Nernst equation and its application

Nernst Equation and Its Application

The Nernst Equation is a fundamental expression in electrochemistry that relates the electrode potential of a half-cell to the standard electrode potential, temperature, and the activities (or concentrations) of the ions involved. It helps in calculating the actual electrode potential under non-standard conditions.

Definition

The Nernst Equation provides a quantitative relationship between the electrode potential and the concentration of ions at a given temperature. It is essential for understanding the behavior of electrochemical cells in real-world conditions.

Mathematical Form of Nernst Equation

For a general redox reaction:

aA + bB ⇌ cC + dD

The Nernst equation is given by:

\(E=E^{0}-\frac{0.0591}{n}\log{\Big( \frac{[C]^{c}[D]^{d}}{[A]^{a}[B]^{b}}\Big)}\) at 25°C

• E: Electrode potential under non-standard conditions
• E°: Standard electrode potential
• n: Number of electrons involved in the redox reaction
• [ ]: Concentrations of the species

For a Half-Cell Reaction

For a half-cell reaction like:

Mn⁺ + ne⁻ ⇌ M

The Nernst equation becomes:

E = E° - (0.0591 / n) log [Mn⁺] at 25°C

Applications of the Nernst Equation

• 1. Determining Cell Potential: Helps calculate the electromotive force (EMF) of an electrochemical cell when conditions differ from the standard state.
• 2. Determining Equilibrium Constant: By setting E = 0 (at equilibrium), the Nernst equation can be rearranged to derive the equilibrium constant.
• 3. pH Determination: Nernst equation is applied in pH meters to determine the hydrogen ion concentration.
• 4. Predicting Redox Reactions: Helps in predicting the spontaneity and direction of redox reactions.
• 5. Concentration Cells: Used in cells where electrode potentials vary due to concentration differences only.

Example

For the half-cell: Cu²⁺ + 2e⁻ ⇌ Cu, E° = +0.34 V

If [Cu²⁺] = 0.01 M, then:

E = 0.34 - (0.0591 / 2) log(1 / 0.01) = 0.34 - 0.0591 = 0.2809 V