The specific conductance of 0.0025 M acetic acid is at a certain temperature. The dissociation constant of acetic acid is ______ . Consider limiting molar conductivity of as 400 S . [2023]

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Solution

Q.
The specific conductance of 0.0025 M acetic acid is $5 \times 10^{- 5} {S cm}^{- 1}$ at a certain temperature. The dissociation constant of acetic acid is ______ $\times 10^{- 7}$ . Consider limiting molar conductivity of ${CH}_{3} COOH$ as 400 S ${cm}^{2}$ ${mol}^{- 1}$ . [2023]

Ans.
(66)

$Λ_{m} = \frac{1000 \times K}{C} = \frac{1000 \times 5 \times 10^{- 5}}{0.0025} = 20 {S cm}^{2} {mol}^{- 1}$

$α = \frac{20}{400} = \frac{1}{20}$

$K_{a} = \frac{C α^{2}}{1 - α^{2}} = \frac{0.0025 \times \frac{1}{20} \times \frac{1}{20}}{1 - \frac{1}{20}} = \frac{0.0025}{19 \times 20} = 66 \times 10^{- 7}$

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