9.6 Coupled Reactions

What are coupled reactions?

A coupled reaction occurs when a thermodynamically unfavorable (endergonic, +ΔG) reaction is driven forward by pairing it with a favorable (exergonic, −ΔG) reaction. Because Gibbs free energy is a state function, the ΔG values of the two reactions can be added together. If the overall sum of ΔG is negative, the combined process is spontaneous, even though one step alone is not.

Adding reactions and ΔG

To couple reactions, add the two chemical equations so intermediate species cancel (like Hess's law), then sum their ΔG° values. If ΔG°total < 0, the overall reaction is spontaneous. This principle explains how metals are extracted from ores: reducing a metal oxide may be nonspontaneous alone, but coupling it with a highly favorable reaction (like carbon oxidation) makes the overall process spontaneous.

Real-world relevance

Coupled reactions explain metallurgical extraction (e.g., using carbon or carbon monoxide to reduce metal oxides) and biological energy transfer, where ATP hydrolysis (exergonic) drives otherwise unfavorable cellular reactions. The key AP idea: use Hess's law-style addition of ΔG° values to determine whether a coupled process is overall spontaneous.

Key terms

Coupled reaction

A pairing of an endergonic (unfavorable) reaction with an exergonic (favorable) one so the overall process is spontaneous.

Why can ΔG values be added?

Gibbs free energy is a state function, so ΔG values of combined reactions add just like enthalpies in Hess's law.

Criterion for overall spontaneity

The sum of ΔG° values for the coupled reactions must be negative.

Metallurgical example

Reducing a metal oxide (unfavorable) is coupled with oxidizing carbon (highly exergonic) to make the overall process spontaneous.

Biological example

ATP hydrolysis (exergonic) is coupled with unfavorable cellular reactions to drive them forward.

Try an AP-style question

Reaction A has ΔG = +20 kJ and Reaction B has ΔG = −30 kJ. When coupled, what is ΔG?

1. −10 kJ
2. −50 kJ
3. +50 kJ
4. +10 kJ