Thermodynamics in biochemistry: express the relationship between the standard free energy change (ΔG°) and the equilibrium constant (Keq). Choose the correct formula.

Introduction / Context:
Connecting free energy changes to equilibrium constants is essential for predicting reaction directionality and coupling reactions in metabolism. This relationship holds for standard conditions and is widely used in bioenergetics.

Given Data / Assumptions:

• R is the gas constant and T is absolute temperature in kelvins.
• Keq is the thermodynamic equilibrium constant.
• Standard state conditions are assumed.

Concept / Approach:
The canonical relationship is ΔG° = -R * T * ln(Keq). A large Keq > 1 implies negative ΔG° (favorable forward direction), while Keq < 1 implies positive ΔG°.

Step-by-Step Solution:

Verification / Alternative check:
Dimensional analysis and sign logic: if Keq > 1, ln Keq positive → ΔG° negative, aligning with exergonic reactions.

Why Other Options Are Wrong:
RTlnkeq (positive sign): Wrong sign. R/T * lnkeq: Incorrect dimensionality. -RT/lnkeq: Algebraically incorrect.

Common Pitfalls:
Confusing ln with log10 and misplacing the minus sign; both errors reverse the interpretation of spontaneity.

Final Answer:
ΔG° = -RTlnkeq