Variation of Molar Conductivity with Concentration

Friedrich Kohlrausch measured the molar conductance of a range of electrolytes across several concentrations and found a clear, repeatable trend: molar conductance rises as a solution is progressively diluted, for every electrolyte tested. The measured molar conductances of NaCl, KCl and HCl at 0.1 M, 0.01 M and 0.0001 M (tabulated alongside this section) illustrate the trend directly — every column of numbers climbs steadily as concentration falls.

From data of exactly this kind, Kohlrausch deduced a simple empirical relationship between molar conductance $\Lambda_m$ and the square root of concentration $\sqrt{C}$:

This has exactly the form of a straight line, $y = mx + c$: plotting $\Lambda_m$ against $\sqrt{C}$ gives a line of negative slope $-k$ and a y-intercept $\Lambda_m^{o}$, called the limiting molar conductivity — the value molar conductance approaches as the solution becomes infinitely dilute, where interionic interactions vanish entirely.

Strong and weak electrolytes behave very differently on this same plot. For a strong electrolyte such as KCl or NaCl, the $\Lambda_m$ vs $\sqrt{C}$ plot is an almost perfect straight line across the whole measurable range, so $\Lambda_m^{o}$ can simply be read off by extrapolating the line to $\sqrt{C} = 0$. Physically, at high concentration a strong electrolyte's ions are numerous and close together, so interionic attraction and viscous drag from extra solvation both suppress conductivity; as dilution increases, the ions spread apart, these effects weaken, and molar conductivity climbs toward its maximum, limiting value at infinite dilution. …