5 moles of liquid $X$ and 10 moles of liquid $Y$ make a solution having a vapour pressure of 70 torr

Question

5 moles of liquid $X$ and 10 moles of liquid $Y$ make a solution having a vapour pressure of 70 torr. The vapour pressures of pure $X$ and $Y$ are 63 torr and 78 torr respectively. Which of the following is true regarding the described solution?

Professor PC Thomas Classes · Answer

$
\begin{aligned}
& 	ext { (d) : Given : } n_X=5, n_Y=10 \
& x_X=\frac{5}{5+10}=\frac{5}{15}=\frac{1}{3} \
& x_Y=\frac{10}{5+10}=\frac{10}{15}=\frac{2}{3} \
& 	ext { Given : } p_{	ext {total }}=70 	ext { torr } \
& p_X^{\circ}=63 	ext { torr, } p_Y^{\circ}=78 	ext { torr } \
& p=p_X+p_Y=\frac{1}{3} 	imes 63+\frac{2}{3} 	imes 78=73 	ext { torr }
\end{aligned}
$
Vapour pressure of solution i.e., 70 torr is less than that predicted by Raoult's law. Hence, it shows negative deviation.