Molar Conductivity and Its Variation with Concentration

Specific conductivity, $\kappa$, describes how well a given volume of solution conducts, but it mixes together two separate effects: how many ions are actually present, and how well each individual ion conducts. To separate out the conducting contribution of the electrolyte itself, independent of how concentrated the solution happens to be, chemists define molar conductivity, $\Lambda_m$, as the conductivity contributed by exactly one mole of dissolved electrolyte: $\Lambda_m = \frac{1000\,\kappa}{C}$ where $C$ is the molar concentration in $\text{mol L}^{-1}$ and the factor of $1000$ converts $\kappa$ (naturally expressed per $\text{cm}^3$) onto the same per-litre basis as $C$. Its unit works out to $\text{S cm}^2\ \text{mol}^{-1}$.

Unlike $\kappa$, which falls on dilution, $\Lambda_m$ rises as a solution is diluted — for two distinct physical reasons that apply to different degrees for different electrolytes. First, in every electrolyte solution, ions in close proximity exert a retarding electrostatic drag on one another's motion (sometimes pictured as each ion dragging a loosely-bound 'ionic atmosphere' of opposite charge behind it); diluting the solution increases the average distance between ions, weakening this drag and increasing each ion's mobility. Second, for a weak electrolyte specifically, dilution also shifts its dissociation equilibrium further toward the ionized form (by Le Chatelier's principle, since dissociation increases the total number of particles, which is favoured at lower concentration), genuinely increasing the number of ions present per mole of electrolyte.

A strong electrolyte, such as $\text{KCl}$ or $\text{NaCl}$, is essentially completely dissociated at every concentration normally studied, so only the mobility effect operates; its $\Lambda_m$ therefore rises gradually and predictably on dilution, following the Debye-Huckel-Onsager relation $\Lambda_m = \Lambda_m^{0} - A\sqrt{C}$ (a straight line when $\Lambda_m$ is plotted against $\sqrt{C}$), and its limiting value $\Lambda_m^{0}$ (molar conductivity at infinite dilution, where inter-ionic effects vanish entirely) can be obtained simply by extrapolating this line to $C=0$. …