Bioenergetics and equilibrium: If the Gibbs free energy change (ΔG) of a chemical reaction is positive and the equilibrium constant (Keq) is less than 1, what does this imply about the reaction's direction under standard biological conditions?

Introduction / Context:
In biochemistry and microbiology, predicting whether a reaction will proceed forward or backward is fundamental for understanding metabolism, enzyme regulation, and pathway flux. Two key indicators are the Gibbs free energy change (ΔG) and the equilibrium constant (Keq). Their relationship determines spontaneity and the favored direction of a reaction under defined conditions.

Given Data / Assumptions:

• ΔG > 0 (positive) for the reaction as written.
• Keq < 1 for the reaction as written.
• Standard biochemical conditions are implied (activities near 1 unless otherwise stated).

Concept / Approach:

The fundamental relationship is ΔG°′ = −R * T * ln(Keq). If Keq < 1, then ln(Keq) is negative, making −R * T * ln(Keq) positive; thus ΔG°′ is positive. A positive ΔG means the forward direction is non-spontaneous under standard conditions, while the reverse reaction would be spontaneous (negative ΔG when written in reverse).

Step-by-Step Solution:

Verification / Alternative check:

Consider Le Châtelier’s principle at equilibrium: when Keq < 1, the equilibrium mixture contains more reactants than products, reinforcing that the forward formation of products is disfavored unless cellular conditions (mass action) are altered.

Why Other Options Are Wrong:

“proceeed in forward direction”: contradicts ΔG > 0 and Keq < 1.

“not take place in any of the direction”: reactions are reversible; direction depends on ΔG and concentrations.

“none of these”: incorrect because the reverse direction is clearly favored.

Common Pitfalls:

Confusing ΔG (actual conditions) with ΔG°′ (standard). Also, ignoring concentration effects: cells can drive endergonic steps by coupling or by changing reactant/product ratios.

Final Answer:

proceed in reverse direction