GATE 2024 CY – Question 34
The partial vapor pressure of 0.1 molal solution of B in liquid A is 60 kPa at 300 K. The partial vapor pressure (in kPa) of a solution containing B with mole fraction of 0.1 in liquid A at 300 K is ___. (Assume the solute B obeys Henry’s law. The molar mass of A is 80 g mol-1.) (rounded off to three decimal places)
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Correct answer: 752.220 to 759.780
Explanation
**Henry's law** for a dilute solute: $p_B=K_Hx_B$, where $x_B$ is the mole fraction.
**Step 1: find $x_B$ for the 0.1 molal solution.** A molal solution has 0.1 mol of B per 1 kg of A. The molar mass of A is 80 g/mol, so 1 kg of A is
$$n_A=\frac{1000}{80}=12.5\text{ mol}.$$
$$x_B=\frac{0.1}{12.5+0.1}=\frac{0.1}{12.6}=0.007937 .$$
**Step 2: Henry's constant.**
$$K_H=\frac{p_B}{x_B}=\frac{60}{0.007937}=7560\text{ kPa}.$$
**Step 3: solution with $x_B=0.1$.**
$$p_B=K_Hx_B=7560\times0.1=\mathbf{756\ kPa}.$$