Derive Nernst's equation for emf of a cell.

Answer 1

Nernst's equation is given by

Ecell = E°cell - (RT/nF) * ln(Q)

Where:
Ecell = cell potential
E°cell = standard cell potential
R = gas constant
T = temperature in Kelvin
n = number of electrons transferred in the balanced redox reaction
F = Faraday constant
Q = reaction quotient

The equation can be derived from the Gibbs free energy equation:

ΔG = ΔG° + RT ln(Q)

Where:
ΔG = change in Gibbs free energy
ΔG° = standard Gibbs free energy change
R = gas constant
T = temperature in Kelvin

Using the equation ΔG = -nFEcell (where Ecell is the cell potential), we can substitute this into the equation above to get:

-nFEcell = -nFE°cell + RT ln(Q)

Dividing by -nF, we get:

Ecell = E°cell - (RT/nF) ln(Q)

This is Nernst's equation for calculating the cell potential of a cell under non-standard conditions.