Transport Number
The science of ionic current distribution in electrolytes.
1. What is a Transport Number?
The Transport Number (also known as the Transference Number or Hittorf’s Number) represents the fraction of the total electric current carried by a specific ion in an electrolyte solution.
Since electricity in an electrolyte is carried by the simultaneous movement of both cations (positive) and anions (negative), each contributes a specific percentage to the total conductivity.
2. Mathematical Relationship
The transport number is determined by the ionic mobility (speed) of the ions. Faster ions carry more current.
The Golden Rule: The sum of transport numbers for all ions in a solution must always equal 1.
3. Factors Influencing the Number
| Factor | Effect on Transport Number |
|---|---|
| Temperature | Rising temperatures bring $t_+$ and $t_-$ closer to 0.5 as speeds equalize. |
| Concentration | High concentrations can lead to complex ions, sometimes resulting in negative values. |
| Nature of Co-ions | The speed of the partner ion affects the percentage share of the current. |
| Hydration | Bulkier, highly hydrated ions move slower and have lower transport numbers. |
4. Experimental Determination
How do we measure these values in the lab? There are two primary methods:
A. Hittorf’s Method
Based on tracking concentration changes near the electrodes (anode and cathode compartments) during electrolysis.
B. Moving Boundary Method
Measures the speed at which a visible boundary between two different electrolyte solutions moves under an electric field. This is generally considered more accurate.
5. Solved Problem Example
Scenario: In a Hittorf cell, a silver nitrate ($AgNO_3$) solution is electrolysed…
Step 1: Identify Concentration Fall
Initial mass ($0.224g$) – Final mass ($0.198g$) = 0.026g (Loss at Anode)
Step 2: Calculate $t_{Ag^+}$ (Cation)
$$t_+ = \frac{\text{Loss at Anode}}{\text{Total Silver in Coulometer}} = \frac{0.026}{0.040} = \mathbf{0.65}$$
Step 3: Calculate $t_{NO_3^-}$ (Anion)
$$t_- = 1 – 0.65 = \mathbf{0.35}$$
Final Answer: The transport numbers for $Ag^+$ and $NO_3^-$ are 0.65 and 0.35 respectively.
