The molar conductivity of a 0.038 M solution of a weak base MOH is 10 S cm ^2 mol ⁻¹ . What is the dissociation constant ( K_b ) of the base? Given: ^ _ M^+ = 50 S cm ^2 mol ⁻¹ ^ _ OH^- = 150 S cm ^2 mol ⁻¹

Step-by-step solution

The limiting molar conductivity of MOH is given by Kohlrausch's law: ^ _m(MOH) = ^ _ M^+ + ^ _ OH^- ^ _m(MOH) = 50 + 150 = 200 S cm ^2 mol ⁻¹ The degree of dissociation is: = _m ^ _m = 10 200 = 0.05 The dissociation constant K_b for the weak base is: K_b = C ^2 1- Substituting the values: K_b = 0.038 (0.05)^2 1 - 0.05 K_b = 0.038 0.0025 0.95 K_b = 9.5 10⁻⁵ 0.95 = 1.0 10⁻⁴ mol L ⁻¹ Answer: 1.0 10⁻⁴ mol L ⁻¹