Standard Cell Potential from Half-Reactions
A galvanic (voltaic) cell produces electrical energy from a spontaneous redox reaction by coupling two half-cells. A standard cell potential from half-reactions calculation combines tabulated standard reduction potentials to compute \(E^\circ_{\text{cell}}\) and determine whether the chosen cell orientation is spontaneous under standard conditions.
Core definitions and essential formulas
\[
E^\circ_{\text{cell}} = E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}
\]
\[
\Delta G^\circ = -n F E^\circ_{\text{cell}}
\]
\(E^\circ_{\text{cathode}}\) and \(E^\circ_{\text{anode}}\) are the tabulated reduction potentials (in volts) for the selected half-reactions; the cathode is the site of reduction and the anode is the site of oxidation (the anode half-reaction is written in reverse when forming the overall reaction). In \(\Delta G^\circ = -n F E^\circ_{\text{cell}}\), \(n\) is the number of electrons transferred in the balanced overall reaction and \(F\) is the Faraday constant. Standard reduction potentials are intensive: multiplying a half-reaction to match electrons does not change its \(E^\circ\).
How to interpret results
A larger, more positive \(E^\circ_{\text{cell}}\) indicates a stronger driving force for the redox process and a more spontaneous galvanic cell as written. Typical units are volts, where \(1\ \mathrm{V} = 1\ \mathrm{J\,C^{-1}}\); the sign of \(E^\circ_{\text{cell}}\) matches spontaneity under standard conditions. Outputs commonly include the balanced overall reaction, \(n\), the chosen cathode/anode roles, and a spontaneity label based on the sign of \(E^\circ_{\text{cell}}\).
- Sign error: adding potentials instead of using \(E^\circ_{\text{cathode}} - E^\circ_{\text{anode}}\).
- Scaling mistake: multiplying \(E^\circ\) when balancing electrons (do not scale \(E^\circ\)).
- Role swap: labeling the more positive reduction potential as the anode in a galvanic setup, flipping the expected sign.
- Nonstandard conditions: interpreting \(E^\circ_{\text{cell}}\) as the actual cell voltage when concentrations/pressures differ.
Micro example: If \(E^\circ_{\text{cathode}} = +0.34\ \mathrm{V}\) and \(E^\circ_{\text{anode}} = -0.76\ \mathrm{V}\),
then \(E^\circ_{\text{cell}} = 0.34 - (-0.76) = +1.10\ \mathrm{V}\).
Use this tool to combine two tabulated half-reactions, build the overall balanced redox equation, and compute \(E^\circ_{\text{cell}}\) for a galvanic or hypothetical arrangement. Do not use it to predict voltages at nonstandard concentrations without additional corrections; a common next step is applying the Nernst equation and connecting \(E\) to equilibrium constants.