Question

Define conductivity and molar conductivity of an electrolyte solution. Discuss the change in their value with the change in concentration of electrolyte.

Hint:

Conductivity = conductance of 1 cm³ of solution (S cm^-1); molar conductivity \(\Lambda_m = \kappa \times 1000 / C\) (S cm² mol^-1). On dilution kappa falls but molar conductivity rises.

Answer 1

Step 1: Conductivity (kappa). Conductivity is the conductance of a solution held between two electrodes each of 1 cm² cross-section and placed 1 cm apart, that is the conductance of 1 cm³ of the solution. It is the reciprocal of resistivity: \(\kappa = \dfrac{1}{\rho} = G \times \dfrac{l}{A}\), where G is conductance and l/A is the cell constant. Unit: S cm^-1 (or S m^-1).
Step 2: Molar conductivity (Lambda_m). It is the conducting power of all the ions produced by one mole of electrolyte, that is the conductivity of a solution containing one mole of electrolyte between electrodes 1 cm apart. \(\Lambda_m = \dfrac{\kappa \times 1000}{C}\), with kappa in S cm^-1 and C in mol L^-1. Unit: S cm² mol^-1.
Step 3: Effect on conductivity. On dilution (decreasing concentration) the conductivity decreases, because the number of ions present in each unit volume falls.
Step 4: Effect on molar conductivity. On dilution the molar conductivity increases, because the volume holding one mole of electrolyte increases. For strong electrolytes the rise is small (ions move more freely as inter-ionic attraction weakens); for weak electrolytes the rise is large near infinite dilution due to the greater degree of dissociation.