0.5 molal aqueous solution of a weak acid $(\mathrm{HX})$ is $20 \%$ ionised. If $\mathrm{K}_f$ for water is…

0.5 molal aqueous solution of a weak acid $(\mathrm{HX})$ is $20 \%$ ionised. If $\mathrm{K}_f$ for water is $1.86 \mathrm{Kg} \mathrm{mol}^{-1}$, the lowering in freezing point of the solution is:
  1. $0.56 \mathrm{~K}$
  2. $1.12 \mathrm{~K}$
  3. $-0.56 \mathrm{~K}$
  4. $-1.12 \mathrm{~K}$

Solution

$\operatorname{As} \Delta \mathrm{T}_f=i k_f \mathrm{~m}$ For
$\begin{aligned}
& \mathrm{HX} \rightleftharpoons \mathrm{H}^{+}+\mathrm{X}^{-} \\
& t=0 \quad 1 \quad 0 \quad 0 \\
& \begin{array}{llll}
t_{\text {eq }} & (1-0.20) & 0.20 & 0.20
\end{array} \\
&
\end{aligned}$
Total no. of moles $=1-0.20+0.20$
$\begin{aligned}
+0.20 & =1+0.20=1.2 \\
\therefore \Delta \mathrm{T}_f & =1.2 \times 1.86 \times 0.5 \\
& =1.1160
\end{aligned}$
Related Theory
The boiling point and freezing point are colligative properties. Due to the addition of solutes, the boiling point tends to increase, and freezing point tends to decrease.

Asked in: NEET 2007

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