What is molar conductivity at zero concentration in ⁻¹ ~cm ^2 ~mol ⁻¹ for aluminium sulphate, if molar ionic conductivities at zero concentration of Al ⁺³ and SO ₄⁻² are 189 ⁻¹ ~cm ^2 ~mol ⁻¹ and 50 1 ⁻¹ ~cm ^2 ~mol ⁻¹ respectively?

Step-by-step solution

The molar conductivity at infinite dilution _m^0 for Al ₂( SO ₄)₃ is determined using Kohlrausch's Law, which states that _m^0 = x _ A ^ y+ ^0 + y _ B ^ x- ^0 . For Al ₂( SO ₄)₃ , the dissociation yields 2 Al ³⁺ and 3 SO ₄²⁻ ions. With _ Al ³⁺ ^0 = 189 , ⁻¹ cm ^2 mol ⁻¹ and _ SO ₄²⁻ ^0 = 50.1 , ⁻¹ cm ^2 mol ⁻¹ , the molar conductivity is _m^0 = 2 189 + 3 50.1 = 378 + 150.3 = 528.3 , ⁻¹ cm ^2 mol ⁻¹ . This value corresponds to option D .