The transport of electric charges, under electric potential differences, by particles of atomic or larger size. This phenomenon is distinguished from metallic conductance, which is due to the movement of electrons. The charged particles that carry the electricity are called ions.
Positively charged ions are termed cations; the sodium ion, Na+, is an example. The negatively charged chloride ion, Cl−, is typical of anions. The negative charges are identical with those of electrons or integral multiples thereof. The unit positive charges have the same magnitude as those of electrons but are of opposite sign. Colloidal particles, which may have relatively large weights, may be ions, and may carry many positive or negative charges. Electrolytic conductors may be solids, liquids, or gases. Semiconductors have properties that are intermediate between the metallic conductors and insulators.
Conductances are usually reported as specific conductances κ, which are the reciprocals of the resistances of cubes of the materials, 1 cm in each dimension, placed between electrodes 1 cm square, on opposite sides. These units are sometimes called mhos, that is, ohms spelled backward. Conductances of solutions are usually measured by Friedrich Kohlrausch's method, in which a Wheatstone bridge is employed. Such a bridge is shown diagrammatically in Fig. 1. The resistances R3 and R4 (usually of the same value) form two arms of the bridge. Resistance R2 is adjustable, and the remaining arm is the cell holding the electrolytic conductor, or as is usually stated, solution of electrolyte. Direct current and the usual galvanometers cannot be used because of an apparent failure of Ohm's law. Passage of direct current produces chemical reactions and a back electromotive force (emf) is generated by the galvanic action of the products. By using an alternating current, the electrochemical reactions occurring when the current is briefly passed in one direction may be reversed when the direction of the current is changed. When a small alternating-current input signal is used, practically all the electric charge passed during each half cycle is stored in the electric double layer, which acts as a capacitor. The electrodes are usually made of platinum and are platinized, that is, coated with finely divided platinum. The surface area, and hence the electrode capacitance, is thereby greatly increased. By making measurements at several frequencies and extrapolating to infinite frequency, the effect of electrode reactions can be eliminated. For less exact measurements, a fixed frequency of 60–1000 Hz is commonly used.
To determine the conductance C, that is, the reciprocal resistance 1/R of the cell of Fig. 1, the resistance R2 of the bridge is adjusted until a minimum of sound is heard in the telephone.
Greater sensitivity may be obtained by electronic amplification of the off-balance signal and by using an oscilloscope to detect the point of balance. When the bridge is in balance, the conductance is given by the relation C = R4/R2 R3. From this the specific conductance κ may be obtained from the equation κ = KC, in which K is the cell constant. Occasionally, this constant can be computed from the dimensions of the cell. Usually, however, it is determined by using a solution whose κ value is accurately known from measurements in such a cell, or by comparison with the specific conductance of mercury.
For precision work, care must be taken to avoid errors due to electrical reactances. This has been done in specially designed bridges. A typical, properly designed conductance cell is shown in Fig. 2. The cell is filled with solution through the center tubes. Electrical contact is made with the electrodes by platinum wires sealed through the glass wall. These connect the mercury in the outside tubes, which are widely spread to avoid errors due to electrical capacity.
Although many substances and mixtures show electrolytic conductance, the greater part of the research on the subject has been on aqueous solutions of salts, acids, and bases. There have been considerable data accumulated for solutions of such electrolytes in nonaqueous solvents, such as alcohols. The data are usually given in terms of equivalent conductance Λ, which is defined by Eq. (1),
in which κ is the specific conductance and c is the concentration in equivalents per liter. Values of Λ change with the concentration and, in general, increase as the solutions measured are made more dilute, that is, as c is decreased. A plot of values of the equivalent conductance λ against for some typical electrolytes is shown in Fig. 3. Svante Arrhenius, who was the first to assume that electrolytic conductance is due to freely moving charged ions, explained the decrease of Λ with increasing c by assuming that the number of ionic carriers gets smaller as the concentration increases, and he computed a degree of dissociation α by formula (2).
The term Λ0 is obtained by determining Λ at a series of low concentrations and extrapolating to a limiting value, termed the equivalent conductance at infinite dilution. Though Eq. (2) has been shown by later work to give nearly the right values of α for certain poorly conducting solutions, it is now considered to be much in error for the so-called strong electrolytes. These include most salts, such as potassium chloride, KCl, and sodium sulfate, Na2SO4, and inorganic acids and bases, such as hydrochloric acid, HCl, and sodium hydroxide, NaOH. For an electrolyte which yields two types of ion, it can be shown that Eq. (3) holds,
in which F is the faraday and U+ and U− are the mobilities, or speeds, under unit potential difference of the positive and negative ions, respectively. For Eq. (2) to hold, these mobilities must be constant from the equivalent concentration c at which Λ is measured to infinite dilution.
