Transport Number

Transport number is the fraction of total current carried by a specific ion in an electrolyte solution. It represents the ratio of current carried by that ion to the total current flowing through the solution. Understanding transport numbers is essential for predicting ionic mobility and how fast ions move under an electric field, directly connecting to electrochemical reaction behavior.

Hittorf's method divides an electrolyte solution into anodic, central, and cathodic compartments. When potential is applied, cations migrate toward the cathode and anions toward the anode, causing measurable concentration changes near each electrode. The central compartment serves as a reference region unaffected by electrode reactions, allowing independent measurement of concentration changes that reflect ion mobility ratios.

The cation-to-anion mobility ratio equals the concentration fall around the anode to that around the cathode. The cation transport number is defined as the concentration fall around the anode divided by the total fall around both electrodes. This relationship allows researchers to calculate transport numbers from measured concentration changes in gram equivalents.

The moving boundary method tracks the movement of a sharp boundary between a principal electrolyte and an indicator electrolyte under an applied electric field. For example, to measure H⁺ transport in HCl, CdCl₂ serves as the indicator because its cation has lower mobility than H⁺ and shares the same anion. By measuring boundary displacement over time, the transport number can be calculated mathematically.

The central compartment in Hittorf's method serves as a reference region that remains relatively unaffected by electrode reactions. This allows researchers to measure concentration changes in the anodic and cathodic compartments independently and accurately. The central compartment's stability ensures that observed concentration changes reflect only ion migration caused by the applied potential.

Anion transport number is obtained by subtracting the cation transport number from unity. Since cations and anions together carry all the current in an electrolyte solution, their transport numbers must sum to one. This relationship provides a simple way to determine anion transport once cation transport is measured or calculated.

Ionic mobility describes how fast an ion moves under an electric field influence. The extent of concentration change near electrodes in Hittorf's method directly reflects the relative mobilities of cations and anions. Transport numbers quantify this mobility difference, connecting the physical behavior of ions in solution to the electrical transport properties measured during electrochemical reactions.