The vapour pressures of chloroform $\left({\mathrm{CHCl}}_3\right),$ dichloromethane $\left({\mathrm{CH}}_2{\mathrm{Cl}}_2\right)$ at $298 \mathrm{K}$ are $200 \mathrm{mmHg}$ and $415 \mathrm{mmHg}$, respectively. An ideal solution is prepared by mixing $59.75 \mathrm{g}$ of ${\mathrm{CHCl}}_3$ and $21.25 \mathrm{g}$ of ${\mathrm{CH}}_2{\mathrm{Cl}}_2$, the mole fractions of chloroform and dichloromethane in vapour phase, respectively are

The expression for moles of ${\mathrm{CHCl}}_3$ is given as,

$\mathrm{n}=\frac{{\mathrm{m}}_{{\mathrm{CHCl}}_3}}{{\mathrm{M}}_{{}_{{\mathrm{CHCl}}_3}}}=\frac{59.75 \mathrm{g}}{119.5 \mathrm{g}·{\mathrm{mol}}^{-1}}=0.5 \mathrm{mol}$

The expression for moles of ${\mathrm{CH}}_2{\mathrm{Cl}}_2$ is given as,

$\mathrm{n}=\frac{{\mathrm{m}}_{{\mathrm{CH}}_2{\mathrm{Cl}}_2}}{{\mathrm{M}}_{{\mathrm{CH}}_2{\mathrm{Cl}}_2}}=\frac{21.25 \mathrm{g}}{85 \mathrm{g}·{\mathrm{mol}}^{-1}}=0.25 \mathrm{mol}$

The mole fraction of ${\mathrm{CH}}_2{\mathrm{Cl}}_2$, is given as:

${\mathrm{\chi }}_{{\mathrm{CH}}_2{\mathrm{Cl}}_2}=\frac{{\mathrm{n}}_{{\mathrm{CH}}_2{\mathrm{Cl}}_2}}{{\mathrm{n}}_{{\mathrm{CH}}_2{\mathrm{Cl}}_2}+{\mathrm{n}}_{{\mathrm{CHCl}}_3}}=\frac{0.25}{0.25+0.5}=\frac{1}{3}$

The mole fraction of ${\mathrm{CHCl}}_3$ in vapour phase is given as:

${\mathrm{y}}_{{\mathrm{CHCl}}_3}=\frac{{\mathrm{p}}_{{\mathrm{CHCl}}_3}}{{\mathrm{p}}_1^0+\left({\mathrm{p}}_2^0-{\mathrm{p}}_1°\right){\mathrm{x}}_2}=\frac{{\displaystyle \frac{200\times 2}{3}} \mathrm{mm} \mathrm{Hg}}{200+(415-200)\times {\displaystyle \frac{1}{3}}}=\frac{400}{815} = 0.491$

$$The mole fraction of ${\mathrm{CH}}_2{\mathrm{Cl}}_2$ in vapour phase is given as,

${\mathrm{y}}_{{\mathrm{CH}}_2{\mathrm{Cl}}_2}=\frac{{\mathrm{p}}_{{\mathrm{CH}}_2{\mathrm{Cl}}_2}}{{\mathrm{p}}_1^0+\left({\mathrm{p}}_2^0-{\mathrm{p}}_1^0\right){\mathrm{x}}_2} = 1-{\mathrm{y}}_{{\mathrm{CHCl}}_3} = 0.509$