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Gibbs energy minimization is a thermodynamic computational method that determines the equilibrium composition of a closed multiphase, multicomponent system by finding the set of phase amounts and species mole numbers that minimize the total Gibbs free energy subject to elemental mass-balance constraints at specified temperature and pressure [1]. At fixed temperature and pressure, the second law requires the total Gibbs energy G to reach a global minimum at equilibrium, equivalently requiring equality of the chemical potential of each species among all phases in which it appears [2]. The formulation does not require selection of independent chemical reactions; instead, G is expressed as a function of the unknown mole numbers using ideal or non-ideal mixing models, and the minimum is found by constrained optimization, commonly via Lagrange multipliers or the RAND algorithm [3]. It is distinguished from equilibrium-constant methods, which solve reaction stoichiometry explicitly, by treating equilibrium as an optimization over the distribution of phases and species rather than over reaction extents [4].
References
- Smith, W.R.; Missen, R.W. Chemical Reaction Equilibrium Analysis: Theory and Algorithms; Krieger Publishing: Malabar, FL, 1991.
- Sandler, S.I. Chemical, Biochemical, and Engineering Thermodynamics, 4th ed.; Wiley: Hoboken, NJ, 2006.
- Van Zeggeren, F.; Storey, S.H. The Computation of Chemical Equilibria; Cambridge University Press: Cambridge, 1970.
- Gordon, S.; McBride, B.J. Computer Program for Calculation of Complex Chemical Equilibrium Compositions and Applications; NASA RP-1311; NASA Lewis Research Center: Cleveland, OH, 1994. https://ntrs.nasa.gov/citations/19950013764
