JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Solutions

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The Total pressure observed by mixing two liquid A and B is 350 mm Hg when their mole fractions are 0.7 and 0.3 respectively.
The Total pressure becomes 410 mm Hg if the mole fractions are changed to 0.2 and 0.8 respectively for A and B. The vapour pressure of pure A is ____ mm Hg. (Nearest integer)
Consider the liquids and solutions behave ideally.

Answer: 314

Solution

For an ideal solution the total vapour pressure is

P = P_{A}^{\circ} X_{A} + P_{B}^{\circ} X_{B}

. The two experiments give

0.7 P_{A}^{\circ} + 0.3 P_{B}^{\circ} = 350

and

0.2 P_{A}^{\circ} + 0.8 P_{B}^{\circ} = 410

. Scaling the first by

8

and the second by

3

and subtracting eliminates

P_{B}^{\circ}

and leaves

5.0 P_{A}^{\circ} = 1570

. The vapour pressure of pure A is

314 mm Hg

JEE Main · 2023 · 24 Jan 2023 · Shift 2 · Integer answer

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