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

For an ideal binary liquid mixture, Raoult's law is

$$P_{\text{Total}} = x_A P_A^\circ + x_B P_B^\circ$$

From the first set of data,

$$0.7P_A^\circ + 0.3P_B^\circ = 350 \qquad ...(1)$$

From the second set of data,

$$0.2P_A^\circ + 0.8P_B^\circ = 410 \qquad ...(2)$$

Multiplying equation (1) by 8,

$$5.6P_A^\circ + 2.4P_B^\circ = 2800$$

Multiplying equation (2) by 3,

$$0.6P_A^\circ + 2.4P_B^\circ = 1230$$

Subtracting,

$$\left(5.6-0.6\right)P_A^\circ + \left(2.4-2.4\right)P_B^\circ = 2800-1230$$

$$5P_A^\circ = 1570$$

$$P_A^\circ = \frac{1570}{5}$$

$$P_A^\circ = 314\ \text{mm Hg}$$

Hence, the vapour pressure of pure liquid A is

$$\boxed{314\ \text{mm Hg}}$$