Molar conductivity:

Molar conductivity is defined as the conductivity of an electrolyte solution divided by the molar concentration of the electrolyte, and so measures the efficiency with which a givenelectrolyte conducts electricity in solution. Its units are siemens per meter per molarity, or siemens meter-squared per mole. The usual symbol is a capital lambda

Λ, or Λ m.

conductivity is dependent on concentration. so, it is not easy for measuring conductivity of different solutions and compare directly. Hence a quantity called molar conductivity is introduced. Molar conductivity is also called as equivalence conductivity.

Friedrich Kohlrausch established that to a high accuracy in dilute solutions, molar conductivity is composed of individual contributions of ions. This is known as the law of independent migration of ions

From its definition, the molar conductivity is given by,

Λ_m = k/c

where,

k is the measured conductivity

c is the electrolyte concentration.

For strong electrolytes, such as salts, strong acids and strong bases, molar conductivity is only weakly dependent on concentration and, to a good approximation, fits to

Λ_m = Λ_m° - K √c

where is the molar conductivity at infinite dilution (or limiting molar conductivity)

K is the Kohlrausch coefficient, which depends on the nature of the specific salt in solution.

In contrast, Friedrich Kohlrausch showed that the molar conductivity is strongly concentration dependent for weak (incompletely dissociated) electrolytes; the more dilute a solution, the greater its molar conductivity, due to increased ionic dissociation. (This, for example, is the case of SDS-coated proteins in the stacking gel of an SDS-PAGE.)

The limiting molar conductivity can be decomposed into contributions from the different ions (law of independent migration of ions):

Λ_m° = ∑_iν_iλ_i

where ( λ ) i is the molar ionic conductivity of ion i. ν i is the number of ions i in the formula unit of the electrolyte (e.g. 2 and 1 for N + and SO4 2- respectively in Na₂SO₄)