{"id":148975,"date":"2024-02-27T19:07:32","date_gmt":"2024-02-27T13:37:32","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=148975"},"modified":"2024-02-27T19:07:32","modified_gmt":"2024-02-27T13:37:32","slug":"calculate-the-mass-of-caci-molar-mass-111-g-mol-1-to-be-dissolved","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/calculate-the-mass-of-caci-molar-mass-111-g-mol-1-to-be-dissolved","title":{"rendered":"Calculate the mass of CaCi, (molar mass = 111 g mol-1) to be dissolved…"},"content":{"rendered":"

Calculate the mass of CaCi, (molar mass = 111 g mol-1) to be dissolved in 500 g of water to lower its freezing point by 2K, assuming that CaCl, undergoes complete dissociation.
\n(Kf for water = 1.86 K kg mol-1)<\/h2>\n

Ans.<\/h3>\n

To calculate the mass of calcium chloride (\ufffd\ufffd\ufffd\ufffd2<\/span>C<\/span>a<\/span>C<\/span>l<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) needed to lower the freezing point of 500 g of water by 2 K, we can use the formula for freezing point depression:<\/h3>\n

\u0394\ufffd\ufffd=\ufffd\u22c5\ufffd\ufffd\u22c5\ufffd<\/span>\u0394<\/span>T<\/span>f<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>i<\/span>\u22c5<\/span><\/span>K<\/span>f<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/h3>\n

Where:<\/h3>\n
    \n
  • \n

    \u0394\ufffd\ufffd<\/span>\u0394<\/span>T<\/span>f<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the freezing point depression,<\/h3>\n<\/li>\n
  • \n

    \ufffd<\/span>i<\/span><\/span><\/span><\/span><\/span> is the van’t Hoff factor,<\/h3>\n<\/li>\n
  • \n

    \ufffd\ufffd<\/span>K<\/span>f<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> is the freezing point depression constant for water, and<\/h3>\n<\/li>\n
  • \n

    \ufffd<\/span>m<\/span><\/span><\/span><\/span><\/span> is the molality of the solution.<\/h3>\n<\/li>\n<\/ul>\n

    Given:<\/h3>\n
      \n
    • \n

      \u0394\ufffd\ufffd=2<\/span>\u0394<\/span>T<\/span>f<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>2<\/span><\/span><\/span><\/span><\/span> K<\/h3>\n<\/li>\n
    • \n

      \ufffd\ufffd=1.86<\/span>K<\/span>f<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>1.86<\/span><\/span><\/span><\/span><\/span> K kg mol\u22121<\/span>\u22121<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> (we need to convert this to molal units)<\/h3>\n<\/li>\n
    • \n

      \ufffd<\/span>m<\/span><\/span><\/span><\/span><\/span> is the molality of the solution<\/h3>\n<\/li>\n<\/ul>\n

      First, let’s calculate the molality (\ufffd<\/span>m<\/span><\/span><\/span><\/span><\/span>) of the solution:<\/h3>\n

      \u0394\ufffd\ufffd=\ufffd\u22c5\ufffd\ufffd\u22c5\ufffd<\/span>\u0394<\/span>T<\/span>f<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>i<\/span>\u22c5<\/span><\/span>K<\/span>f<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u22c5<\/span><\/span>m<\/span><\/span><\/span><\/span><\/span><\/h3>\n

      Rearranging the equation to solve for \ufffd<\/span>m<\/span><\/span><\/span><\/span><\/span>:<\/h3>\n

      \ufffd=\u0394\ufffd\ufffd\ufffd\u22c5\ufffd\ufffd<\/span>m<\/span>=<\/span><\/span>i<\/span>\u22c5<\/span>K<\/span>f<\/span><\/span>\u200b<\/span><\/span>\u0394T<\/span>f<\/span><\/span>\u200b<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

      We know that \ufffd<\/span>i<\/span><\/span><\/span><\/span><\/span> for \ufffd\ufffd\ufffd\ufffd2<\/span>C<\/span>a<\/span>C<\/span>l<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> is 3 because it dissociates into three ions (1 calcium ion and 2 chloride ions).<\/h3>\n

