The molar conductivity of a strong electrolyte XY at concentrations 0.01 M and 0.04 M are 148 S cm ^2 mol ⁻¹ and 146 S cm ^2 mol ⁻¹ respectively. If the limiting molar conductivities of strong electrolytes HY and XZ are 425 S cm ^2 mol ⁻¹ and 125 S cm ^2 mol ⁻¹ respectively, the limiting molar conductivity of the weak acid HZ is ________ S cm ^2 mol ⁻¹ .

Step-by-step solution

For a strong electrolyte, the molar conductivity varies with concentration according to the Debye-Hückel-Onsager equation: _m = _m^0 - A c Using the given data for XY : At c = 0.01 M , c = 0.1 148 = _m^0(XY) - A(0.1) ... (i) At c = 0.04 M , c = 0.2 146 = _m^0(XY) - A(0.2) ... (ii) Subtracting equation (ii) from (i): 148 - 146 = A(0.2 - 0.1) 2 = 0.1 A A = 20 Substituting the value of A in equation (i): 148 = _m^0(XY) - 20(0.1) _m^0(XY) = 148 + 2 = 150 S cm ^2 mol ⁻¹ According to Kohlrausch's law of independent migra