The transport number (or transference number) of an ionic species in an electrolyte solution is not an absolute constant value. It depends on several intrinsic variables, such as the environment, speed, and specific combination of ions present. Fundamentally, the transport number of a given cation is bound to the identity and mobility of its counter-anion, and vice versa.
1. Effect of Concentration
The concentration of the electrolytic solution affects ionic migration rates by modifying interionic forces. In highly dilute solutions, the mathematical relationship showing the variation of the transport number with concentration follows a linear trend:
In this expression, t and t₀ represent the transport numbers of the selected ion at concentration C and at infinite dilution respectively, while A acts as a constant parameter. Generally, transport values exhibit minimal deviations across mild concentration ranges unless complexation chemistry takes place.
For example, the transport number of Cd2+ in a cadmium iodide (CdI2) solution drops sharply toward zero as concentration increases, eventually crossing into negative values at high concentrations. This phenomenon is caused by coordination complexation equilibrium points:
CdI2 + 2I− ⇌ [CdI4]2−
As complexation progresses, free cadmium cations are converted into bulky [CdI4]2− complex anions, which migrate in the opposite direction toward the anode. Consequently, the depletion zone around the anode behaves unexpectedly. If the high-mobility [CdI4]2− ions migrate away from the cathode space faster than free Cd2+ migrates toward it, the mass analysis shows an accumulation rather than a loss around the anode. This behavior produces a negative net calculated transport value at elevated concentration ranges.
2. Effect of Temperature
An increase in temperature reduces the intensity of interionic attractions and breaks up solvent structures. This thermal dispersion brings different transport numbers closer to an equal split of 0.5 at elevated temperatures. This indicates that as thermal kinetic energy overrides weak chemical differences, counter-ions approach uniform migration velocities.
3. Effect of Hydration
The degree of ionic hydration alters the effective hydrodynamic radius of an ion, affecting its migration velocity. Ions with a high charge density (high ionic potential) bind strongly to polar water molecules. For instance, because the Li+ cation has a smaller unhydrated ionic radius than Na+, its electric field is more concentrated, making it much more heavily hydrated in solution.
This extensive hydration shell makes the moving hydrodynamic radius of hydrated Li+ larger than that of a hydrated Na+ ion. Consequently, Na+ travels faster through an aqueous medium than Li+, resulting in a lower transport fraction for the lithium ion compared to the sodium ion under equivalent conditions.