Question:
In a solvent $50 \%$ of an acid HA dimerizes and the rest dissociates. The van't Hoff factor of the acid is________ $\times 10^{-2}$.
(Round off to the nearest integer)
Solution:
$2 \mathrm{HA} \rightleftharpoons \mathrm{H}_{2} \mathrm{~A}_{2} \mathrm{HA} \rightleftharpoons \mathrm{H}^{+}+\mathrm{A}$
Now, $\mathrm{i}=\frac{\text { final moles }}{\text { initial moles }}=\frac{0.25 \mathrm{a}+0.5 \mathrm{a}+0.5 \mathrm{a}}{0.5 \mathrm{a}+0.5 \mathrm{a}}$
$=1.25=125 \times 10^{-2}$