University13 min

Nernst equation: from standard potential to actual potential

Write Nernst for any couple, compute the emf of a cell away from standard conditions and derive an equilibrium constant from it.

The essentials

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The formula

For α Ox+n eX−→β Red\alpha\,\text{Ox} + n\,\ce{e^-} \rightarrow \beta\,\text{Red}: E=E∘+RTnFln⁡aOxαaRedβE = E^\circ + \frac{RT}{nF}\ln\frac{a_{\text{Ox}}^{\alpha}}{a_{\text{Red}}^{\beta}} At 25 ∘C25\ ^\circ\text{C}, in dilute solution: E=E∘+0.059nlog⁡[Ox]α[Red]βE = E^\circ + \frac{0.059}{n}\log\frac{[\text{Ox}]^{\alpha}}{[\text{Red}]^{\beta}} The oxidant sits in the numerator: adding some raises EE.
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Where 0.059 V comes from

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Activities

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Full cell and equilibrium constant

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Two cases to recognise

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