The molar conductivity of 0.007 M acetic acid is 20 S cm² mol^-1. What is the dissociation constant of acetic acid? Choose the correct option.
$[\begin{array}{l} \land_{H^{+}}^{0} = 350 S {cm}^{2} {mol}^{- 1} \\ \land_{{CH}_{3} {COO}^{-}}^{0} = 50 S {cm}^{2} {mol}^{- 1} \end{array}]$

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2.50 x 10^-5 mol L^-1

1.75 x 10^-5 mol L^-1

1.75 x 10^-4 mol L^-1

2.50 x 10^-4 mol L^-1

answer is D.

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Detailed Solution

Degree of dissociation (α) of CH₃COOH
$\begin{array}{l} = \frac{Λ_{C}}{Λ_{0}} = \frac{20}{350 + 50} = \frac{1}{20} \\ K_{a} = \frac{{Cα}^{2}}{1 - α} \\ 1 - α \approx 1 \\ K_{a} = {Cα}^{2} \\ K_{a} = 0 .007 \times \frac{1}{20} \times \frac{1}{20} \\ K_{a} = 1 .75 \times 10^{- 5} \end{array}$