Electrochemistry and the Nernst Equation Cheat Sheet

A printable reference covering redox reactions, cell potential, Gibbs free energy, equilibrium constants, and the Nernst equation for grades 11-12.

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Electrochemistry connects chemical reactions with electrical energy. This cheat sheet covers voltaic cells, electrolytic cells, electrode potentials, and how concentration changes affect voltage. Students need these ideas to predict whether redox reactions are spontaneous and to solve common cell potential problems. The Nernst equation is especially important because real cells are often not at standard conditions. The core idea is that oxidation loses electrons and reduction gains electrons. Standard cell potential is found from $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$ , and spontaneity is linked to $\Delta G^\circ = -nFE^\circ_{\text{cell}}$ . At $25^\circ\text{C}$ , nonstandard voltage is calculated with $E = E^\circ - \frac{0.0592}{n}\log Q$ . A positive cell potential means the reaction is thermodynamically favorable as written.

Key Facts

Oxidation is loss of electrons, reduction is gain of electrons, and the mnemonic OIL RIG means oxidation is loss and reduction is gain.
In a voltaic cell, oxidation occurs at the anode, reduction occurs at the cathode, and electrons flow from anode to cathode.
The standard cell potential is $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$ using standard reduction potentials.
A reaction is spontaneous under standard conditions when $E^\circ_{\text{cell}} > 0$ and $\Delta G^\circ < 0$ .
Free energy and cell potential are related by $\Delta G^\circ = -nFE^\circ_{\text{cell}}$ , where $F = 96485\ \text{C/mol e}^-$ .
At $25^\circ\text{C}$ , the Nernst equation is $E = E^\circ - \frac{0.0592}{n}\log Q$ .
At equilibrium, $E = 0$ and $E^\circ = \frac{0.0592}{n}\log K$ at $25^\circ\text{C}$ .
Pure solids and pure liquids are not included in $Q$ or $K$ because their activities are treated as $1$ .

Vocabulary

Anode: The electrode where oxidation occurs and electrons are produced.
Cathode: The electrode where reduction occurs and electrons are consumed.
Cell potential: The voltage of an electrochemical cell, written as $E_{\text{cell}}$ , that measures the driving force for electron flow.
Standard reduction potential: The tendency of a half-reaction to gain electrons under standard conditions, written as $E^\circ_{\text{red}}$ .
Reaction quotient: The concentration ratio $Q$ for a reaction at nonstandard conditions, calculated like $K$ but using current concentrations.
Faraday constant: The charge carried by one mole of electrons, $F = 96485\ \text{C/mol e}^-$ .

Common Mistakes to Avoid

Switching the anode and cathode is wrong because oxidation always happens at the anode and reduction always happens at the cathode.
Adding reduction potentials instead of using $E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}$ gives the wrong sign for the cell voltage.
Multiplying $E^\circ$ values by stoichiometric coefficients is wrong because electrode potential is an intensive property and does not scale with amount.
Including solids or liquids in $Q$ is wrong because pure solids and pure liquids have activity equal to $1$ .
Using the Nernst equation without matching $n$ to the balanced redox equation is wrong because $n$ must equal the number of electrons transferred.

Practice Questions

1 For a voltaic cell with $E^\circ_{\text{cathode}} = +0.80\ \text{V}$ and $E^\circ_{\text{anode}} = -0.76\ \text{V}$ , calculate $E^\circ_{\text{cell}}$ .
2 Calculate $\Delta G^\circ$ for a cell with $n = 2$ and $E^\circ_{\text{cell}} = 1.10\ \text{V}$ using $\Delta G^\circ = -nFE^\circ_{\text{cell}}$ .
3 At $25^\circ\text{C}$ , find $E$ for a cell with $E^\circ = 0.34\ \text{V}$ , $n = 2$ , and $Q = 10$ using $E = E^\circ - \frac{0.0592}{n}\log Q$ .
4 Explain why increasing the product concentration in a voltaic cell usually decreases the cell potential according to the Nernst equation.

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