Nernst equation
The Nernst equation gives the cell potential when concentrations are not standard: E = E° − (RT/nF) ln Q. At 25 °C, E = E° − (0.0592/n) log Q. As the cell runs, Q grows, E falls, and at equilibrium E = 0.
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Analogy
A battery going flat: as products pile up, the push gets weaker until it's gone.
Example
Q = 1.0 / 0.010 = 100, n = 2E = 1.10 − (0.0592/2) × log 100E = 1.10 − 0.0296 × 2E = 1.04 V
In practice
A pH meter is a cell whose voltage changes with [H⁺] according to the Nernst equation.
Practice
Flashcards
- What does the Nernst equation correct for?Non-standard concentrations.
Questions people ask
Why does a battery go flat?
As the cell reacts, reactants are used up and products build up, so Q increases. By the Nernst equation, E falls as Q rises. When Q reaches K, E becomes zero and the battery can do no more work. The reaction is at equilibrium.
How are E° and K related?
At equilibrium, E = 0 and Q = K, so E° = (RT/nF) ln K. At 25 °C, this is E° = (0.0592/n) log K. A larger positive E° means a larger K. This ties electrochemistry to the equilibrium constant and to ΔG°.