Question

Write and derive Nernst equation.

Hint:

The Nernst equation allows us to calculate the potential of an electrochemical cell when concentrations of the reactants and products are not at standard conditions.

Answer 1

Step 1: Nernst Equation.
The Nernst equation relates the cell potential to the concentration of the ions involved in the reaction. It is given by: \[ E = E^0 - \frac{0.0592}{n} \log Q \] where: - \( E \) is the cell potential under non-standard conditions, - \( E^0 \) is the standard cell potential, - \( n \) is the number of electrons transferred in the reaction, - \( Q \) is the reaction quotient (the ratio of concentrations of products to reactants).

Step 2: Derivation of the Nernst Equation.
The Nernst equation can be derived from the Gibbs free energy equation. The change in Gibbs free energy is related to the cell potential as: \[ \Delta G = -nFE \] where \( F \) is the Faraday constant, \( n \) is the number of moles of electrons, and \( E \) is the cell potential. At standard conditions, \( \Delta G^0 = -nFE^0 \), where \( E^0 \) is the standard electrode potential. The relationship between \( \Delta G \) and the reaction quotient \( Q \) is given by: \[ \Delta G = \Delta G^0 + RT \ln Q \] Substituting the expressions for \( \Delta G \) and \( \Delta G^0 \) into the equation, we get: \[ -nFE = -nFE^0 + RT \ln Q \] Rearranging the terms, we obtain the Nernst equation: \[ E = E^0 - \frac{RT}{nF} \ln Q \] At room temperature (298 K), \( \frac{RT}{F} \approx 0.0592 \) V, and the Nernst equation becomes: \[ E = E^0 - \frac{0.0592}{n} \log Q \]

Step 3: Conclusion.
The Nernst equation is essential for calculating the electrode potential of a cell under non-standard conditions.