Free energy coupling (diagram)
The coupling of the exergonic ATP hydrolysis reaction to the endergonic glutamine synthesis reaction. [2]
In thermodynamics, free energy coupling refers to the rule that the free energy changes of coupled reactions are additive. Specifically, given a set of reactions, i through k, typically occurring under isothermal-isobaric (biological) conditions, the total Gibbs free energy change, for the mixture of reactions will be the summation of the free energies of the component reactions:

\Delta G_{total} = \sum_{i=1}^k \Delta G_i

G = U + PV – TS

In other words, the energy released from one reaction (spontaneous ones) will, in effect, drive other reactions which are not energetically favored (non-spontaneous ones).

In short, given two or more reactions in which one is not energetically favorable the logic of free energy coupling, which seems to be based on the rule that state functions are additive, stipulates that the set of coupled or energetically connected reactions in contact will proceed, when mixed together, as long the magnitude of the free energy change for the exergonic reaction[s] is greater than that of the endergonic reaction[s], whereby the free energy released from one or more powerful reactions will drive the weaker free energy absorbing reactions.

If, for example, the one spontaneous reaction is mixed with a non-spontaneous reaction, such as shown below:

A → BNatural (Spontaneous)DGAB le 0
C → DUnnatural (Non-spontaneous)  \Delta G_{CD} > 0 \,

the non-spontaneous reaction can be driven into reaction as long as: |ΔGAB| > |ΔGCD|.

The basics of this rule seem to stem from Hess’ law of heat summations. This logic applied to summations of Gibbs free energies, however, seems to have arisen in the 1941 paper “Metabolic Generation and Utilization of Phosphate Bond Energy” of German-born American biochemist Fritz Lipmann’s and the recognition of the universal energy currency of phosphates, e.g. ATP, in biological systems, and how the energy released from the high energy phosphate triple bond can be used to drive many energetically unfavorable biochemical reactions. [1]

1. (a) Lipmann, Fritz. (1941). “Metabolic Generation and Utilization of Phosphate Bond Energy”. New York. In: Advances in Enzymology and Related Subjects, Vol. 1 (1941), (pg. 99-162). Interscience Publishers.
(b) Fox, Ronald F. (1988). Energy and the Evolution of Life (pg. 2). New York: W.H. Freeman and Company.
2. Purves, William K, Sadava, David, and Orians, Gordon H. (2004). Life: the Science of Biology (section: ATP couples exergonic and endergonic reactions, pgs. 112-13). MacMillian.

Further reading
● Delbruck, Max. (1944). “Problems of Modern Biology in Relation to Atomic Physics: Part III: Energy-Coupling”, A Series of Lectures, April and May, Vanderbilt University School of Medicine.
● Andrews, Andres J. and Luger, Karolin. (2010). “Chapter eleven: A Coupled Equilibrium Approach to Study Nucleosome Thermodynamics” (abs), Methods in Enzymology, 488: 265-85.

External links
Bioenergetics (see: Energy Coupling), Biochemistry and Biophysics Program at Rensselear Polytechnic Institute –

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