80 mole percent of is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of at 38°C is ______ mm Hg. (Nearest integer) Given: Vapour pressure of water at 38°C is 50 mm Hg. [2023]

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Solution

Q.
80 mole percent of ${MgCl}_{2}$ is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of ${MgCl}_{2}$ at 38°C is ______ mm Hg. (Nearest integer)

Given: Vapour pressure of water at 38°C is 50 mm Hg. [2023]

Ans.
(48)

$\begin{matrix} {MgCl}_{2} & \to & {Mg}^{2 +} & + & 2 {Cl}^{-} \\ 1 - α & α & 2 α \\ i = 1 + 2 α & (∵ α = 0.8) \\ i = 2.6 \end{matrix}$

$\frac{Δ P}{P^{0}} = \frac{i \times n_{2}}{n_{1}} = \frac{2.6 \times 1}{55.5} = 0.0468$

$\frac{50 - P_{s}}{P_{s}} = 0.0468$

$1.0468 P_{s} = 50$

$P_{s} = 47.76 \approx 48 mm Hg$

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