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Kohlrausch Law

The molar con...

Question

The molar conductivity of $0.007 M$ acetic acid is $20 S c m^{2} m o l^{- 1}$ . What is the dissociation constant of acetic acid ? choose the correct option.
$[\begin{matrix} Λ_{H^{+}}^{\circ} = 350 S c m^{2} m o l^{- 1} Λ_{C H_{3} C O O^{-}}^{\circ} = 50 S c m^{2} m o l^{- 1} \end{matrix}]$

(NEET 2021)

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Solution

$Λ_{C H_{3} C O O H}^{o} = Λ_{C H_{3} C O O^{-}}^{o} + Λ_{H^{+}}^{o}$

$Λ_{C H_{3} C O O H}^{o} = 350 + 50 = 400 S c m^{2} m o l^{- 1}$

$Λ_{C H_{3} C O O H} = 20 S c m^{2} m o l^{- 1} (G i v e n)$

$α = \frac{Λ_{C H_{3} C O O H}^{o}}{Λ_{C H_{3} C O O H}^{o}} = \frac{20}{400} = 5 \times 10^{- 2}$

$K_{α} = c α^{2} = 0.007 \times (5 \times 10^{- 2})^{2} K_{α} = 1.75 \times 10^{- 5} m o l L^{- 1}$

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