The molar conductivity of a 0.018 mol L ⁻¹ solution of acetic acid is 39.05 S cm ^2 mol ⁻¹ . If the limiting molar conductivities of H ^+ and CH ₃ COO ^- ions are 349.6 S cm ^2 mol ⁻¹ and 40.9 S cm ^2 mol ⁻¹ respectively, the acid dissociation constant ( K_a ) of acetic acid is:

Step-by-step solution

Limiting molar conductivity of acetic acid is: _m^ = ^ ( H ^+) + ^ ( CH ₃ COO ^-) _m^ = 349.6 + 40.9 = 390.5 S cm ^2 mol ⁻¹ Degree of dissociation, = _m _m^ = 39.05 390.5 = 0.1 Using Ostwald's dilution law, the acid dissociation constant K_a is: K_a = C ^2 1 - K_a = 0.018 (0.1)^2 1 - 0.1 K_a = 0.018 0.01 0.9 = 1.8 10⁻⁴ 0.9 = 2.0 10⁻⁴ Answer: 2.0 10⁻⁴