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ADP contains the same adenosine unit as ATP, with two phosphate groups instead of three. One ATP converted by the stated hydrolysis gives one ADP and one inorganic phosphate: $3=2+1$ accounts for the phosphate groups while adenine and ribose are retained. ADP is therefore a reusable material carrier, rather than ATP with its entire structure discarded.

Regeneration reverses the net chemical reaction:At the same stipulated reference conditions its $\Delta G^{\circ \prime }$ is $+30.5\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$, the negative of the hydrolysis value. It is an endergonic reaction and requires energy input through energy coupling; a catalyst alone cannot supply that input. Recycling the material carrier does not recycle the expended driving energy. Cellular respiration and light-dependent reactions supply routes for regeneration. See Cooper, The Cell: ATP generation and energy coupling.

ADP is a nucleotide with two phosphate groups. Formation of ATP from ADP and phosphate couples to energy supply in light-dependent reactions; the Calvin cycle returns ADP after using ATP. ^[ref].

An endergonic reaction has positive molar reaction change in Gibbs free energy under the specified conditions. Sustained net forward conversion needs a driving process, such as energy coupling. See OpenStax Biology 2e, 6.2: endergonic reactions.

Energy coupling links an endergonic reaction to an exergonic reaction through a reaction mechanism, so that the combined transformation has a favourable change in Gibbs free energy. ATP hydrolysis is a common driving chemical reaction. A shared reaction intermediate, produced in one step and consumed in another, can physically connect the transformations; merely placing two independent chemical reactions in the same chemical solution does not establish energy coupling. See Alberts et al., Molecular Biology of the Cell: coupled reactions and activated intermediates.

For a computed example, stipulate an endergonic reaction $\mathrm{A}⟶\mathrm{B}$ with $\Delta G_1^{\circ \prime }=+20\mathrm{kJ}\mathrm{mo}{\mathrm{l}}^{-1}$ under precisely the same biochemical standard state conditions as the quoted ATP hydrolysis value. Assume a reaction mechanism couples one ATP hydrolysis to each A-to-B conversion. The formal sum isThe sum $+20+(-30.5)=-10.5$ gives an exergonic reaction. The $+20$ is a chosen teaching value, not a measured property of an identified substance. Outside these reference conditions, add the actual $\Delta G_1$ and $\Delta G_2$, each evaluated using consistent thermodynamic activities; mixing a standard value for one chemical reaction with an unrelated cellular value for the other gives no justified prediction.

Why do the changes in Gibbs free energy add? Gibbs free energy is a state function. Adding consistent reaction changes cancels any shared reaction intermediate and leaves the difference between the combined reactants and combined reaction products. This explains the thermodynamic accounting; it does not construct the reaction mechanism. In many ATP-dependent routes, phosphorylation transfers a phosphate group to a substrate or an enzyme, and subsequent transformation consumes that modified material. The shared material is what connects the steps. Other reaction mechanisms use ATP differently. See Alberts et al., Molecular Biology of the Cell: ATP-driven biosynthesis.

The useful achievement is that a common regenerated nucleotide can connect many different processes in metabolism. The net negative change in Gibbs free energy permits the coupled conversion, but supplies no reaction rate: enzymes can lower activation energy barriers without changing the endpoint difference. Energy coupling changes which overall chemical reaction is being considered; catalysis accelerates an available route. See OpenStax Biology 2e, 6.2: free-energy changes and reaction barriers.

A historical landmark is Fritz Lipmann's ^[ref]. Its sections on the phosphate cycle, generation and utilization of phosphate-bond energy, and group transfer organized these processes around a reusable chemical carrier. The historical terminology should be read with the modern distinction between net hydrolysis and the cost of breaking a chemical bond.