the freezing point depression formula: \u0394Tf=i\u22c5Kf\u22c5m\\Delta T_f = i \\cdot [&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-16846","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16846","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=16846"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16846\/revisions"}],"predecessor-version":[{"id":16847,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/16846\/revisions\/16847"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=16846"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=16846"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=16846"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}