Chemistry - Liquid Solution Question with Solution | TestHub

Explain the question: Calculate the total vapor pressure of a solution with equal masses of A and B.

Concept: Raoult's Law and Dalton's Law of Partial Pressures.

Solution:

From the given pressure-composition graph, the vapor pressure of pure liquid A ($P_A^0$) is 40 torr, and the vapor pressure of pure liquid B ($P_B^0$) is 30 torr. Since the solution contains equal masses (let's say 'w' grams) of A and B, we first calculate their mole fractions. The moles of A are $n_A=w/80$, and the moles of B are $n_B=w/120$. The mole fraction of A is:

$$X_A=\frac{n_A}{n_A+n_B}=\frac{w/80}{w/80+w/120}=\frac{1/80}{5/240}=\frac{240}{5\times 80}=0.6$$

Consequently, the mole fraction of B is $X_B=1-0.6=0.4$. The total pressure $P_{total}$ is calculated using Raoult's and Dalton's laws:

$$P_{total}=P_A^0{X}_A+P_B^0{X}_B$$

Substituting the values, we get:

$$P_{total}=(40\times 0.6)+(30\times 0.4)=24+12=36torr$$

The question asks for the value of $X/6$.

The value of $X/6$ is $36/6=6$.