MCQ
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]
  • A
    $0$
  • $1$
  • C
    $2$
  • D
    $3$

Answer

Correct option: B.
$1$
b
$\Delta T _{ b }= iK _{ b } m _{1} \quad \Delta T _{ f }= iK _{ f } m _{2}$

$\frac{\Delta T _{ b }}{\Delta T _{ f }}=\frac{ K _{ b } \times 1}{ K _{ f } \times 2}$ $\Rightarrow \frac{3}{6}=\frac{1}{2}=\frac{ K _{ b }}{ K _{ f }} \times \frac{1}{2}$

$\frac{ K _{ b }}{ K _{ f }}=\frac{1}{1} \Rightarrow x =1$

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