Conductance and conductivity

The fundamental measurement used to study the motion of ions is that of the electrical resistance, R, of the solution. The conductance, G, of a solution is the inverse of its resistance R: G = 1/R. As resistance is expressed in ohms, Ω, the conductance of a sample is expressed in Ω−1. The reciprocal ohm used to be called the mho, but its official designation is now the siemens, S, and 1 S = 1 Ω⁻¹= 1 C V⁻¹ s⁻¹. The conductance of a sample decreases with its length l and increases with its cross-sectional area A. We therefore write

G=

where κis the conductivity. With the conductance in siemens and the dimensions in metres, it follows that the SI units of κ are siemens per metre (S m⁻¹). The conductivity of a solution depends on the number of ions present, and it is nor mal to introduce the molar conductivity, Λ_m, which is defined as

Λm=

where c is the molar concentration of the added electrolyte. The SI unit of molar conductivity is siemens metre-squared per mole (S m² mol⁻¹), and typical values are about 10 mS m² mol⁻¹ (where 1 mS = 10⁻³ S).

The molar conductivity is found to vary with the concentration. One reason for this variation is that the number of ions in the solution might not be proportional to the concentration of the electrolyte. For instance, the concentration of ions in a solution of a weak acid depends on the concentration of the acid in a complicated way, and doubling the concentration of the acid added does not double the number of ions. Secondly, because ions interact strongly with one another, the conductivity of a solution is not exactly proportional to the number of ions present. 3 The concentration dependence of molar conductivities indicates that there are two classes of electrolyte. The characteristic of a strong electrolyte is that its molar conductivity depends only slightly on the molar concentration (and in general decreases slightly as the concentration is increased, Fig. 21.14). The characteristic of a weak electrolyte is that its molar conductivity is normal at concentrations close to zero, but falls sharply to low values as the concentration increases. The classification depends on the solvent employed as well as the solute: lithium chloride, for example, is a strong electrolyte in water but a weak electrolyte in propanone.

Fig. 21.14 The concentration dependence of the molar conductivities of (a) a typical strong electrolyte (aqueous potassium chloride) and (b) a typical weak electrolyte (aqueous acetic acid).

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مواضيع ذات صلة

Strong electrolytes

Superconductors

Induced magnetic moments

Magnetic susceptibility

Nonlinear optical phenomena

Light emission by solid-state lasers and light-emitting diodes

Light absorption by molecular solids, metallic conductors, and semiconductors

Insulators and semiconductors

The occupation of orbitals

The formation of bands

Molecular solids and covalent networks

Energetics