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 -

Question

Phenol does not undergo nucleophilic substitution reaction easily due to:

Answer 1

To find the dissociation constant $ K_a $ of a weak monobasic acid, we can use the formula relating the degree of dissociation, concentrations, and conductance:

The degree of dissociation ($\alpha$) is given by:

$\alpha = \frac{\Lambda_c}{\Lambda_0}$

where:

$\Lambda_c$ is the equivalent conductance at concentration $c = \frac{ M }{32} = 0.03125\ M$.
$\Lambda_0$ is the equivalent conductance at infinite dilution.

Inserting the given values:

$\Lambda_0 = 400\, \text{mho cm}^2$,
$\Lambda_c = 8\, \text{mho cm}^2$.

The degree of dissociation ($\alpha$) is:

$\alpha = \frac{8}{400} = 0.02$

The dissociation constant $K_a$ is given by:

K_a = c\alpha^2

Substituting the known values ($c = 0.03125\ M$, $\alpha = 0.02$):

K_a = 0.03125 \times (0.02)^2\

Calculating the above expression:

K_a = 0.03125 \times 0.0004 = 1.25 \times 10^{-5}\

Therefore, the dissociation constant of the acid is:

$1.25 \times 10^{-5}$.

Hence, the correct answer is $1.25 \times 10^{-5}$.

Answer 2