A 0.09 M solution of a weak monobasic acid HA has an acid dissociation constant K_a = 1.0 10⁻³ at 298 K . The limiting molar conductivities of H^+ and A^- at this temperature are 350 S cm^2 mol⁻¹ and 50 S cm^2 mol⁻¹ respectively. The specific conductance of the solution is x 10⁻⁴ S cm⁻¹ . The value of x is ___________.

Step-by-step solution

The limiting molar conductivity of the acid HA is given by Kohlrausch's law: _m^ = _m^ ( H^+ ) + _m^ ( A^- ) = 350 + 50 = 400 S cm^2 mol⁻¹ Using Ostwald's dilution law, the acid dissociation constant is: K_a = C ^2 1- 1.0 10⁻³ = 0.09 ^2 1- 10⁻³(1- ) = 0.09 ^2 1 - = 90 ^2 90 ^2 + - 1 = 0 (10 - 1)(9 + 1) = 0 Since must be positive, = 0.1 . The molar conductivity _m is: _m = _m^ = 0.1 400 = 40 S cm^2 mol⁻¹ The relationship between molar conductivity and specific conductance is: _m = 1000 C = _m C 1000 = 40 0.09 1000 =