Question

Vapour pressure of a pure liquid $X$ is $2$ atm at $300 \,K$. It is lowered to $1$ atm on dissolving $1\, g$ of $Y$ in $20\, g$ of liquid $X$. If molar mass of $X$ is $200$, what is the molar mass of $Y$ ?

• A. $20$
• B. $50$
• C. $100$
• D. $200$

Answer 1

Answer: (A)

$\frac{p^{\circ} - p_{A}}{p^{\circ}_{A}} = \frac{n_{B}}{n_{A}}$
$\frac{2-1}{2} = \frac{W_{B}}{M_{B}}\times\frac{M_{A}}{W_{A}}$
$\Rightarrow \frac{1}{2} = \frac{1}{M_{B}}\times\frac{200}{20}$
$\Rightarrow M_{B} = \frac{200 \times 2}{20 } = 20$