A 0.1 M solution of a hypothetical weak acid HA has a dissociation constant of 1.0 10⁻⁵ . The limiting ionic conductivities of H ^+ and A ^- are 350 S cm ^2 mol ⁻¹ and 50 S cm ^2 mol ⁻¹ respectively. What is the molar conductivity of the solution?

Step-by-step solution

The limiting molar conductivity of the weak acid HA is given by Kohlrausch's law: _m^ = ^ _ H ^+ + ^ _ A ^- = 350 + 50 = 400 S cm ^2 mol ⁻¹ For a weak acid, the degree of dissociation ( ) is related to the dissociation constant ( K_a ) and concentration ( c ) by K_a c ^2 (since is very small). = K_a c = 1.0 10⁻⁵ 0.1 = 10⁻⁴ = 0.01 The molar conductivity ( _m ) is related to by: = _m _m^ _m = _m^ = 0.01 400 = 4 S cm ^2 mol ⁻¹ Answer: 4 S cm ^2 mol ⁻¹