If the conductivity k is in W -1cm-1 and the concentration C is in mol cm-3, then the molar conductivity L is in W-1 cm2 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 C1/2
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