Question

Two solutions $A$ and $B$ are prepared by dissolving $1 g$ of non-volatile solutes $X$ and $Y$. respectively in $1 \,kg$ of water. The ratio of depression in freezing points for $A$ and $B$ is found to be $1: 4$. The ratio of molar masses of $X$ and $Y$ is :

• A. $1: 4$
• B. $1: 0.25$
• C. $1: 0.20$
• D. $1: 5$

Answer 1

Answer: (B)

$ \frac{\Delta T _{ fx }}{\Delta T _{ fy }}=\frac{ k _{ f } \cdot m _{ x }}{ k _{ f } \cdot m _{ y }}=\frac{\frac{1 / M _{ x }}{1}}{\frac{1 / M _{ y }}{1}} $
$ \Rightarrow \frac{1}{4}=\frac{ M _{ y }}{ M _{ x }} $
$ \Rightarrow M _{ x }: M _{ y }=1: 0.25$