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Solutions question

2008 · Shift 0 · Q24
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Solutions question

2008 · Shift 0 · Q24

JEE MainChemistrySolutionsMCQ+4 / −1
The vapour pressure of water at 20oC is 17.5 mm Hg. If 18 g of glucose (C6H12O6C_6H_{12}O_6C6​H12​O6​) is added to 178.2 g of water at 20oC, the vapour pressure of the resulting solution will be
  1. A
    17.675 mm Hg
  2. B
    15.750 mm Hg
  3. C
    16.500 mm Hg
  4. D
    17.325 mm Hg
View written solutionFree

Correct answer: D

  1. Use Raoult’s law for a non-volatile solute

Since glucose is a non-volatile solute, only water contributes to vapour pressure.

Psolution=Xwater Pwater0P_{\text{solution}} = X_{\text{water}}\, P^0_{\text{water}}Psolution​=Xwater​Pwater0​

where:

  • Pwater0=17.5 mm HgP^0_{\text{water}} = 17.5\ \text{mm Hg}Pwater0​=17.5 mm Hg
  • XwaterX_{\text{water}}Xwater​ = mole fraction of water in solution
  1. Calculate moles of water

Mass of water = 178.2 g178.2\ \text{g}178.2 g

Molar mass of water = 18 g mol−118\ \text{g mol}^{-1}18 g mol−1

nwater=178.218=9.9 moln_{\text{water}} = \frac{178.2}{18} = 9.9\ \text{mol}nwater​=18178.2​=9.9 mol

  1. Calculate moles of glucose

Mass of glucose = 18 g18\ \text{g}18 g

Molar mass of glucose:

6(12)+12(1)+6(16)=72+12+96=180 g mol−16(12) + 12(1) + 6(16) = 72 + 12 + 96 = 180\ \text{g mol}^{-1}6(12)+12(1)+6(16)=72+12+96=180 g mol−1

nglucose=18180=0.1 moln_{\text{glucose}} = \frac{18}{180} = 0.1\ \text{mol}nglucose​=18018​=0.1 mol

  1. Find mole fraction of water

Xwater=nwaternwater+nglucose=9.99.9+0.1=9.910=0.99X_{\text{water}} = \frac{n_{\text{water}}}{n_{\text{water}} + n_{\text{glucose}}} = \frac{9.9}{9.9 + 0.1} = \frac{9.9}{10} = 0.99Xwater​=nwater​+nglucose​nwater​​=9.9+0.19.9​=109.9​=0.99

  1. Calculate vapour pressure of solution

Psolution=0.99×17.5=17.325 mm HgP_{\text{solution}} = 0.99 \times 17.5 = 17.325\ \text{mm Hg}Psolution​=0.99×17.5=17.325 mm Hg

  1. Match with options

17.325 mm Hg\boxed{17.325\ \text{mm Hg}}17.325 mm Hg​

So the correct option is D.

  1. Comparison with stored correct answer

Stored correct answer: D

Our derived answer: D

Hence, they agree.

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