The specific conductance of a solution containing one electrolyte depends on the concentration of the electrolyte. Therefore, it is convenient to divide the specific conductance by concentration. This quotient, termed
molar conductivity, is denoted by : : \Lambda_\text{m} =\frac{\kappa}{c}.
Strong electrolytes Strong electrolytes are hypothesized to
dissociate completely in solution. The conductivity of a solution of a strong electrolyte at low concentration follows
Kohlrausch's Law: : \Lambda_\text{m} = \Lambda_\text{m}^0 - K \sqrt{c}, where is known as the limiting molar conductivity, is an empirical constant, and is the electrolyte concentration. ("Limiting" here means "at the limit of the infinite dilution".) In effect, the observed conductivity of a strong electrolyte becomes directly proportional to concentration at sufficiently low concentrations, i.e. when : \Lambda_\text{m}^0 \gg K \sqrt{c}. As the concentration is increased, however, the conductivity no longer rises in proportion. Moreover, Kohlrausch also found that the limiting conductivity of an electrolyte, : and , are the limiting molar conductivities of the individual ions. The following table gives values for the limiting molar conductivities for some selected ions. : \Lambda_\text{m} = \Lambda_\text{m}^0 - (A + B\Lambda_\text{m}^0) \sqrt{c}, where and are constants that depend only on known quantities such as temperature, the charges on the ions and the
dielectric constant and
viscosity of the solvent. As the name suggests, this is an extension of the
Debye–Hückel theory, due to
Onsager. It is very successful for solutions at low concentration.
Weak electrolytes A weak electrolyte is one that is never fully dissociated (there is a mixture of ions and neutral molecules in equilibrium). In this case there is no limit of dilution below which the relationship between conductivity and concentration becomes linear. Instead, the solution becomes ever more fully dissociated at weaker concentrations, and for low concentrations of "well behaved" weak electrolytes, the degree of dissociation of the weak electrolyte becomes proportional to the inverse square root of the concentration. Typical weak electrolytes are
weak acids and
weak bases. The concentration of ions in a solution of a weak electrolyte is less than the concentration of the electrolyte itself. For acids and bases the concentrations can be calculated when the value or values of the
acid dissociation constant are known. For a
monoprotic acid HA obeying the inverse square root law, with a dissociation constant , an explicit expression for the conductivity as a function of concentration , known as
Ostwald's dilution law, can be obtained: : \frac{1}{\Lambda_\text{m}} = \frac{1}{\Lambda_\text{m}^0} + \frac{\Lambda_\text{m} c}{K_\text{a}{(\Lambda_\text{m}^0)}^2}. Various solvents exhibit the same dissociation if the ratio of relative permittivities equals the ratio cubic roots of concentrations of the electrolytes (Walden's rule).
Higher concentrations Both Kohlrausch's law and the Debye–Hückel–Onsager equation break down as the concentration of the electrolyte increases above a certain value. The reason for this is that as concentration increases the average distance between cation and anion decreases, so that there is more interactions between close ions. Whether this constitutes
ion association is a moot point. However, it has often been assumed that cation and anion interact to form an
ion pair. So an "ion-association" constant can be derived for the association equilibrium between ions A+ and B−: : A+ + B− A+B−with = . Davies describes the results of such calculations in great detail, but states that should not necessarily be thought of as a true
equilibrium constant, rather, the inclusion of an "ion-association" term is useful in extending the range of good agreement between theory and experimental conductivity data. Various attempts have been made to extend Onsager's treatment to more concentrated solutions. The existence of a so-called
conductance minimum in solvents having the
relative permittivity under 60 has proved to be a controversial subject as regards interpretation. Fuoss and Kraus suggested that it is caused by the formation of ion triplets, and this suggestion has received some support recently. Other developments on this topic have been done by
Theodore Shedlovsky, R. M. Fuoss, Fuoss and Shedlovsky, Fuoss and Onsager.
Non-polar liquids Pioneering works Onsager, Fuoss, Kraus in 20th century proved that ionization in nonpolar liquids is possible and it leads to controllable electrolytic conductivity. Onsager created the first theory of this conductivity that takes into account formation of ion pairs predicted by Bjerrum. Ion pairs occur in non-polar liquid because of much stronger electrostatic attraction between cation and anion. This attraction brings them together, but they retain their solvation layer in such new entity called “ion pair”. Solvation layers of ions in non-polar liquids are formed by neutral molecules of
amphiphile solute as described on the page
Ion. Formation of ion-pairs leads to electrolytic conductivity reduction, which was taken into account by Onsager theory.
Mixed solvents systems The limiting equivalent conductivity of solutions based on mixed solvents like water alcohol has minima depending on the nature of alcohol. For methanol the minimum is at 15 molar % water, and for the ethanol at 6 molar % water.
Conductivity versus temperature Generally the conductivity of a solution increases with temperature, as the mobility of the ions increases. For comparison purposes reference values are reported at an agreed temperature, usually 298 K (≈ 25 °C or 77 °F), although occasionally 20 °C (68 °F) is used. So-called "compensated" measurements are made at a convenient temperature but the value reported is a calculated value of the expected value of conductivity of the solution, as if it had been measured at the reference temperature. Basic compensation is normally done by assuming a linear increase of conductivity versus temperature of typically 2% per kelvin. This value is broadly applicable for most salts at
room temperature. Determination of the precise temperature coefficient for a specific solution is simple, and instruments are typically capable of applying the derived coefficient (i.e. other than 2%). Measurements of conductivity \sigma versus temperature can be used to determine the
activation energy E_\text{A}, using the
Arrhenius equation : \sigma = \sigma_0 e^{-E_\text{A}/RT}, where \sigma_0 is the exponential prefactor, the
gas constant, and the
absolute temperature in
kelvins.
Solvent isotopic effect The change in conductivity due to the
isotope effect for deuterated electrolytes is sizable. == Applications ==