The Nernst Equation: Concentration and Equilibrium

Standard potentials apply only when every dissolved species is at 1 M. The Nernst equation shows how a cell's voltage changes with concentration, and why it falls to zero when the cell reaction reaches equilibrium: a flat battery. Work through the three stages in order.

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Predict, then see: starting from 1 M in both half-cells,

Or explore freely:

[Zn²⁺] (anode) 1 M

[Cu²⁺] (cathode) 1 M

Remember

Nernst equation: E_cell = E°_cell − (RT/nF) ln Q. At 298.15 K, RT/F = 0.02569 V (or 0.0592 V with log₁₀ Q).
Q = [products]/[reactants], each raised to the power of its coefficient. Solids count as 1; gases enter as their pressure in bar. For the Daniell cell, Zn + Cu²⁺ → Zn²⁺ + Cu, Q = [Zn²⁺]/[Cu²⁺] and n = 2.
A smaller Q (more reactant, less product) gives a larger E_cell: Le Chatelier's principle. Because E_cell depends on ln Q, a tenfold change in Q shifts it by only 0.0592 V/n.
ΔG = −nFE_cell = RT ln(Q/K), and ln K = nFE°_cell/RT. Q < K: E_cell > 0, the forward reaction is spontaneous. Q = K: E_cell = 0, equilibrium. Q > K: the reverse reaction is spontaneous.

Standard reduction potentials are those in the Lecture 1 table. Concentrations are used in place of activities, as in the lectures.