Inverse Chemical Equilibrium Problems: General Formulation and Algorithm

Abstract In a forward chemical equilibrium problem (FCEP), the state of minimum Gibbs energy for a chemical system is sought, in which temperature, pressure, elemental amounts, and thermodynamic model parameters are prescribed. We herein present a mathematical framework for characterizing and solving inverse chemical equilibrium problems (ICEP), a class of problems for which one or more of those prescribed conditions in a FCEP are unknown in advance. In an ICEP, complementary conditions must be imposed, which are referred to here as equilibrium constraints. Examples of ICEPs include those in which a certain property is known at equilibrium (e.g., volume is specified instead of pressure; enthalpy is specified instead of temperature; pH is specified instead of the amount of element H). The equilibrium constraints may also be specified by equations that govern the relationship between several equilibrium properties (e.g., the equations relating temperature, pressure, density, energy, and velocity of the gases produced during the detonation of an explosive).