Question

Define conductivity and molar conductivity for the solution of an electrolyte. Discuss their variation with concentration.

Answer 1

Conductivity of a solution is defined as the conductance of a solution of 1 cm in length and area of cross-section 1 sq. cm. The inverse of resistivity is called conductivity or specific conductance. It is represented by the symbol κ. If àis resistivity, then we can write: 
\(\kappa = \frac{1}{\rho}\)
The conductivity of a solution at any given concentration is the conductance (G) of one unit volume of solution kept between two platinum electrodes with the unit area of cross-section and at a distance of unit length. 
\(G = \kappa \frac{a}{l} = \kappa.1 = \kappa\)
i.e., 
(Since a = 1, l = 1) 
Conductivity always decreases with a decrease in concentration, both for weak and strong electrolytes. This is because the number of ions per unit volume that carry the current in a solution decreases with a decrease in concentration.

Molar conductivity: Molar conductivity of a solution at a given concentration is the conductance of volume V of a solution containing 1 mole of the electrolyte kept between two electrodes with the area of cross-section A and distance of unit length.
\(\land_m = \kappa \frac{A}{l}\)
Now, l = 1 and A = V (volume containing 1 mole of the electrolyte).
∴\(\land_m = \kappa V\)
Molar conductivity increases with a decrease in concentration. This is because the total volume V of the solution containing one mole of the electrolyte increases on dilution.
The variation of \(∧_m\) with \(\sqrt{c}\) for strong and weak electrolytes is shown in the following plot: