Question

Liquids $A$ and $B$ form an ideal solution in the entire composition range. At $350\, K$, the vapor pressures of pure $A$ and pure $B$ are $7 \times 10^3$ Pa and $12 \times 10^3\, Pa$, respectively. The composition of the vapor in equilibrium with a solution containing $40$ mole percent of $A$ at this temperature is :

• A. $x_A = 0.37; x_B = 0.63$
• B. $x_A = 0.28; x_B = 0.72$
• C. $x_A = 0.76; x_B = 0.24$
• D. $x_A = 0.4; x_B = 0.6$

Answer 1

Answer: (B)

$x_A = 0.28; x_B = 0.72$

Answer 2

$y_{A} = \frac{P_{A}}{P_{Total }} = \frac{P^{\circ}_{A}x_{A}}{P^{\circ}_{A}x_{A} \times p^{\circ}_{B}x_{B}}$
$= \frac{7 \times10^{3} \times0.4}{7 \times10^{3} \times0.4 +12 \times10^{3} \times0.6}$
$= \frac{2.8}{10} = 0.28$
$y_{B} = 0.72$