Hittorf studied the concentration changes around the electrodes as a result of the passage of current through an electrolyte. He made a law, which is known as Hittorf law for the migration of ions. This law states that, “the loss of concentration around any electrode is proportional to the speed of the ion moving away from it’.
Let us consider an electrolytic cell containing equal number of positive and negative ions. The cell is divided into three compartments namely Anode, Central and Cathode by two porous diagrams AA’ and BB’. These diagrams can allow the ions to pass through them. Let the number of equivalents of positive and negative ions present in each compartment before electrolysis is five as shown row 1 of the diagram.
Let the cations and anions move with the same speed. If four Faraday of electricity are passed through the cell, four equivalents of positive ions in the cathode compartment will accept electrons from the cathode and deposit. Similarly four equivalents of negative ions in the anode compartment will lose electrons to the anode and deposit. The result of these changes is shown by row II.
Since the cations and anions have same speed, each mast carry one half of the total current. That is the cations must transport two Faraday of electricity from left to right and the anions carry two Faraday from right to left. As a result, the concentration in the central compartment remains unchanged while in the cathode and anode compartments, it has decreased by two equivalents as shown by row III.
Let the cations and anions move with different speed. Let the cations move three times faster than the anions and again four Faraday of electricity are passed through the cell. Now the cations would carry three times more current relative to the anions. Thus three equivalents of cat ions must migrate from anode to central and from central to cathode compartment. At the same time, only one equivalent of anions leaves the cathode compartment.
The result of these changes is shown by row (V). Considering these migrations of ions, it appears that the concentration in the central compartment does not change by the passage of current. But the concentration in the cathode and anode compartments has changed to different extent. The concentration in the Cathode compartment has fallen by one equivalent while in the anode compartment; it has fallen to three equivalents. From these observations it appears that the amount of electrolyte lost from each compartment is proportional to the speed of the ion migration away from it. Thus
U+/U- = t+/t
Thus the number of equivalents of electrolyte lost from any compartment is directly proportional to the transport number of the ion moving away from that compartment. This is known as the Hittorf a rule.