Question

Discuss the variation of conductivity and molar conductivity with concentration.

Answer 1

Both conductivity and molar conductivity change with the change in concentration of electrolyte. Conductivity always decreases with decreasing the concentration of both weak and strong electrolytes. This can be explained by the fact that with dilution, the number of ions carrying electric current per unit volume decreases. The conductivity of a solution at any concentration is the conductivity of a unit volume of the solution placed between two platinum electrodes having a unit cross-sectional area and situated at unit distance from each other.

This is clear from the following equation:

C = `"κA"/"l"` = κ  ...(Both A and I are in appropriate units m or cm)

The molar conductivity of a solution at a given concentration is the conductivity of volume V of the solution containing one mole of electrolyte dissolved in it and placed between two electrodes of cross-sectional area A, located at a unit distance from each other. So,

Plot of c^1/2 versus molar conductivity for potassium chloride (a strong electrolyte) in aqueous solution.

∧_m = `"κA"/"l"` = κ

Since l = 1 and A = V (volume in which one mole of electrolyte is dissolved.)

∧_m = κ V

Molar conductivity increases with decreasing concentration. This is because the total volume (V) in which one mole of electrolyte is present also increases. It has been found that on dilution of the solution, the increase in volume is much more than the decrease in κ.

Strong Electrolytes: For strong electrolytes, the value of Δm increases gradually with dilution and it can be represented by the following equation:

∧_m = `∧_"m"^0 - "Ac"^(1//2)`

It can be seen that if ∧_m is plotted against c^1/2, we get a straight line with intercept A and slope equal to ‘A’. The value of constant ‘A’ at a given solvent and temperature depends on the type of electrolyte, i.e., on the charges of the cation and anion produced on dissociation of the electrolyte in solution. Thus, \[\ce{NaCl, CaCl2, MgSO4}\] are known as 1-1, 2-1 and 2-2 electrolytes, respectively. The value of ‘A’ is the same for all electrolytes of the same type.