Bioenergetics: linking redox potential to standard free energy What is the correct relationship between the standard free energy change and the standard redox potential difference (n = moles of electrons, F = Faraday's constant, E° = standard redox potential difference)?

Introduction / Context:
In microbial metabolism, electron transport chains convert redox potential differences into usable energy. The quantitative link between a redox couple’s potential difference and the Gibbs free energy change allows prediction of directionality and ATP-generating capacity of respiratory pathways.

Given Data / Assumptions:

• E° is the standard oxidation–reduction potential difference (volts).
• n is the number of electrons transferred.
• F is Faraday’s constant (approximately 96,485 C per mol e^-).

Concept / Approach:

The thermodynamic relation is ΔG° = -n F E°. A positive E° (favorable electron flow from donor to acceptor) yields a negative ΔG°, signifying a spontaneous process under standard conditions. This underpins how microbes harness energy by transferring electrons to acceptors with higher redox potentials.

Step-by-Step Solution:

Verification / Alternative check:

Example: If E° = +0.2 V and n = 2, ΔG° = -2 * 96485 * 0.2 ≈ -38.6 kJ/mol, consistent with energy release usable for ATP synthesis.

Why Other Options Are Wrong:

• ΔG° = n F E°: Wrong sign; would predict positive ΔG° for favorable E°.
• Expressions with lnE°: Dimensional inconsistency; E° is already in volts.
• ΔG° = -R T E°: Mixes gas constant relation improperly; the correct relation uses nF.

Common Pitfalls:

• Forgetting the negative sign, which inverts spontaneity predictions.

Final Answer:

ΔG° = -nFE°