Molar Conductivity

Two solutions at different concentrations contain different numbers of ions per unit volume, and so naturally show different specific conductance — this makes κ a poor basis for comparing how well different electrolytes conduct. Molar conductivity, symbol $\Lambda_m$, fixes this by standardising the amount of electrolyte considered: it is defined as the conductance of the volume of solution — call it V m³ — that contains exactly one mole of the dissolved electrolyte, measured between electrodes exactly 1 m apart.

Since the specific conductance κ is, by definition, the conductance of 1 m³ of the solution, the conductance of the V m³ containing one mole of electrolyte follows simply as

To turn this into something computable from an ordinary concentration reading, recall that molarity is defined as $M = \dfrac{n}{V(\text{in dm}^3)}$, so the volume containing exactly one mole of solute is $V = \dfrac{1}{M}\ \text{dm}^3\,\text{mol}^{-1}$. Converting this volume-per-mole into SI units (m³ per mol) and substituting into the relation above gives the standard working formula:

or, in the more commonly used CGS-flavoured form with κ in S cm⁻¹ and M in mol L⁻¹, simply $\Lambda_m = \dfrac{1000\,\kappa}{M}$ (S cm² mol⁻¹). This single equation is the workhorse of every molar-conductivity numerical in the chapter: given any two of κ, M and $\Lambda_m$, the third follows immediately. …