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 (integer)
14
Solution
$$
\begin{aligned}
&\frac{\mathrm{y}_{\mathrm{B}}}{1-\mathrm{y}_{\mathrm{B}}}=\frac{\mathrm{P}_{\mathrm{B}}^{\mathrm{o}}}{\mathrm{P}_{\mathrm{A}}^{\mathrm{o}}}\left[\frac{\mathrm{X}_{\mathrm{B}}}{1-\mathrm{X}_{\mathrm{B}}}\right] \\\\
&\Rightarrow \frac{\mathrm{y}_{\mathrm{B}}}{1-\mathrm{y}_{\mathrm{B}}}=\frac{100}{50}\left[\frac{0.7}{0.3}\right]=\frac{14}{3} \\\\
&\Rightarrow \mathrm{y}_{\mathrm{B}}=\frac{14}{17}
\end{aligned}
$$
About this question
Subject: Chemistry · Chapter: States of Matter · Topic: Gas Laws
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