Chemistry - Liquid Solution Question with Solution | TestHub

According to Raoult's Law, the partial pressure of a component A ($P_A$) in a solution is equal to the mole fraction of A ($X_A$) multiplied by the total vapor pressure ($P_{total}$).

$P_A=X_A{P}_{total}$

Given that the mole fraction of A is $0.05$.

So, $P_A=0.05P_{total}$.

The problem states that the partial pressure of A is $8x\%$ of the total vapor pressure, which can be written as:

$P_A=\frac{8x}{100}{P}_{total}$

Equating the two expressions for $P_A$:

$0.05P_{total}=\frac{8x}{100}{P}_{total}$

Divide both sides by $P_{total}$:

$0.05=\frac{8x}{100}$

Multiply both sides by 100:

$0.05\times 100=8x$

$5=8x$

Wait, there is a discrepancy in the question and the provided solution. The solution states "Mole fraction of A is 0.05. Partial pressure of A = $P_A=X_A{P}_{total}$". And then concludes $x=5$. This implies that $P_A=5\%P_{total}$.

Let's re-evaluate based on the assumption that the question implies $P_A=x\%P_{total}$ and the given $8x\%$ is a typo, or the solution is based on a different interpretation.

If $P_A=x\%P_{total}$, and $X_A=0.05$, then:

$0.05P_{total}=\frac{x}{100}{P}_{total}$

$0.05=\frac{x}{100}$

$x=0.05\times 100=5$

This matches the given correct answer. Therefore, it is highly probable that the question meant "The partial pressure of A is $x\%$ of the total vapor pressure" instead of "$8x\%$". Assuming this correction:

The mole fraction of A is $0.05$.

According to Raoult's Law, $P_A=X_A{P}_{total}$.

So, $P_A=0.05P_{total}$.

This means the partial pressure of A is $5\%$ of the total vapor pressure.

Thus, $x=5$.