{"id":148969,"date":"2024-02-27T19:00:01","date_gmt":"2024-02-27T13:30:01","guid":{"rendered":"https:\/\/www.mapsofindia.com\/my-india\/?p=148969"},"modified":"2024-02-27T19:00:01","modified_gmt":"2024-02-27T13:30:01","slug":"a-solution-containing-2-g-of-glucose-m-180-g-mol-1-in-100-g-of-water","status":"publish","type":"post","link":"https:\/\/www.mapsofindia.com\/my-india\/quiz\/a-solution-containing-2-g-of-glucose-m-180-g-mol-1-in-100-g-of-water","title":{"rendered":"A solution containing 2 g of glucose (M = 180 g mol-1) in 100 g of water…"},"content":{"rendered":"

A solution containing 2 g of glucose (M = 180 g mol-1) in 100 g of water is prepared at 303 K. If the vapour pressure of pure water at 303 K is 32.8 mm Hg, what would be the vapour pressure of the solution?<\/h3>\n

Ans.<\/h3>\n

To find the vapor pressure of the solution, we can use Raoult’s law, which states that the vapor pressure of a solution is directly proportional to the mole fraction of the solvent in the solution.<\/h3>\n

The mole fraction of the solvent (water) in the solution can be calculated using the formula:<\/h3>\n

\ufffdsolvent=moles\u00a0of\u00a0solventtotal\u00a0moles\u00a0in\u00a0solution<\/span>X<\/span>solvent<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>total\u00a0moles\u00a0in\u00a0solution<\/span><\/span><\/span>moles\u00a0of\u00a0solvent<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

First, we need to find the number of moles of glucose and water in the solution.<\/h3>\n
    \n
  1. \n

    Moles of glucose: Mass\u00a0of\u00a0glucose=2\u2009g<\/span>Mass\u00a0of\u00a0glucose<\/span><\/span>=<\/span><\/span>2<\/span>g<\/span><\/span><\/span><\/span><\/span><\/span> Molar\u00a0mass\u00a0of\u00a0glucose=180\u2009g\/mol<\/span>Molar\u00a0mass\u00a0of\u00a0glucose<\/span><\/span>=<\/span><\/span>180<\/span>g\/mol<\/span><\/span><\/span><\/span><\/span><\/span> Number\u00a0of\u00a0moles\u00a0of\u00a0glucose=MassMolar\u00a0mass=2\u2009g180\u2009g\/mol=0.0111\u2009mol<\/span>Number\u00a0of\u00a0moles\u00a0of\u00a0glucose<\/span><\/span>=<\/span><\/span>Molar\u00a0mass<\/span><\/span><\/span>Mass<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>180g\/mol<\/span><\/span><\/span>2g<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0.0111<\/span>mol<\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n<\/li>\n
  2. \n

    Moles of water: Mass\u00a0of\u00a0water=100\u2009g<\/span>Mass\u00a0of\u00a0water<\/span><\/span>=<\/span><\/span>100<\/span>g<\/span><\/span><\/span><\/span><\/span><\/span> Molar\u00a0mass\u00a0of\u00a0water=18\u2009g\/mol<\/span>Molar\u00a0mass\u00a0of\u00a0water<\/span><\/span>=<\/span><\/span>18<\/span>g\/mol<\/span><\/span><\/span><\/span><\/span><\/span> Number\u00a0of\u00a0moles\u00a0of\u00a0water=MassMolar\u00a0mass=100\u2009g18\u2009g\/mol=5.56\u2009mol<\/span>Number\u00a0of\u00a0moles\u00a0of\u00a0water<\/span><\/span>=<\/span><\/span>Molar\u00a0mass<\/span><\/span><\/span>Mass<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>18g\/mol<\/span><\/span><\/span>100g<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>5.56<\/span>mol<\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n<\/li>\n<\/ol>\n

    Now, we can calculate the mole fraction of water: \ufffdsolvent=5.56\u2009mol5.56\u2009mol+0.0111\u2009mol\u22480.9998<\/span>X<\/span>solvent<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>5.56mol<\/span>+<\/span>0.0111mol<\/span><\/span><\/span>5.56mol<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span>0.9998<\/span><\/span><\/span><\/span><\/span><\/h3>\n

    Now, according to Raoult’s law, the vapor pressure of the solution (\ufffdsolution<\/span>P<\/span>solution<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>) is equal to the mole fraction of the solvent multiplied by the vapor pressure of the pure solvent (\ufffdsolvent<\/span>P<\/span>solvent<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span>).<\/h3>\n

    \ufffdsolution=\ufffdsolvent\u00d7\ufffdsolvent<\/span>P<\/span>solution<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>X<\/span>solvent<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u00d7<\/span><\/span>P<\/span>solvent<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span><\/span> \ufffdsolution=0.9998\u00d732.8\u2009mm\u00a0Hg<\/span>P<\/span>solution<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>=<\/span><\/span>0.9998<\/span>\u00d7<\/span><\/span>32.8<\/span>mm\u00a0Hg<\/span><\/span><\/span><\/span><\/span><\/span> \ufffdsolution\u224832.78\u2009mm\u00a0Hg<\/span>P<\/span>solution<\/span><\/span><\/span><\/span>\u200b<\/span><\/span><\/span><\/span><\/span>\u2248<\/span><\/span>32.78<\/span>mm\u00a0Hg<\/span><\/span><\/span><\/span><\/span><\/span><\/h3>\n

    So, the vapor pressure of the solution is approximately 32.78\u2009mm\u00a0Hg<\/span>32.78<\/span>mm\u00a0Hg<\/span><\/span><\/span><\/span><\/span><\/span>.<\/h3>\n","protected":false},"excerpt":{"rendered":"

    A solution containing 2 g of glucose (M = 180 g mol-1) in 100 g of water is prepared at 303 K. If the vapour pressure of pure water at 303 K is 32.8 mm Hg, what would be the vapour pressure of the solution? Ans. To find the vapor pressure of the solution, we […]<\/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-148969","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\/148969","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=148969"}],"version-history":[{"count":1,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/148969\/revisions"}],"predecessor-version":[{"id":148970,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/posts\/148969\/revisions\/148970"}],"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=148969"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/categories?post=148969"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mapsofindia.com\/my-india\/wp-json\/wp\/v2\/tags?post=148969"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}