{"id":159041,"date":"2024-10-31T08:05:36","date_gmt":"2024-10-31T08:05:36","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=159041"},"modified":"2024-10-31T08:05:39","modified_gmt":"2024-10-31T08:05:39","slug":"the-heat-capacity-of-ice-is-2-09-j-gc-and-the-heat-of-fusion-of-ice-is-6-02-kj-mol","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2024\/10\/31\/the-heat-capacity-of-ice-is-2-09-j-gc-and-the-heat-of-fusion-of-ice-is-6-02-kj-mol\/","title":{"rendered":"The heat capacity of ice is 2.09 J\/g\u00b0C and the heat of fusion of ice is 6.02 kJ\/mol."},"content":{"rendered":"\n

The heat capacity of ice is 2.09 J\/g\u00b0C and the heat of fusion of ice is 6.02 kJ\/mol. An ice cube at \u221212.0\u00b0C is placed into a glass of water at room temperature.
Does the melting of the ice or the warming of the ice from \u221212.0\u00b0C play a larger role in cooling the liquid water? A. They contribute equally B. The warming of the ice from \u221212.0\u00b0C C. The melting of the ice D. Cannot determine from the information given<\/p>\n\n\n\n

The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n

To determine whether the warming of the ice from \u221212.0\u00b0C or the melting of the ice contributes more to cooling the liquid water, we need to consider the energy changes involved in both processes.<\/p>\n\n\n\n

Step 1: Calculate the energy required to warm the ice.<\/h3>\n\n\n\n
    \n
  1. Heat Capacity of Ice (C):<\/strong> 2.09 J\/g\u00b0C<\/li>\n\n\n\n
  2. Mass of Ice (m):<\/strong> Assuming 1 g for simplicity (this can be scaled later).<\/li>\n\n\n\n
  3. Temperature Change (\u0394T):<\/strong> From -12.0\u00b0C to 0\u00b0C, so \u0394T = 0 – (-12.0) = 12.0\u00b0C.<\/li>\n<\/ol>\n\n\n\n

    Using the formula for heat transfer:
    [ q = m \\times C \\times \\Delta T ]<\/p>\n\n\n\n

    Plugging in the values:
    [ q_{warming} = 1 \\, \\text{g} \\times 2.09 \\, \\text{J\/g\u00b0C} \\times 12.0 \\, \\text{\u00b0C} = 25.08 \\, \\text{J} ]<\/p>\n\n\n\n

    Step 2: Calculate the energy required to melt the ice.<\/h3>\n\n\n\n
      \n
    1. Heat of Fusion (\u0394H_fusion):<\/strong> 6.02 kJ\/mol = 6020 J\/mol.<\/li>\n\n\n\n
    2. Molar Mass of Water:<\/strong> 18.02 g\/mol, so for 1 g of ice:
      [ \\text{Moles of ice} = \\frac{1 \\, \\text{g}}{18.02 \\, \\text{g\/mol}} \\approx 0.0555 \\, \\text{mol} ]<\/li>\n<\/ol>\n\n\n\n

      Now calculate the energy required to melt 1 g of ice:
      [ q_{melting} = 0.0555 \\, \\text{mol} \\times 6020 \\, \\text{J\/mol} \\approx 334.11 \\, \\text{J} ]<\/p>\n\n\n\n

      Conclusion<\/h3>\n\n\n\n

      Now, comparing the two values:<\/p>\n\n\n\n

        \n
      • Warming of the ice:<\/strong> 25.08 J<\/li>\n\n\n\n
      • Melting of the ice:<\/strong> 334.11 J<\/li>\n<\/ul>\n\n\n\n

        The melting of the ice requires significantly more energy than the warming of the ice. Therefore, the process of melting plays a much larger role in cooling the liquid water than the warming of the ice does.<\/p>\n\n\n\n

        Thus, the correct answer is C. The melting of the ice<\/strong>.<\/p>\n","protected":false},"excerpt":{"rendered":"

        The heat capacity of ice is 2.09 J\/g\u00b0C and the heat of fusion of ice is 6.02 kJ\/mol. An ice cube at \u221212.0\u00b0C is placed into a glass of water at room temperature.Does the melting of the ice or the warming of the ice from \u221212.0\u00b0C play a larger role in cooling the liquid water? […]<\/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-159041","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159041","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=159041"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/159041\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=159041"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=159041"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=159041"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}