The hydrolysis of adenosine triphosphate plays such an important role in energy metabolism that the thermodynamic properties of the species involved have been determined, including the standard Gibbs energies and enthalpies of formation of its magnesium complex ions. When the pH and pMg are specified in addition to temperature, pressure, and ionic strength, the criterion for spontaneous change and equilibrium is provided by the transformed Gibbs energy G' that is defined by a Legendre transform. The use of a Legendre transform makes it possible to express all the thermodynamic properties of a reactant by use of a single function of temperature, pH, pMg and ionic strength. The expression for the standard transformed Gibbs energy of formation of a reactant like ATP (a sum of species) is a function of temperature, pressure, pH, pMg, and ionic strength. Nine Maxwell relations are used to calculate various thermodynamic properties and relations between them. It is of particular interest to see that the derivatives of the standard transformed enthalpy and entropy with respect to pH and pMg are determined by the temperature derivatives of the average numbers of hydrogen ions and magnesium ions bound. Ten transformed thermodynamic properties for ATP + H2O = ADP + Pi are calculated as functions of temperature, pH, pMg, and ionic strength.