n(u + v) = ηC = ηne(u + v),
and it follows that the charge, e, on 1 gram-equivalent of each kind of ion is equal to 1/η. We know that Ohm’s Law holds good for electrolytes, so that the current C is also given by k·dP/dx, where k denotes the conductivity of the solution, and dP/dx the potential gradient, i.e. the change in potential per unit length along the lines of current flow. Thus
| n | (u + v) = kdP/dx; |
| η |
therefore
| u + v = η | k | dP | . | |
| n | dx |
Now η is 1.036×10-4, and the concentration of a solution is usually expressed in terms of the number, m, of gram-equivalents per litre instead of per cubic centimetre. Therefore
| u + v = 1.036×10-1 | k | dP | . | |
| m | dx |
When the potential gradient is one volt (108 C.G.S. units) per centimetre this becomes
u + v = 1.036×10-7×k/m.
Thus by measuring the value of k/m, which is known as the equivalent conductivity of the solution, we can find u + v, the velocity of the ions relative to each other. For instance, the equivalent conductivity of a solution of potassium chloride containing one-tenth of a gram-equivalent per litre is 1119×10-13 C.G.S. units at 18° C. Therefore