Question

Liquid A has a vapor pressure of 264 torr at 20∘C, and liquid B has a vapor pressure of 96.5 torr at the same temperature. If 5.50 moles of liquid A and 8.50 moles of liquid B are combined to form an ideal solution, what is the total vapor pressure (in torr) above the solution at 20.0∘C?

Answer 1

Answer: 161.8 torr

Explanation:

According to Raoult's law, the vapor pressure of a component at a given temperature is equal to the mole fraction of that component multiplied by the vapor pressure of that component in the pure state.

$p_1=x_1p_1^0$ and $p_2=x_2P_2^0$

where, x = mole fraction

$p^0$ = pressure in the pure state

According to Dalton's law, the total pressure is the sum of individual pressures.

$p_{total}=p_1+p_2$$p_{total}=x_Ap_A^0+x_BP_B^0$

$x_{A}=\frac{\text {moles of A}}{\text {moles of A+moles of B}}=\frac{5.50}{5.50+8.50}=0.39$,

$x_{B}=\frac{\text {moles of B}}{\text {moles of A+moles of B}}=\frac{8.50}{5.50+8.50}=0.61$,

$p_{A}^0=264torr$

$p_{B}^0=96.5torr$

$p_{total}=0.39\times 264+0.61\times 96.5=161.8torr$

The total vapor pressure above the solution is 161.8 torr.