Question

An ideal solution of two liquids A and B is placed in a cylinder containing piston. Piston is pulled out isothermally so that the volume of the liquid decreases but that of vapours increases. Negligibly small amount of liquid was left and mole fraction of A in vapour is 0.4. If $P_A^0=0.4$atm and $P_B^0=1.2$atm at the experimental temperature, which of the following is the total pressure at which the liquid is almost evaporated?

• A. 0.334atm
• B. 0.667atm
• C. 1atm
• D. 2atm

Answer 1

The correct option is B

0.667atm

$P_T=P_A^0{x}_A+P_B^0{x}_B;y_A=\frac{P_A^0{X}_A}{P_T}=\frac{0.4x_A}{P_T};\therefore x_A=P_T;y_B=\frac{P_B^0{x}_B}{P_T}=\frac{1.2x_B}{P_T}\therefore x_B=2x_B;x_A+x_B=1;x_B=\frac{1}{3};x_A=\frac{2}{3};\therefore P_T=0.4\times \frac{2}{3}+1.2\times \frac{1}{3}=0.667atm$