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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.[1]

## Description

From its definition, the molar conductivity is given by[2]:

$\Lambda_{\mathrm{m}} = \frac{\kappa}{c}$

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 to[3]

$\Lambda_{\mathrm{m}} =\Lambda_{\mathrm{m}}^\circ - K\sqrt{c}$

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, 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 proteins in polyacrylamide gel electrophoresis.)

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)

## References

1. ^ Castellan, G.W. Physical Chemistry. Benjamin/Cummings, 1983.
2. ^ The best test preparation for the GRE Graduate Record Examination Chemistry Test. Published by the Research and Education Association, 2000, ISBN: 0-8789-600-8. p. 149.
3. ^ Atkins, P. W. (2001). The Elements of Physical Chemistry. Oxford University Press. ISBN 0198792905.