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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.

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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.

[∧°H+ = 350 S cm2mol–1 

∧°HCH3COO- = 50 S cm2mol–1 ]

(1) 1.75 × 10–4 mol L–1

(2) 2.50 × 10–4 mol L–1

(3) 1.75 × 10–5 mol L–1

(4) 2.50 × 10–5 mol L–1

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Correct answer: (3) 1.75 × 10–5 mol L–1

Explanation:

∧°M(CH3COOH) = ∧°M(CH2COO-) + ∧°MH+

= 350 + 50 = 400 S cm2 mol–1

α = \(\frac{\wedge_M^C}{\wedge_M^0}\)

α = \(\frac{20}{400}\)

= 5 x 10–2

Ka(CH3COOH) = Cα2

= 0.007 x (5 x 10–2)2

= 1.75 x 10–5 mol L–1

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