The equivalent conductance of $\frac{\mathrm{M}}{32}$ solution of a weak monobasic acid is $8.0…
The equivalent conductance of $\frac{\mathrm{M}}{32}$ solution of a weak monobasic acid is $8.0 \mathrm{~mho~} \mathrm{cm}^2$ and at infinite dilution is $400 \mathrm{~mho~} \mathrm{cm}^2$. The dissociation constant of this acid is
$1.25 \times 10^{-5}$
$1.25 \times 10^{-6}$
$6.25 \times 10^{-4}$
$1.25 \times 10^{-4}$
Solution
Degree of dissociation, $\alpha=\frac{\Lambda^c}{\Lambda^{\infty}}$ where, $\Lambda^c$ and $\Lambda^{\infty}$ are equivalent conductances at a given concentration and at infinite dilution respectively.
$\Rightarrow \quad \alpha=\frac{8.0}{400}=2 \times 10^{-2}$
From Ostwald's dilution law (for weak monobasic acid)
$\begin{aligned}
\mathrm{K}_{\mathrm{a}} & =\frac{\mathrm{C} \alpha^2}{(1-\alpha)} \\
\text { or } \quad & \mathrm{C} \alpha^2 \\
& =\frac{1}{32}\left(2 \times 10^{-2}\right)^2 \\
\text { or } & =1.25 \times 10^{-5}
\end{aligned}$