$TITLE CHEMICAL EQUILIBRIUM PROBLEM  (CHEM,SEQ=21)
*  THE PROBLEM IS TO FIND THE EQUILIBRIUM COMPOSITION OF A
*  MIXTURE OF DIFFERENT ATOMS.
*
*  REFERENCE: BRACKEN J AND MC CORMICK I P, SELECTED APPLICATIONS OF
*            NONLINEAR PROGRAMMING, JOHN WILEY AND SONS, NEW YORK, 1968.
*            (CHAPTER 5)

 SETS  C  COMPOUNDS / H, H2, H2O, N, N2, NH, "NO", O, O2, OH /
       I  ATOMS     / H  HYDROGEN, N  NITROGEN, O  OXYGEN /

        TABLE  A(I,C)  ATOMS PER COMPOUND

      H  H2  H2O  N  N2  NH "NO" O  O2  OH
 H    1   2    2          1              1
 N                1   2   2   2
 O             1              1  1   2   1

 PARAMETERS MIX(I)   NUMBER OF ELEMENTS IN MIXTURE / H=2, N=1, O=1 /
            GIBBS(C) GIBBS FREE ENERGY AT 3500 K AND 750 PSI /
            H  -10.021,  H2  -21.096,  H2O -37.986,  N   -9.846, N2 -28.653
            NH -18.918, "NO" -28.032,  O  -14.640,   O2 -30.594, OH -26.11 /
            GPLUS(C) GIBBS ENERGY PLUS PREASSURE ;

  GPLUS(C) = GIBBS(C) + LOG(750*.07031); DISPLAY GPLUS;

 VARIABLES X(C)    NUMBER OF MOLS IN MIXTURE
           XB      TOTAL NUMBER OF MOLS IN MIXTURE
           ENERGY  TOTAL FREE ENERGY IN MIXTURE
 POSITIVE VARIABLES X, XB;

 EQUATIONS CDEF(I) COMPONENT DEFINITION
           EDEF    ENERGY DEFINITION
           XDEF    TOTAL MOL DEFINITION ;

 CDEF(I)..  SUM(C, A(I,C)*X(C)) =E= MIX(I);

 XDEF..     XB =E= SUM(C, X(C));

 EDEF..     ENERGY =E= SUM(C, X(C)*(GPLUS(C) + LOG(X(C)/XB)));

 X.LO(C) = .001; XB.LO = .01;

 MODEL MIXER CHEMICAL MIX FOR N2H4+O2 / ALL /;

 SOLVE MIXER MINIMIZING ENERGY USING NLP;