80 mole percent of $\mathrm{MgCl}_{2}$ is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of $\mathrm{MgCl}_{2}$ at $38^{\circ} \mathrm{C}$ is $\_\_\_\_$ mm Hg. (Nearest integer) Given : Vapour pressure of water at $38^{\circ} \mathrm{C}$ is 50 mm Hg

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Solutions

80 mole percent of

MgCl_{2}

is dissociated in aqueous solution. The vapour pressure of 1.0 molal aqueous solution of

MgCl_{2}

3 8^{\circ} C

____

mm Hg. (Nearest integer)

Given : Vapour pressure of water at

3 8^{\circ} C

is 50 mm Hg

Answer: 48

Solution

MgCl X_{2}

dissociates as

MgCl X_{2} Mg X^{2 +} + 2 Cl X^{-}

, so with a degree of dissociation

α = 0.8

the van't Hoff factor is

i = 1 + 2 α = 2.6

. For a

1.0

molal solution the solute is

1 mol

and the water is

1000/18 = 55.56 mol

. The relative lowering of vapour pressure is

\frac{p ^{\circ} - p _{s}}{p ^{\circ}} = \frac{i n _{2}}{n _{1}} = \frac{2.6 \times 1}{55.56} = 0.0468

p_{s} = 50 (1 - 0.0468) = 47.66 mm Hg

To the nearest integer, the vapour pressure of the solution is 48 mm Hg.

JEE Main · 2023 · 12 Apr 2023 · Shift 1 · Integer answer

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