Question

The elevation in boiling point for 1 molal solution of non-volatile solute $A$ is $3 K$. The depression in freezing point for 2 molal solution of $A$ in the same solvent is $6 K$. The ratio of $K_b$ and $K_f$ i.e., $K_b / K_f$ is $1: X$. The value of $X$ is [nearest integer]

Answer 1

$ \Delta T _{ b }= iK _{ b } m _1 \Delta T _{ f }= iK _{ f } m _2 $
$\frac{\Delta T _{ b }}{\Delta T _{ f }}=\frac{ K _{ b } \times 1}{ K _{ f } \times 2} $
$\Rightarrow \frac{3}{6}=\frac{1}{2}=\frac{ K _{ b }}{ K _{ f }} \times \frac{1}{2} $
$ \frac{ K _{ b }}{ K _{ f }}=\frac{1}{1} \Rightarrow x =1$