The vapor-liquid equilibria ratio K i = y i / x i for the components of coexisting equilibrium vapor and liquid mixtures is a complex function of the conditions and compositions of the coexisting phases. Many investigators have attempted to develop a generalized method for predicting vapor-liquid equilibrium. However, most of these methods in their present form include some parameter (or parameters) which depends on the mixtures. In other words, most of these methods do not satisfy the need for generality. Chao and Seader (1961) developed a general correlation of vapor-liquid equilibria in hydrocarbon mixtures. Their method is quite popularly used by industry today. Lee and Edmister (1971) developed a new generalized method for predicting vapor-liquid equilibrium to compare with Chao-Seader's correlation.When a reader applies Lee-Edmister's correlation to evaluate vapor-liquid equilibrium, he may find that the calculated result does not give a good comparison with the experimental result. This is because of an error in their correlation of activity coefficient in liquid solution yi. Lee and Edmister derived the activity coefficient y i from an expression of the excess Gibbs free energy of a mixture, which was proposed by them. A reader may not be able to follow their derivation to obtain the present form n n

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CONCLUSIONSIt has been shown that reaction systems with active intermediates are amenable to a straightforward analysis of the constraints imposed b stoichiometry and kinetics.These constraints yield consi B erable information about the structure of the general solution. Examples have been given of the application of the analysis to systems of varying complexity. ACKNOWLEDGMENT tion for their generous support of this work. The authors are indebted to the Calouste Gulbenkien Founda-NOTATION c = vector of concentrations cl, c2 = vectors of concentrations of stable and active spek N r t = time x, y = state variables Greek Letters p = stoichiometric matrix PI, Pz = partitioned stoichiometric matrix 8, c = small parameters 7 Y cies, respectively = vector of rate constants = basis for null space of PzT = vector of rates of reaction = dimensionless extent of reaction = vectors in null space of P Z T