An electrolytic solution contains three varieties of particles, positive ions or cations, negative ions or anions, and undissociated neutral molecules. The molecular concentration of such a solution, with the corresponding constants, depends on the total number of these particles, i.e. the sum of the ions and the undissociated neutral molecules. We may indicate an ion by placing above it the sign of its electrical charge, one sign for each valency. Thus Na+ and Cl- indicate the two ions of a salt solution; Cu++ and SO4-- the two ions of a solution of sulphate of copper. A point is sometimes substituted for the + sign, and a comma for the - sign. Thus Na. and Cl,; Cu.. and SO4,,.
My friend Dr. Lewis Jones has given a very vivid picture of the processes which go on in an electrolytic solution when an electric current is passing. He compares an electrolytic cell to a ballroom, in which are gyrating a number of dancing couples, representing the neutral molecules, and a number of isolated ladies and gentlemen representing the anions and cations respectively. If we suppose a mirror at one end of the ballroom and a buffet at the other, the ladies will gradually accumulate around the mirror, and the gentlemen around the buffet. Moreover, the dancing couples will gradually be dissociated in order to follow this movement.
Degree of Dissociation.—The degree of dissociation is the fraction of the molecules in the solution which have undergone dissociation. Let n be the total number of molecules of the solute, and n″ the number of dissociated molecules. Then n″ / n = a will represent the degree of dissociation. Let k be the number of ions into which each molecule is split. Then a = n″k / nk, i.e. the degree of dissociation is the ratio of the number of ions actually present in a solution to the number which would be present if all the molecules of the solute were dissociated.
Let n′ be the total number of particles present in a solution
containing n molecules, each of which is composed of k ions. Then if a is the degree of dissociation,
n′ = n - an + ank,
n′ = n[1 + a (k - 1)],
n′ / n = 1 + a (k - 1) = i.
We thus obtain i the coefficient of dissociation, in terms of the degree of dissociation a and the number of ions in each molecule k.
If there is no dissociation, i.e. if a = 0, then n′ = n, and i = 1. If all the molecules are dissociated, a = 1, and i = k.