      So,<\/h3>\n

      \ufffd=2\u2009K3\u00d71.86\u2009K\u00a0kg\u00a0mol\u22121<\/span>m<\/span>=<\/span><\/span>3\u00d7<\/span>1.86K\u00a0kg\u00a0mol<\/span>\u22121<\/span><\/span><\/span><\/span>2K<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

      \ufffd=25.58\u22480.358\u2009mol\u00a0kg\u22121<\/span>m<\/span>=<\/span><\/span>5.582<\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span>0.358<\/span>mol\u00a0kg<\/span>\u22121<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

      Now, we can calculate the number of moles of \ufffd\ufffd\ufffd\ufffd2<\/span>C<\/span>a<\/span>C<\/span>l<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> needed:<\/h3>\n

      Molality=moles\u00a0of\u00a0solutemass\u00a0of\u00a0solvent\u00a0in\u00a0kg<\/span>Molality<\/span><\/span>=<\/span><\/span>mass\u00a0of\u00a0solvent\u00a0in\u00a0kg<\/span>moles\u00a0of\u00a0solute<\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

      0.358\u2009mol\u00a0kg\u22121=moles\u00a0of\u00a0\ufffd\ufffd\ufffd\ufffd20.500\u2009kg<\/span>0.358<\/span>mol\u00a0kg<\/span>\u22121<\/span><\/span><\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0.500kg<\/span>moles\u00a0of\u00a0<\/span>C<\/span>a<\/span>C<\/span>l<\/span>2<\/span><\/span>\u200b<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

      moles\u00a0of\u00a0\ufffd\ufffd\ufffd\ufffd2=0.358\u00d70.500\u2009mol\u22480.179\u2009mol<\/span>moles\u00a0of\u00a0<\/span><\/span>C<\/span>a<\/span>C<\/span>l<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0.358<\/span>\u00d7<\/span><\/span>0.500<\/span>mol<\/span><\/span>\u2248<\/span><\/span>0.179<\/span>mol<\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

      Now, we can calculate the mass of \ufffd\ufffd\ufffd\ufffd2<\/span>C<\/span>a<\/span>C<\/span>l<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> using its molar mass:<\/h3>\n

      mass=moles\u00d7molar\u00a0mass<\/span>mass<\/span><\/span>=<\/span><\/span>moles<\/span><\/span>\u00d7<\/span><\/span>molar\u00a0mass<\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

      mass=0.179\u00d7111\u2009g\u2009mol\u22121\u224819.869\u2009g<\/span>mass<\/span><\/span>=<\/span><\/span>0.179<\/span>\u00d7<\/span><\/span>111<\/span>g<\/span><\/span>mol<\/span>\u22121<\/span><\/span><\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span>19.869<\/span>g<\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

      So, approximately 19.869 grams of \ufffd\ufffd\ufffd\ufffd2<\/span>C<\/span>a<\/span>C<\/span>l<\/span>2<\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> need to be dissolved in 500 grams of water to lower its freezing point by 2 K.<\/h3>\n","protected":false},"excerpt":{"rendered":"

      Calculate the mass of CaCi, (molar mass = 111 g mol-1) to be dissolved in 500 g of water to lower its freezing point by 2K, assuming that CaCl, undergoes complete dissociation. (Kf for water = 1.86 K kg mol-1) Ans. To calculate the mass of calcium chloride (\ufffd\ufffd\ufffd\ufffd2CaCl2\u200b) needed to lower the freezing point […]<\/p>\n","protected":false},"author":21830,"featured_media":114041,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[12119],"tags":[],"class_list":{"0":"post-148975","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-quiz"},"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/148975","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/users\/21830"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/comments?post=148975"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/148975\/revisions"}],"predecessor-version":[{"id":148976,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/148975\/revisions\/148976"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media\/114041"}],"wp:attachment":[{"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/media?parent=148975"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=148975"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=148975"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}