On the Reduction of Certain Multiplicative Chemical Equilibrium Systems to Mathematically Equivalent Additive Systems

The vectorial formulation of the chemical equilibrium problem, represented by tableaux, provides a concise method for consolidating a large amount of fact and hypothesis relating to large chemical systems involving reactions and states of complex molecules. This formulation plus the associated techniques for minimizing the free energy of the entire system allows equilibrium states under varying conditions to be calculated in a rapid and efficient manner on electronic computers. In biological systems involving hemoglobin, for example, it is possible to account for and to compute the effects of simultaneous changes in pH, CO2, O2, and metabolite concentrations on the oxygenation of hemoglobin. The effects of changes in temperature and total pressure may also be introduced into the model in a convenient fashion. A subsequent paper will present the results of such numerical calculations using the approach developed in this paper.