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 given electrolyte conducts electricity in solution. It is the conducting power of all the ions produced by dissolving one mole of an electrolyte 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. It can also be defined as follows: Molar conductivity of a solution at a given concentration is the conductance of the volume (V) of the solution containing one mole of electrolyte kept between two electrodes with area of cross section (A) and at a distance of unit length.

Friedrich Kohlrausch's researches in 1875-79 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:

where:

Two cases should be distinguished: strong electrolytes and weak electrolytes.

For strong electrolytes, such as salts, strong acids and strong bases, the molar conductivity depends only weakly on concentration. Based on experimental data Friedrich Kohlrausch (around the year 1900) proposed the non-linear law for strong electrolytes:

where

This law is valid for low electrolyte concentrations only; it fits into the Debye-Hückel-Onsager equation :.

For weak electrolytes (i.e. incompletely dissociated electrolytes), however, the molar conductivity strongly depends on concentration: The more dilute a solution, the greater its molar conductivity, due to increased ionic dissociation. For example, acetic acid has a higher molar conductivity in dilute aqueous acetic acid than in concentrated acetic acid. This is also the case of SDS-coated proteins in the stacking gel of an SDS-PAGE.

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