Chemistry - Liquid Solution Question with Solution | TestHub

The pure vapor pressures are $P_A^{\circ }=600$ torr and $P_B^{\circ }=400$ torr.

Since $P_A^{\circ }>P_B^{\circ }$, component A is more volatile.

For an ideal solution:

1. The total vapor pressure $P_{total}=P_A^{\circ }{x}_A+P_B^{\circ }{x}_B$. Since $x_A+x_B=1$, $P_{total}=P_A^{\circ }{x}_A+P_B^{\circ }(1-x_A)=(P_A^{\circ }-P_B^{\circ })x_A+P_B^{\circ }$.

Given $P_A^{\circ }=600$ torr and $P_B^{\circ }=400$ torr, $P_{total}=(600-400)x_A+400=200x_A+400$.

Since $0\le x_A\le 1$, the minimum $P_{total}$ is $400$ torr (when $x_A=0$) and the maximum $P_{total}$ is $600$ torr (when $x_A=1$).

Therefore, the vapor pressure of the solution cannot exceed 600 torr. (Option C is correct)

2. For the more volatile component (A), its mole fraction in the vapor phase ($y_A$) is always greater than its mole fraction in the liquid phase ($x_A$), i.e., $y_A>x_A$.

This is because the more volatile component preferentially evaporates. (Option B is correct)

3. For the less volatile component (B), its mole fraction in the vapor phase ($y_B$) is always less than its mole fraction in the liquid phase ($x_B$), i.e., $y_B<x_B$. (Option D is incorrect)

4. Comparing $y_A$ and $y_B$:

$y_A=\frac{P_A^{\circ }{x}_A}{P_{total}}$ and $y_B=\frac{P_B^{\circ }{x}_B}{P_{total}}$.

$y_A/y_B=(P_A^{\circ }{x}_A)/(P_B^{\circ }{x}_B)$.

Since $P_A^{\circ }>P_B^{\circ }$, $y_A$ is not always greater than $y_B$. For example, if $x_A$ is very small and $x_B$ is large, $y_B$ could be greater than $y_A$. (Option A is incorrect)

The correct statements are B and C.

Final Answer: The final answer is B, C.

The more volatile component (A) has $y_A>x_A$. The total vapor pressure of the solution will always be between the pure vapor pressures of the components, so it cannot exceed 600 torr (the vapor pressure of the more volatile component).