Ion transport number

Ion transport number, also known as the transference number or ionic transference number, is a dimensionless quantity in electrochemistry that describes the fraction of the total current carried in an electrolytic solution by a given ion species. The concept is crucial for understanding the behavior of ions in electrolytes and is fundamental in the study of electrochemical cells, batteries, and fuel cells.

Definition

The ion transport number, denoted as \(t_+\) for cations and \(t_-\) for anions, is defined for each ion species based on the equation:

\[t_i = \frac{I_i}{I_{\text{total}}}\]

where:

• \(t_i\) is the transport number of ion \(i\),
• \(I_i\) is the current carried by ion \(i\),
• \(I_{\text{total}}\) is the total current flowing through the electrolyte.

The sum of the transport numbers of all ions in the solution equals 1:

\[\sum t_i = 1\]

Measurement

The transport number can be measured using several methods, including the Hittorf method, the moving boundary method, and the electrolytic conductivity method. Each technique has its advantages and limitations, and the choice of method depends on the specific characteristics of the electrolyte and the ions involved.

Hittorf Method

The Hittorf method involves measuring the concentration changes of ions near the electrodes in an electrolytic cell after passing a known quantity of electricity. This method is particularly useful for aqueous solutions.

Moving Boundary Method

The moving boundary method, also known as the Landsberg method, involves observing the movement of the boundary between two electrolytes in a tube. This method is suitable for electrolytes with sharply different ionic compositions.

Electrolytic Conductivity Method

The electrolytic conductivity method calculates transport numbers based on the changes in the electrolyte's conductivity as a function of concentration. This method is applicable to a wide range of electrolytes.

Importance in Electrochemistry

Ion transport numbers are essential for understanding and predicting the behavior of electrochemical systems. They influence the efficiency and performance of devices such as batteries and fuel cells by determining how ions move through the electrolyte under an applied electric field. In battery technology, for example, a higher transport number for the desired ion species can lead to more efficient charge and discharge cycles.

Applications

• In battery technology, optimizing the ion transport number of the electrolyte can improve energy density and battery life.
• In fuel cell technology, understanding ion transport numbers helps in the design of more efficient membrane materials.
• In electroplating and electrorefining, controlling the transport numbers of ions can lead to more uniform deposition of metals.

See Also

• Electrolyte
• Electrochemical cell
• Conductivity (electrolytic)
• Electrode potential