Cell Potential & Thermodynamic Favorability

• Standard Electrode Potential ($E^\circ$): This is the potential of a half-cell measured under standard conditions ($298\text{ K}$, $1.00\text{ mol dm}^{-3}$ ion concentration, and $100\text{ kPa}$ pressure for gases). It indicates the tendency of a species to be reduced.

• Standard Hydrogen Electrode (SHE): Since absolute potentials cannot be measured, all electrode potentials are referenced against the SHE, which is assigned a value of exactly $0.00\text{ V}$.

• Cell Potential ($E^\circ_{\text{cell}}$): Also known as electromotive force (EMF), it is the difference in potential between the reduction half-reaction and the oxidation half-reaction.

• Thermodynamic Link: The relationship between electrical work and chemical energy is defined by the equation $\Delta G^\circ = -nFE^\circ_{\text{cell}}$.

• Variable Definitions: In this formula, $n$ represents the number of moles of electrons transferred in the balanced redox equation, and $F$ is the Faraday constant (approximately $96,485\text{ C mol}^{-1}$).

• Spontaneity Criteria: A reaction is considered thermodynamically favored (spontaneous) when $\Delta G^\circ$ is negative, which mathematically requires $E^\circ_{\text{cell}}$ to be positive.

Calculating Standard Cell Potential

• Identify Half-Reactions: Determine which species is being reduced (higher $E^\circ$) and which is being oxidized (lower $E^\circ$).
• Apply the Formula: Use the standard subtraction method:

$E^\circ_{\text{cell}} = E^\circ_{\text{reduction}} - E^\circ_{\text{oxidation}}$

• Stoichiometry Rule: Never multiply the $E^\circ$ value by the coefficients in the balanced equation. Potential is an intensive property, meaning it does not depend on the amount of substance present.

Predicting Spontaneity

• If $E^\circ_{\text{cell}} > 0$, the forward reaction is spontaneous.
• If $E^\circ_{\text{cell}} < 0$, the forward reaction is non-spontaneous and requires external energy (electrolysis) to proceed.

• Intensive vs. Extensive: While $\Delta G^\circ$ is an extensive property (scales with the amount of matter), $E^\circ$ is intensive. This is why $n$ is included in the conversion formula to balance the units.

• The 'More Positive' Rule: In a spontaneous cell, the half-reaction with the more positive $E^\circ$ value will always occur as reduction at the cathode.

• Unit Consistency: When calculating $\Delta G^\circ$, ensure your $E^\circ$ is in Volts and your result will be in Joules (not kJ). Always convert to kJ for final answers if requested.

• Check the $n$ value: The $n$ in $\Delta G^\circ = -nFE^\circ$ must be the total number of electrons cancelled out when combining the two half-reactions.