Transport Number

The transport number is the fraction of the total current carried by an ion in an electrolyte solution. It is defined as the ratio of the current carried by a specific ion to the total current flowing through the solution. The transport number, t, is central to understanding ionic mobility, which describes how fast an ion moves under the influence of an electric field. This link connects the physical behavior of ions in solution to the chemical processes that occur during electrochemical reactions. Several methods are used to determine transport numbers, most commonly Hittorf’s method and the moving boundary method.

Hittorf’s method is based on measuring concentration changes that occur near the electrodes when an electric potential is applied. The electrolyte solution is divided into anodic, central, and cathodic compartments using a suitable vessel. When a potential difference is applied, cations move toward the cathode and anions toward the anode, producing measurable concentration changes near each electrode. Separating the solution into compartments allows these changes to be measured independently, while the central compartment serves as a reference region that remains relatively unaffected by electrode reactions. The extent of concentration change near the electrodes reflects the relative mobilities of the ions. The ratio of cation to anion mobility equals the ratio of the concentration decrease near the anode to that near the cathode. Accordingly, the transport number of cations is defined as the concentration fall around the anode divided by the total fall around both electrodes. When concentrations are expressed in gram equivalents, the cation transport number equals the gram equivalents lost from the anodic compartment divided by the total loss from both compartments. This value corresponds to the gram equivalents deposited at the electrodes, which can also be determined using a copper coulometer. The anion transport number is obtained by subtracting the cation value from unity.

An alternative approach is the moving boundary method, which determines transport numbers by tracking the movement of a sharp boundary between two electrolytes under an applied electric field. One electrolyte is the principal electrolyte containing the ion of interest, while the other is an indicator electrolyte. For example, to determine the transport number of H⁺ ions in HCl, HCl serves as the principal electrolyte and CdCl₂ as the indicator. CdCl₂ is selected because its cation has lower mobility than H⁺ and shares the same anion. The solutions are arranged so that HCl lies above CdCl₂. When a small current is applied, ion migration causes the boundary between the two electrolytes to move. By measuring the displacement of this boundary over time, the transport number of the ion can be calculated.