Electrolytic and Metallic Conduction

Electrolytic Conduction

Conductance of Electrolytic Solutions

the symbol ‘R’ and it is measured in ohm (Ω)

which in terms of SI base units is equal to (kg m2)/(s3 A2).

The constant of proportionality, ρ (Greek, rho), is called resistivity (specific resistance). Its SI units are ohm metre (Ω m).

The inverse of resistance, R, is called conductance, G, and we have the relation:

The SI unit of conductance is siemens, represented by the symbol ‘S’ and is equal to ohm^–1 (also known as mho) or Ω^–1. The inverse of resistivity, called conductivity (specific conductance) is represented by the symbol, κ (Greek, kappa). The SI units of conductivity are S m ^–1 but quite often, is expressed in S cm^–1. Conductivity of a material in S m^–1 is its conductance when it is 1 m long and its area of cross section is 1 m². It may be noted that 1 S cm^–1 = 100 S m^–1.

Molar conductivity 

In the above equation, if it is expressed in S m^–1 and the concentration,

C in mol m^-3 then the units of Λ_m are in S m² mol^-1. It may be noted that:

1 mol m^-3 = 1000(L/m³) × molarity (mol/L), and hence

If we use S cm^-1 as the units for  and mol cm^-3, the units of concentration, then the units for  are S cm² mol^-1. It can be calculated by using the equation:

1 S m²mol^-1 = 10⁴ S cm²mol^-1

Example

Resistance of a conductivity cell filled with 0.1 mol L^-1 KCl solution is 100 Ω. If the resistance of the same cell when filled with 0.02 mol L^-1 KCl solution is 520 Ω, calculate the conductivity and molar conductivity of 0.02 mol L^-1 KCl solution. The conductivity of 0.1 mol L^-1 KCl solution is 1.29 S/m.

Solution

The cell constant is given by the equation:

Cell constant = G* = conductivity × resistance

= 1.29 S/m × 100 Ω = 129 m^-1 = 1.29 cm^-1

Conductivity of 0.02 mol L-1 KCL solution = cell constant / resistance

Concentration = 0.02 mol L^-1

= 1000 × 0.02 mol m^-3

= 20 mol m^-3

Molar conductivity 

Alternatively, 

= 0.248 × 10^-2 S cm^-1

And Λ_m =  × 1000 cm³ L^-1 molarity^-1

Conductivity always decreases with decrease in concentration both, for weak and strong electrolytes. This can be explained by the fact that the number of ions per unit volume that carry the current in a solution decreases on dilution.

Molar conductivity of a solution at a given concentration is the conductance of the volume V of solution containing one mole of electrolyte.

Λ_m = k V

Molar conductivity increases with decrease in concentration. This is because the total volume, V, of solution containing one mole of electrolyte also increases. It has been found that decrease in κ on dilution of a solution is more than compensated by increase in its volume.

For strong electrolytes, Λ increases slowly with dilution and represented by the equation:

The value of the constant ‘A’ for a given solvent and temperature depends on the type of electrolyte. NaCl, CaCl2, MgSO4 are known as 1-1, 2-1 and 2-2 electrolytes respectively. All electrolytes of a particular type have the same value for ‘A’.

shows change in molar conductivity with c ^½ for weak and strong electrolytes.