Thermodynamics in biochemistry: express the relationship between the standard free energy change (ΔG°) and the equilibrium constant (Keq). Choose the correct formula.
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AΔG° = -RTlnkeq
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BΔG° = RTlnkeq
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CΔG° = R/Tlnkeq
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DΔG° = -RT/lnkeq
Answer
Correct Answer: ΔG° = -RTlnkeq
Explanation
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:
Recall definition: ΔG = ΔG° + RT ln Q; at equilibrium, ΔG = 0 and Q = Keq.Rearrange to obtain: ΔG° = -RT ln Keq.Select the matching expression.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