Page:Elementary Text-book of Physics (Anthony, 1897).djvu/345

§ 285] it has not yet come into common use, and we will therefore retain the term dissociation.

We have already seen that a current in an electrolyte may be considered as the transfer of charges on the moving ions. If the ions in solution be dissociated from each other, and if the effect of the electromotive force in the circuit be merely directive, it is plain that the quantity of current transferred will depend on the relative velocity with which the ions move past each other in the solution as well as on their number. Starting with this conception, we will show that the conductivity of an electrolyte is proportional to the sum of the velocities of its ions. The discovery of this fact by Kohlrausch laid the foundation for the dissociation theory.

Let us suppose a series of electrolytic cells, e'ach one of which is a cubical box with sides of unit length, and so arranged that a current passes in them between two opposite faces which serve as electrodes. The column of the electrolyte between the electrodes is then one centimetre long and has a cross-section of one square centimetre. Let the electrolytes used in these cells be prepared by dissolving in equal volumes of the same solvent masses of the substances to be decomposed which are proportional to the sums of the ionic weights of their constituent ions (§ 280). Equal volumes of these solutions will then contain the same number of univalent ions.

If a current be sent through the series of cells containing these solutions, the same number of univalent, ions will be liberated in each. The difference of potential between the terminals of the cells will be in general different for each of them. We have from Ohm's law the relation $$I = k(V_{1} - V_{2}),$$ where the current $$I$$ is the same for each cell and the difference of potential $$V_{1} - V_{2}$$ and the conductivity $$k$$ (§ 275) different for the different cells. Now consider a cross-section in one of the cells parallel with the electrodes; let $$u$$ and $$v$$ represent the velocities of the ions evolved in this cell. Let $$2M$$ represent the number of univalent ions in the cell, and let $$c$$ represent the ionic charge. Now the relative velocity of the ions which pass through the cross-section taken in the cell is $$u + v;$$ the