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Coupled Reactions

Reactions are coupled when the energy released by one reaction is directly used to drive another, maintaining energy conservation within the system.
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The statement of the theorem

Consider two reactions, R1R_1 and R2R_2, where R1R_1 provides the energy to drive R2R_2. Let ΔG1\Delta G_1 and ΔG2\Delta G_2 be the standard free energy changes. The coupling requires that the energy released by R1R_1 is sufficient to overcome the free energy barrier of R2R_2. The overall free energy change ΔGcoupled\Delta G_{\text{coupled}} is the sum of the individual changes: \begin{equation} \Delta G_{\text{coupled}} = \Delta G_1 + \Delta G_2 \end{equation}. For the coupling to be thermodynamically favorable, the energy released by the exergonic reaction (e.g., R1R_1) must satisfy ΔG1 (exergonic)≥∣ΔG2∣ (endergonic)\Delta G_1 \text{ (exergonic)} \ge |\Delta G_2| \text{ (endergonic)}. This ensures the net reaction proceeds spontaneously.