Cell EMF and Standard Potentials Quick Review

Electromotive Force (EMF)

The EMF of a galvanic (voltaic) cell is the maximum potential difference between its two electrodes when no current flows. Under standard conditions (all solutes $1\;\text{M}$, gases $1\;\text{atm}$), this value is the standard cell potential $\Delta E^{\circ}$. Electrical work relates to Gibbs free energy by $G = qE$, so for a charge $nF$ transferred, $\Delta G^{\circ} = -nF\Delta E^{\circ}$.

Standard Hydrogen Electrode (SHE)

The SHE is defined as $\text{Pt}|\,\text{H}<em>2(1\;\text{atm})|\,\text{H}^+(1\;\text{M})$ with $E^{\circ}</em>{\text{red}} = 0\;\text{V}$. All other half-cell potentials are measured relative to it, giving absolute reference values for reduction potentials.

Reduction vs. Oxidation Potentials

• Reduction potential $E^{\circ}<em>{\text{red}}$: tendency of a species to gain electrons. • Oxidation potential $E^{\circ}</em>{\text{ox}}$: tendency to lose electrons, numerically $E^{\circ}<em>{\text{ox}} = -E^{\circ}</em>{\text{red}}$.

Calculating $\Delta E^{\circ}$

For a cell written Anode || Cathode, use only reduction potentials:
$\Delta E^{\circ} = E^{\circ}<em>{\text{cathode, red}} - E^{\circ}</em>{\text{anode, red}}$
(Do not multiply by stoichiometric coefficients.)

Example (Zn–Cu):
\begin{aligned}
E^{\circ}{\text{red}}(\text{Cu}^{2+}/\text{Cu}) &= +0.337\;\text{V}\ E^{\circ}{\text{red}}(\text{Zn}^{2+}/\text{Zn}) &= -0.763\;\text{V}\
\Delta E^{\circ} &= 0.337 - ( -0.763) = 1.100\;\text{V}
\end{aligned}

Sign and Spontaneity

• $\Delta E^{\circ} > 0$ → cell reaction is spontaneous as written.
• $\Delta E^{\circ} < 0$ → reverse reaction is spontaneous; swap electrode roles.

Example (Li–Ag):
$E^{\circ}<em>{\text{red}}(\text{Li}^+/\text{Li}) = -3.045\;\text{V},\; E^{\circ}</em>{\text{red}}(\text{Ag}^+/\text{Ag}) = +0.799\;\text{V}$
$\Delta E^{\circ} = 0.799 - ( -3.045) = -3.844\;\text{V}$ ⇒ cell must be reversed; lithium batteries exploit the spontaneous oxidation of Li.

Standard Cell Notation

• Single bar | separates phases; double bar || denotes salt bridge.
• Convention: Anode (oxidation) on the left, Cathode (reduction) on the right.
Example: $\text{Zn}|\text{Zn}^{2+}(1\,\text{M})||\text{Cu}^{2+}(1\,\text{M})|\text{Cu}$.

Quick Checks

1. Oxidation occurs at the anode (left); reduction at the cathode (right).
2. Reduction potentials are always tabulated vs. the SHE (0 V reference).
3. Positive $\Delta E^{\circ}$ implies a spontaneous cell reaction.