Nernst Reaction Quotient and Energy

Worked example: Q = 10, E0 = 0.05, n = 1, T = 298.15K

Using the constants R = 8.31446261815324 J/(mol K) and F = 96485.33212331001 C/mol, we can calculate the cell potential.

1. Thermal voltage per electron: (R * T) / F = (8.31446261815324 * 298.15) / 96485.33212331001 ≈ 0.025692579121085843 V.
2. Since ln(10) ≈ 2.302585, the Nernst term is roughly 0.0256925 * 2.302585 ≈ 0.059159 V.
3. Cell potential E = E0 - (RT/nF)lnQ = 0.05 - 0.059159 = -0.009159349684782325 V.
4. Reaction Gibbs energy ΔG = -nFE = -1 * 96485.33212331001 * -0.009159349684782325 = 883.7428963697575 J/mol.

Reproduce the calculation in the module

Open the Nernst Reaction Quotient and Energy experiment. Its controls let you adjust standard potential, temperature, electrons, and reaction quotient.

1. Set Standard potential V to 0.05, Temperature K to 298.15, Electrons to 1, and Reaction quotient to 10. Check that the Cell potential V becomes approximately -0.009.
2. Change Reaction quotient to 1. Since ln(1) = 0, the Nernst term vanishes and E becomes equal to E0 = 0.05 V.
3. Change Electrons to 2 with Q=10. This halves the coefficient of the Nernst term, reducing the voltage penalty and giving a higher E = 0.02042032515760884 V compared to n=1.

Limitations

The calculation assumes standard potential is constant across temperatures, which is not true for real cells. Activities are not strictly equivalent to concentrations, especially at higher ionic strengths, which would require activity coefficients. The quotient Q must be strictly positive; the Nernst equation is undefined for Q=0 or negative values, and it does not predict kinetics or current flow when the cell is short-circuited.

References

For definitions of electrochemical potential and activities, see the IUPAC Gold Book on the Nernst Equation.