Molar Conductivity

Molar Conductivity Molar and Equivalent Conductivities The electrical conductivity EC is an easy-to-measure parameter; its exact calculation, however, is rather non-trivial. Today exist a variety of approaches 1, but all of them are no more than approximations (especially for waters of arbitrary composition). In any case, physical-based approaches to EC start always from the concept of molar or equivalent conductivities: (1a) electrical conductivity (specific conductance) EC 2,3 in S/m (or ?S/cm) (1b) molar conductivity ?m = EC / c in S cm2 mol-1 (1c) equivalent conductivity ?eq = ?m / |z| in S cm2 eq-1 Here c symbolizes the molar concentration of the electrolyte (in mol/L) and z refers to the electrical charge. The molar conductivity ?m is defined as the conductivity of a 1 molar aqueous solution placed between two plates (electrodes) 1 cm apart. The equivalent conductivity refers to the normality of the solution (rather than molarity). It accounts for the obvious fact that ions with higher z are able to transport more charge. Introducing the (2) equivalent concentration: ceq = |z| c the equivalent conductivity in Eq.(1c) becomes (3) ?eq = EC / ceq Kohlrausch’s Law for Strong Electrolytes (Limiting Conductivities) Strong electrolytes (in contrast to weak electrolytes) are salts, acids and bases that dissociate completely. For strong electrolytes one might expect a linear relationship between EC and the concentration, i.e. EC = const · c, where the molar conductivity ?macts as proportionality constant. Unfortunately, nature is not so simple: ?m is not constant and diminishes when c raises. About 100 years ago F. Kohlrausch deduced from experimental data the “Square-Root Law”: (4a) ?eq = ?0eq?Kceq????eq = ?eq0?Kceq or, equivalently, (4b) ?m = ?0m?K?c??m = ?m0?K?c with K’ = K / |z|1.5 It is valid for strong electrolytes4 at low concentrations, c ? 10 mM. The Kohlrausch parameter K depends on the type of electrolyte. A theoretical explanation of the square-root dependence of c was provided by Debey, Hückel and Onsager about 50 years later. Limiting Conductivities. In the very special case of zero concentration, c ? 0 (infinite dilution), the above equations collapse to the