Cell Potential at Nonstandard Conditions
A galvanic (voltaic) cell generates electrical work from a redox reaction by pairing two half-cells: the anode (oxidation) and the cathode (reduction). A cell potential at nonstandard conditions calculation uses the reaction quotient \(Q\) to compute the actual cell potential \(E_{\text{cell}}\) from the standard value \(E^\circ_{\text{cell}}\).
Core definitions and essential formulas
\[
E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}
\]
\[
E_{\text{cell}} = E^\circ_{\text{cell}} - \frac{R T}{n F}\,\ln Q
\]
\[
Q=\frac{\prod a(\text{products})^{\nu}}{\prod a(\text{reactants})^{\nu}}
\]
\(E^\circ_{\text{cathode}}\) and \(E^\circ_{\text{anode}}\) are tabulated reduction potentials (V) for the chosen half-reactions; \(n\) is the number of electrons transferred in the balanced overall reaction. \(R\) is the gas constant, \(T\) is temperature in kelvin, and \(F\) is the Faraday constant. \(Q\) is built from activities \(a\) raised to stoichiometric coefficients \(\nu\); pure solids and liquids have \(a=1\) (omit from \(Q\)), and \(e^{-}\) never appears in \(Q\).
How to interpret results
A larger \(E_{\text{cell}}\) (more positive) indicates a stronger driving force for the cell reaction in the stated direction, while a smaller \(E_{\text{cell}}\) means reduced spontaneity. Because \(E_{\text{cell}} = E^\circ_{\text{cell}} - \dfrac{R T}{n F}\ln Q\), increasing \(Q\) decreases \(E_{\text{cell}}\), and decreasing \(Q\) increases \(E_{\text{cell}}\). Typical outputs include \(E^\circ_{\text{cell}}\), \(Q\), \(E_{\text{cell}}\), and often a spontaneity check; volt is the standard unit, with \(1\ \mathrm{V}=1\ \mathrm{J\,C^{-1}}\).
- Wrong \(Q\) setup: including solids/liquids or flipping products and reactants.
- Temperature error: using Celsius instead of kelvin in the Nernst term.
- Wrong \(n\): not using the electron count from the balanced overall reaction.
- Log confusion: mixing \(\ln\) and \(\log_{10}\) without the \(2.303\) factor.
Micro example: If \(E^\circ_{\text{cell}}=1.10\ \mathrm{V}\), \(n=2\), \(T=298\ \mathrm{K}\), and \(Q=100\),
then \(E_{\text{cell}} \approx 1.10 - \dfrac{0.05916}{2}\log_{10}(100)=1.10-0.05916=1.04\ \mathrm{V}\).
Use this tool to evaluate real cell voltage changes from concentration or pressure shifts and to compare reaction direction using \(Q\). Do not use it to compute equilibrium composition directly; a common next step is combining Nernst with mass-balance relations or linking \(E\) to \(\Delta G\) and equilibrium constants.