Q35 / 150 · MHT CET 2021 (21 Sep Shift 1) · Chemistry

What is vapour pressure of a solution containing $0.1 \mathrm{~mol}$ of non-volatile solute dissolved in $16.2 \mathrm{~g}$ of water? $$ \left(\mathrm{P}_1^{\circ}=32 \mathrm{~mm} \mathrm{Hg}\right) $$

  • A
    $21.6 \mathrm{~mm} \mathrm{Hg}$
  • Correct answer
    B
    $28.8 \mathrm{~mm} \mathrm{Hg}$
  • C
    $15.7 \mathrm{~mm} \mathrm{Hg}$
  • D
    $18.1 \mathrm{~mm} \mathrm{Hg}$

Solution

$$ \begin{aligned} & \frac{\mathrm{P}^{\circ}-\mathrm{P}_{\mathrm{s}}}{\mathrm{P}^{\circ}}=\mathrm{X}_{\text {solute }} \\ & \frac{32-\mathrm{P}_{\mathrm{s}}}{32}=\frac{\mathrm{n}_{\text {solute }}}{\mathrm{n}_{\text {solute }}+\mathrm{n}_{\text {solvent }}} \\ & \mathrm{n}_{\text {solvent }}=\mathrm{n}_{\text {water }}=\frac{16.2}{18}=0.9 \\ & \frac{32-\mathrm{P}_{\mathrm{s}}}{32}=\frac{0.1}{0.1+0.9}=0.1 \\ & 32-\mathrm{P}_{\mathrm{s}}=32 \times 0.1 \\ & \mathrm{P}_{\mathrm{s}}=32-3.2 \\ & =28.8 \mathrm{~mm} \mathrm{Hg} \end{aligned} $$

Hence, the correct answer is option: 'B'.

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