linguistic:paraphrasing, structural:summarization, structural:scholar_edition
Minimization of Gibbs energy

(For proof see Lagrange multipliers.) This is a set of (m + k) equations in (m + k) unknowns (the N and the λ) and may, therefore, be solved for the equilibrium concentrations N as long as the chemical activities are known as functions of the concentrations at the given temperature and pressure. (In the ideal case, activities are proportional to concentrations.) (See Thermodynamic databases for pure substances.) Note that the second equation is just the initial constraints for minimization.