Mass Action Laws and the Gibbs Free Energy Function

Abstract

Next article Mass Action Laws and the Gibbs Free Energy FunctionN. Z. Shapiro and L. S. ShapleyN. Z. Shapiro and L. S. Shapleyhttps://doi.org/10.1137/0113020PDFPDF PLUSBibTexSections ToolsAdd to favoritesExport CitationTrack CitationsEmail SectionsAbout[1] J. Willard Gibbs, The scientific papers of J. Willard Gibbs. Vol. I: Thermodynamics, Dover Publications Inc., New York, 1961xxvi+434 MR0128829 0098.20905 Google Scholar[2] S. R. Brinkley, Note on the conditions of equilibrium for systems of many components, J. Chem. Phys., 14 (1946), 563–564 10.1063/1.1724195 CrossrefISIGoogle Scholar[3] S. R. Brinkley, Calculation of the equilibrium composition of systems of many constituents, J. Chem. Phys., 15 (1947), 107–110 10.1063/1.1746420 CrossrefISIGoogle Scholar[4] F. J. Krieger and , W. B. White, A simplified method for computing the equilibrium composition of gaseous systems, J. Chem. Phys., 16 (1948), 358–360 10.1063/1.1746887 CrossrefISIGoogle Scholar[5] H. J. Kandiner and , S. R. Brinkley, Calculation of complex equilibrium relations, Ind. Eng. Chem., 42 (1950), 850–855 10.1021/ie50485a030 CrossrefISIGoogle Scholar[6] W. B. White, , S. M. Johnson and , G. B. Dantzig, Chemical equilibrium in complex mixtures, J. Chem. Phys., 28 (1958), 751–755 10.1063/1.1744264 CrossrefISIGoogle Scholar[7] R. J. Clasen, The linear-logarithmic programming problem, RM-3707-PR, The RAND Corporation, 1963 Google Scholar[8] J. Warga, A convergent procedure for solving the thermochemical equilibrium problem, J. Soc. Indust. Appl. Math., 11 (1963), 594–606 10.1137/0111044 MR0165983 0199.22701 LinkISIGoogle Scholar[9] J. V. Maloney, Jr., , J. C. DeHaven, , E. C. DeLand and , G. B. Bradham, Analysis of chemical constituents of blood by digital computer, RM-3541-PR, The RAND Corporation, 1963 Google Scholar[10] G. B. Dantzig, , J. C. DeHaven, , I. Cooper, , S. M. Johnson, , E. C. DeLand, , H. E. Kanter and , C. F. Sams, A mathematical model of the human external respiratory system, Perspectives in Biol. and Med., 4 (1961), 324–376 CrossrefISIGoogle Scholar[11] J. C. DeHaven, , E. C. DeLand, , N. S. Assali and , W. Manson, Physiochemical characteristics of placental transfer, The RAND Corporation P-2565, 1962 Google Scholar[12] J. C. DeHaven and , E. C. DeLand, Reactions of hemoglobin and steady states in the human respiratory system: An investigation using mathematical models and an electronic computer, RM-3212-PR, The RAND Corporation, 1962 Google Scholar[13] E. A. Guggenheim, Thermodynamics, An Advanced Treatment for Chemists and Physicists, North-Holland, Amsterdam, 1959 Google Scholar[14] N. Z. Shapiro, Conditions for a homogeneous mixture to be ideal, RM-3677-PR, The RAND Corporation, 1963 Google Scholar[15] W. Fenchel, Convex cones and functions, 1953, Department of Mathematics, Princeton University, unpublished Google Scholar[16] E. Eisenberg, manuscript to be published Google Scholar[17] N. Z. Shapiro, A generalized technique for eliminating species in complex chemical equilibrium calculations, RM-4205-PR, The RAND Corporation, 1964 Google Scholar[18] N. Z. Shapiro, On the behavior of a chemical equilibrium system when its free energy parameters are changed, RM-4128-PR, The RAND Corporation, 1964 Google Scholar[19] G. B. Dantzig and , J. C. DeHaven, On the reduction of certain multiplicative chemical equilibrium systems to mathematically equivalent additive systems, J. Chem. Phys., 36 (1962), 2620–2627 10.1063/1.1732342 CrossrefISIGoogle Scholar Next article FiguresRelatedReferencesCited ByDetails A Scaling Theorem and AlgorithmsSIAM Journal on Applied Mathematics, Vol. 33, No. 2 | 12 July 2006AbstractPDF (486 KB)Chemical Equilibrium Problems with Unbounded Constraint SetsSIAM Journal on Applied Mathematics, Vol. 18, No. 4 | 31 July 2006AbstractPDF (744 KB)A Generalized Technique for Eliminating Species in Complex Chemical Equilibrium CalculationsSIAM Journal on Applied Mathematics, Vol. 17, No. 5 | 12 July 2006AbstractPDF (954 KB)On Membrane EquilibriaSIAM Journal on Applied Mathematics, Vol. 16, No. 5 | 28 July 2006AbstractPDF (2303 KB)Approximating One Convex Function by AnotherSIAM Journal on Applied Mathematics, Vol. 16, No. 5 | 28 July 2006AbstractPDF (511 KB)Stoichiometric Equations are Mathematical EquationsSIAM Journal on Applied Mathematics, Vol. 15, No. 3 | 13 July 2006AbstractPDF (340 KB) Volume 13, Issue 2| 1965Journal of the Society for Industrial and Applied Mathematics History Submitted:28 January 1964Published online:13 July 2006 InformationCopyright © 1965 Society for Industrial and Applied MathematicsPDF Download Article & Publication DataArticle DOI:10.1137/0113020Article page range:pp. 353-375ISSN (print):0368-4245ISSN (online):2168-3484Publisher:Society for Industrial and Applied Mathematics