CONDUCTIVITY OF SOLUTIONS Knowledge of the conductivity of salt solutions has been ad vanced by several observers since Faraday discovered his laws of electrolysis. A gram molecule, or mol, of a salt is a quantity of the salt equal to its molecular weight in grams. Consider a solution containing ni gram molecules of a salt per cu.cm. When a current is passed through the solution, part of the salt, the anion, is de posited on the anode, and part on the negative electrode, or cathode. The quantity of electricity required to deposit one gram molecule of the anion, or the cation, is proportional to the chemical valency of the ion. Let F denote the amount of electricity re quired to deposit one gram molecule, or mol, of a univalent ion, so that the amount of electricity associated with one mol of an ion of valency V is VF.
The amount of electricity required to electrolyze one gram molecule of a salt is always some multiple, N, of F, depending on the valency of the ions. N may be called the valency of the salt, and the molecular weight of the salt divided by N is called a gram equivalent of the salt. In the solution containing m mols of salt per cu.cm., the charge associated with the anion is —mNF, and that with the cation is -}-mNF. When a current is passed through the solution, the anion moves towards the anode, and the cation towards the cathode. The velocities are proportional to the electric field strength, X, so that, if u is the velocity of the anion, due to unit field, and v that of the cation, then i=XmNF(u+v), where i denotes the current density. If M denotes the number of gram equivalents of the salt per cu.cm., M=mN, so that i=XMF(u+v). The velocities u and v here are the average velocities for all the anion and cation molecules ; if at any instant some are not charged, and so not moving, the velocities of those which are charged will be greater than u and v.
If the solution is contained in two vessels connected by a tube and the anode is put in one and the cathode in the other, then, when a current is passed, the relative amounts of the anion and cation which pass through the tube will be proportional to the velocities a and v. These amounts can be determined by analysing the solutions in the two vessels, so that the ratio u/v can be found. In this way Hittorf, during the years 1853-1859, determined the ratio u/v for many salts.
In 1876-77, Kohlrausch (1840-1910) determined the specific conductivities of a great many salt solutions. He found that if m denotes the mols per cu.cm. in a solution of any salt, and k its conductivity, then, as m is diminished, the ratio k/m increases but becomes constant for dilute solutions. The conductivity is equal to the current density i divided by the electric intensity, X, and so is equal to mNF(u+v). For dilute solutions of different salts, Kohlrausch found that the values of k/m, or NF(u+v), could be expressed as the sums of two numbers, one for the anion and one for the cation. Since N and F are known, Kohlrausch's meas urements enabled u--1--v to be calculated, and so, with Hittorf's values of u/v, both u and v were determined.
In 1887, Arrhenius suggested that in dilute salt solutions the salt is completely dissociated into ions. For example, in a dilute solution of sodium chloride, NaC1, there are no molecules of NaC1 but only positively charged sodium atoms, Na+, and negatively charged chlorine atoms, C1-. These charged atoms, or ions as they are now called, have chemical properties quite dif ferent from those of the uncharged substances. For example the Na+ ions do not act chemically on water as metallic sodium does. By means of this theory Arrhenius explained the results of Hittorf and Kohlrausch, and his theory has since been confirmed by many other experimental investigations. (See ELECTROLYSIS.)