E standard equals RT over nF times ln K, giving equilibrium constants from voltages.
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At equilibrium a cell has no net driving force, so its potential is zero, and the standard cell potential is then related to the equilibrium constant by E° = (0.0592/n) log K at 25 C. A relatively small standard potential corresponds to an equilibrium constant far from unity, while a large potential indicates a very large K. The relationship converts a voltage measurement into a quantitative equilibrium constant. It is derived from the Nernst equation by setting the reaction quotient equal to K. The method is useful for finding equilibrium constants from electrochemical data.
Key ideas: At equilibrium E = 0 and Q = K, so E standard = (RT/nF) ln K; at 25 C, log10 K = nE standard / 0.0592. For E standard = 1.10 V and n = 2, K is about 1e37, which is why the Zn/Cu reaction runs essentially to completion. A dead battery is a cell at equilibrium.
Common mistakes and connections: Mistake: using E standard where E nonstandard is needed, or confusing n (electrons transferred) with the sum of coefficients. Also, K derived this way refers to the overall reaction as written; reversing it gives 1/K. Connects equilibrium constants measured by electrochemistry to solubility products (Ksp from cell voltage).
log K = nE0/0.0592, so even a modest E0 gives a huge equilibrium constant; the Zn-Cu cell has K near 10^37. The interactive lesson shows this as a live animation or chart.
For the zinc-copper reaction, log K = 2(1.10)/0.0592 ≈ 37, so K ≈ 1.6 × 10^37.
E standard equals RT over nF times ln K, giving equilibrium constants from voltages.
Cell Potential and Equilibrium is a advanced topic in Acids, Bases & Electrochemistry. It builds on beginner and intermediate topics, so review those first if needed.
Study these earlier topics in Acids, Bases & Electrochemistry first: Spontaneity from Cell Potential, Nernst Equation, Cell Potential and Free Energy.
The next topics in Acids, Bases & Electrochemistry are Concentration Cells and Faraday's Constant.
Yes. The interactive lesson includes a self-check question on Cell Potential and Equilibrium, and the Acids, Bases & Electrochemistry quiz draws on every topic in this area.
Cell Potential and Equilibrium is topic 57 of 105 in Acids, Bases & Electrochemistry.