The molar conductivity of 0.007 M acetic acid is 20 S cm$^2$ mol$^{-1}$. What is the dissociation constant of

Question

The molar conductivity of 0.007 M acetic acid is 20 S cm$^2$ mol$^{-1}$. What is the dissociation constant of acetic acid? Choose the correct option. $\left[ \Lambda_{H^+}^\circ = 350 	ext{ S cm}^2 	ext{ mol}^{-1}, \Lambda_{CH_3COO^-}^\circ = 50 	ext{ S cm}^2 	ext{ mol}^{-1} ight]$

Accepted Answer

Given $\Lambda_m = 20 	ext{ S cm}^2 	ext{ mol}^{-1}$. $\Lambda_{CH_3COOH}^\circ = \Lambda_{CH_3COO^-}^\circ + \Lambda_{H^+}^\circ = 50 + 350 = 400 	ext{ S cm}^2 	ext{ mol}^{-1}$. Degree of dissociation $\alpha = \frac{\Lambda_m}{\Lambda_m^\circ} = \frac{20}{400} = \frac{1}{20}$. Dissociation constant $K_a = \frac{C\alpha^2}{1-\alpha} \approx C\alpha^2 = 7 	imes 10^{-3} 	imes (\frac{1}{20})^2 = 7 	imes 10^{-3} 	imes \frac{1}{400} = 1.75 	imes 10^{-5} 	ext{ mol L}^{-1}$.

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