# Molar conductivity

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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. Its units are siemens per meter per molarity, or siemens meter-squared per mole. The usual symbol is a capital lambda, Λ, or Λm.

## History

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.

## Description

From its definition, the molar conductivity is given by: $\Lambda_{\mathrm{m}} = \frac{\kappa}{c}$

where:

• κ 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 into the Debye - Huckel - Onsager equation : $\Lambda_{\mathrm{m}} =\Lambda_{\mathrm{m}}^\circ - K\sqrt{c}$

where:

• $\Lambda_{\mathrm{m}}^\circ$ 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): $\Lambda_{\mathrm{m}}^\circ = \Sigma_i \nu_i \lambda_i$

where:

• λi is the molar ionic conductivity of ion i.
• νi is the number of ions i in the formula unit of the electrolyte (e.g. 2 and 1 for Na+ and SO42- respectively in Na2SO4)

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