USE OF THE FUNDAMENTAL EQUATION TO DERIVE EXPRESSIONS FOR THE TRANSFORMED GIBBS ENERGY, ENTROPY, AND ENTHALPY OF A GASEOUS REACTION SYSTEM AT A SPECIFIED PARTIAL-PRESSURE OF A REACTANT

When the chemical potentials or partial pressures of some reactants are externally fixed, a Legendre transform can be used to define a new thermodynamic potential that provides the criterion of equilibrium and leads to a new fundamental equation that provides the means for computing the equilibrium composition and deriving equations for the transformed thermodynamic properties of the equilibrium system. This method is applied to a simple system and to the polymerization of the alkylbenzenes in the presence of ethylene, which involves an infinite number of isomer groups.