Since the advent of the Debye-Hückel theory of interionic attractions, strong electrolytes have been considered to be completely dissociated, that is, the term α of Eq. (3) is equal to unity for these substances. The decreases observed in the values of the equivalent conductances Λ, with increases in concentration, are assumed to be due to reductions in the values of the ionic mobilities U+ and U−. According to the theory of P. Debye and E. Hückel, the ion possesses an ionic atmosphere distributed with radial symmetry around the ion as center. This is due to the fact that interionic attractions and repulsions, together with thermal vibrations, tend to produce a slight preponderance of negative ions around a positive ion, and vice versa. The presence of this atmosphere leads to the lowering of ionic mobilities with increasing ion concentrations. The adaptation of the Debye-Hückel theory for conducting solutions is due to Lars Onsager. His equation for very dilute uni-univalent electrolytes, such as sodium chloride, is shown in Eq. (4), in which θ and σ are given for uni-univalent electrolytes by Eqs. (5) and (6),
in which D is the dielectric constant at the absolute temperature T and η is the viscosity.
Equation (4) yields accurate values of the data for strong electrolytes up to concentrations of about 0.001 M, above which there are small deviations. Modifications of Eq. (4) for solutions of salts of higher valence types, such as calcium chloride, CaCl2, and lanthanum chloride, LaCl3, are available and have also been found to agree with the data for dilute solutions.
Onsager, in his derivation of Eq. (4), treated the ions as point charges. Later Raymond Fuoss and Onsager extended the theory to include the radii of the ions and also the effects of higher concentrations. The ion sizes obtained from conductance data agree closely with those calculated from activity measurements. See also: Activity (thermodynamics)
Equation (4), or its empirical and theoretical extensions, can be used to obtain values of Λ0 from the data on equivalent conductances of dilute solutions. Some typical figures for limiting equivalent conductances Λ0 of typical strong electrolytes in aqueous solution at 25°C (77°F) are listed below.
The fraction of the current carried by a given type of ion is known as the transference number, t, which depends on the relative mobilities of the ions. This relation is shown in Eqs. (7).
The ionic mobilities, and therefore the transference numbers, vary somewhat with concentration, but the limiting equivalent conductances Λ0 for various electrolytes can be accurately represented as the sum of the limiting ionic conductances. Thus, for potassium chloride, Λ0,KCl = λ0,K + + λ0,Cl − , and the value of λ0,Cl − is the same whether it is derived from measurements on HCl, NaCl, or KCl solutions. This additive relation is known as Kohlrausch's law of the independent mobility of ions. However, it is necessary to obtain the value of λ0 for at least one ion constituent independently in order to establish the ion conductances of the other ions. The relation used is shown in Eqs. (8),
in which λ0 is the limiting equivalent conductance of an electrolyte and t0+ and t0− are the limiting transference numbers of the positive and negative ion constituents, respectively.
The same value of λ0,Cl − , within 0.02%, is obtained from precision conductance and transference measurements on solutions of hydrogen, lithium, sodium, and potassium chlorides. Values of the limiting ionic conductance at 25°C (77°F) are given below for some ions.
In addition to the study of water solutions of electrolytes, considerable study has been given to electrolytes in nonaqueous and mixed solvents. In general, the same principles as those outlined above apply to the interpretation of the results. However, fewer of the electrolytes are completely dissociated, and the degrees of dissociation of the weaker acids and bases are lower. This is due to the fact that, in general, the dielectric constants of nonaqueous solvents are smaller than those of water, so that the attractions between positive and negative ions are greater.
It will be observed that in this article discussion is confined to quite dilute solutions of electrolytes. For concentrated solutions few generalizations of any value can be given.
Molten salts exhibit a wide range of conductivities, depending upon their structures. Salts of alkali and alkaline earth metals usually are largely ionic in character and are highly conductive in the molten state, whereas heavy metal salts may be essentially covalent and exhibit little or no conductivity. Thus the conductivities of liquid arsenic chloride (AsCl3) and bismuth chloride (BiCl3) near their melting points are approximately 10−6 and 0.44 ohm−1 cm−1, respectively, reflecting the more ionic structure of BiCl3.
If, instead of using quite low potentials in the measurement of electrolytic conductances, voltages of the order of 100,000 are employed, the conductances observed are no longer constant but tend to increase with the potential used. Under these conditions Ohm's law evidently is not valid. This increase of conductance with high potentials is called the Wien effect. This effect is in accord with the interionic attraction theory. When the velocity of the ions becomes sufficiently great, the ion atmospheres do not have time to form to their full extent, so that both the electrophoretic and time of relaxation effects exert less influence on the conductance. However, a large Wien effect is also found for weak acids and bases. It would appear that the high potentials produce, temporarily, additional ionization of these substances. This explanation has been proposed and discussed theoretically by Onsager. If very high frequencies are used in the measurements, an increase in the conductance, termed the Debye-Falkenhagen effect, is observed. This can also be explained by the interionic attraction theory.
Electrical conduction in solids can range from purely electronic (in metals and semiconductors) to purely ionic (in solids that are electronic insulators but have ions with appreciable mobilities). Examples of purely ionic solid conductors are silver iodide and silver sulfide, in which all of the current is carried by silver ions. In other cases, such as metallic oxides, both ions may serve as charge carriers. Ionic conduction must lead to transport of matter and to chemical reactions at the electrodes, whereas electronic conduction leads only to a transfer of charge. See also: Electrochemistry; Electromotive force (cells)