Previous article Next article Approximating One Convex Function by AnotherJon Folkman and Norman ShapiroJon Folkman and Norman Shapirohttps://doi.org/10.1137/0116080PDFBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] R. J. Clasen, The numerical solution of the chemical equilibrium problem, RM- 4345, The RAND Corporation, Santa Monica, California, 1965 Google Scholar[2] George B. Dantzig, , Jon Folkman and , Norman Shapiro, On the continuity of the minimum sets of a continuous function, J. Math. Anal. Appl., 17 (1967), 519–548 10.1016/0022-247X(67)90139-4 MR0207426 (34:7241) 0153.49201 CrossrefISIGoogle Scholar[3] E. A. Guggenheim, Thermodynamics: an Advanced Treatment for Chemists and Physicists, North-Holland, Amsterdam, 1967, and John Wiley, New York CrossrefGoogle Scholar[4] N. Z. Shapiro and , L. S. Shapley, Mass action laws and the Gibbs free energy function, J. Soc. Indust. Appl. Math., 13 (1965), 353–375 10.1137/0113020 MR0180121 (31:4356) LinkISIGoogle Scholar Previous article Next article FiguresRelatedReferencesCited byDetails Molecular Simulation of Chemical Reaction Equilibrium by Computationally Efficient Free Energy Minimization23 August 2018 | ACS Central Science, Vol. 4, No. 9 Cross Ref Computing complex chemical equilibria by generalized linear programmingMathematical and Computer Modelling, Vol. 10, No. 7 Cross Ref Computational Aspects of Chemical Equilibrium in Complex Systems Cross Ref A Generalized Technique for Eliminating Species in Complex Chemical Equilibrium CalculationsN. Z. Shapiro12 July 2006 | SIAM Journal on Applied Mathematics, Vol. 17, No. 5AbstractPDF (954 KB) Volume 16, Issue 5| 1968SIAM Journal on Applied Mathematics History Submitted:06 February 1968Published online:28 July 2006 InformationCopyright © 1968 © Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0116080Article page range:pp. 993-997ISSN (print):0036-1399ISSN (online):1095-712XPublisher:Society for Industrial and Applied Mathematics

It is proved that a mixture is “ideal” at some fixed temperature and pressure if the partial molar Gibbs free energy of each species depends only on the mole fraction of that species.

: This memorandum obtains necessary and sufficient conditions so that the solution of a constrained minimization problem will vary continuously when the constraints and objective function are varied. It also obtains special results in the case that the constraints are linear inequalities.