Question

Liquids $A$ and $B$ form an ideal solution in the entire composition range. At $350K$, 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)

$x_A=0.28;x_B=0.72$

$y_A=\frac{P_A}{P_{Total}}=\frac{P_A^o{x}_A}{P_A^o{x}_A\times P_B^o{x}_B}$
$=\frac{7\times {10}^3\times 0.4}{7\times {10}^3\times 0.4+12\times {10}^3\times 0.6}$
$=\frac{2.8}{10}=0.28$
$y_B=0.72$.

Hence, the correct option is $B$