Question

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 1

314

Answer 2

Raoult's Law for ideal solutions states $P_T = P_A^0 \chi_A + P_B^0 \chi_B$.

The given conditions translate to the following system of equations: $350 = 0.7 P_A^0 + 0.3 P_B^0 \quad (1)$ $410 = 0.2 P_A^0 + 0.8 P_B^0 \quad (2)$

Multiply by 10 to clear decimals: $3500 = 7 P_A^0 + 3 P_B^0 \quad (1')$ $4100 = 2 P_A^0 + 8 P_B^0 \quad (2')$

To find $P_A^0$, we eliminate $P_B^0$. Multiply (1') by 8 and (2') by 3: $28000 = 56 P_A^0 + 24 P_B^0$ $12300 = 6 P_A^0 + 24 P_B^0$

Subtracting the second modified equation from the first yields $15700 = 50 P_A^0$. Solving for $P_A^0$: $P_A^0 = \frac{15700}{50} = 314$