## Molar Conductivity

If the conductivity k
is in W
^{-1}cm^{-1}
and the concentration C is in mol cm^{-3},
then the molar conductivity L is
in W^{-1} cm^{2}
mol^{-1} and is defined
by

Variation of molar conductivity with concentration.

With respect to this behavior there are
two classes, strong and weak electrolytes, that have different
characteristics. For strong electrolytes Kohlrausch determined
the empirical relationship of L to
C^{1/2}

where the molar conductivity at infinite dilution is arrived at by plotting the molar conductivity at various concentrations vs. concentration and extrapolating to zero concentration.

Weak electrolytes vary in a non-linear manner. They dissociate to a greater extent with increasing dilution. Using ethanoic acid as an example we have the equilibrium

with concentrations of the dissociated species expressed as a C and the undissociated acid as (1-a)C. The dissociation constant can be expressed as

where a is the degree of dissociation. Arrhenius showed that a can be given as

Combining the last two equations gives