JEE MAIN - Chemistry (2022 - 28th June Morning Shift - No. 18)
The vapour pressures of two volatile liquids A and B at 25$$^\circ$$C are 50 Torr and 100 Torr, respectively. If the liquid mixture contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is $${x \over {17}}$$. The value of x is ______________.
Answer
14
Explanation
$$
\begin{aligned}
&\frac{\mathrm{y}_{\mathrm{B}}}{1-\mathrm{y}_{\mathrm{B}}}=\frac{\mathrm{P}_{\mathrm{B}}^{\mathrm{o}}}{\mathrm{P}_{\mathrm{A}}^{\mathrm{o}}}\left[\frac{\mathrm{X}_{\mathrm{B}}}{1-\mathrm{X}_{\mathrm{B}}}\right] \\\\
&\Rightarrow \frac{\mathrm{y}_{\mathrm{B}}}{1-\mathrm{y}_{\mathrm{B}}}=\frac{100}{50}\left[\frac{0.7}{0.3}\right]=\frac{14}{3} \\\\
&\Rightarrow \mathrm{y}_{\mathrm{B}}=\frac{14}{17}
\end{aligned}
$$
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