Conductivity or specific conductance (κ) is the conductance of 1 cm³ of the solution in C.G.S. units, while molar conductivity is the conductance of a solution containing one mole of an electrolyte. Consider C molar solution, i.e., C moles of an electrolyte present in 1 litre or 1000 cm³ of the solution.

∴ C moles of an electrolyte are present in 1000 cm³ solution.

∴ 1 mole of an electrolyte is present in \(\frac{1000}{C}\) cm solution.

Now,

∴ Conductance of 1 cm³ of this solution is κ,

∴ Conductance of \(\frac{1000}{C}\) cm³ of the solution is \(\frac{k\times 1000}{C}\)

This represents molar conductivity, ∧_m.

∴ ∧_m = \(\frac{k\times 1000}{C}\)cm²mol^-1(in C.G.S units)

[ In case of SI units :

Consider a solution in which C moles of an electrolyte are present in 1m³ of solution. 

Conductivity κ is the conductance of 1m³ of solution.

∵ C moles of an electrolyte are present in 1m³ solution.

∴ 1 mol of an electrolyte is present in \(\frac{1}{C}\) solution.

∵ Conductance of 1m³ of this solution is κ.

∴ Conductance of \(\frac{1}{C}\)m³ of the solution is \(\frac{k}{C}\).

This represents molar conductivity, ∧_m.

∴ ∧_m = \(\frac{k}{C}\)Ω^-1 m² mol^-1 (In SI units).]