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The equivalent conductance of $\frac{M}{32}$ solution of a weak monobasic acid is 8.0 mho $cm^2$ and at infinite dilution is 400 mho $cm^2$. The dissociation constant of this acid is
A
$1.25\times10^{-4}$
B
$1.25\times10^{-5}$
C
$1.25\times10^{-6}$
D
$6.25\times10^{-4}$
Detailed Solution
Degree of dissociation: $\alpha = \frac{\Lambda}{\Lambda^\circ} = \frac{8.0}{400} = 0.02$
For a weak monobasic acid HA of concentration C: $K_a = \frac{C\alpha^2}{1 - \alpha} \approx C\alpha^2$ (since $\alpha$ is small)
$C = \frac{1}{32}$ M
$K_a = \frac{1}{32}\times(0.02)^2 = \frac{4\times10^{-4}}{32}$
$K_a = 1.25\times10^{-5}$
For a weak monobasic acid HA of concentration C: $K_a = \frac{C\alpha^2}{1 - \alpha} \approx C\alpha^2$ (since $\alpha$ is small)
$C = \frac{1}{32}$ M
$K_a = \frac{1}{32}\times(0.02)^2 = \frac{4\times10^{-4}}{32}$
$K_a = 1.25\times10^{-5}$