Thermodynamic equations high pressure chemical reactions

Most of the studies reported in this chapter fail to include the phase behavior of the reacting mixture. Since multiple phases can occur in the mixture critical region, reaction studies need to be complemented with phase behavior studies so that we may gain an understanding of the fundamentals of the thermodynamics and kinetics of chemical reactions in solution. Chapter 5 describes how a simple cubic equation of state can be used to extend and complement the phase behavior studies. An equation of state can be used to determine the location of phase-border curves in P-T space and, with transition-state theory, to correlate the pressure dependence of the reaction rate constant when the pressure effect is large (i.e., at relatively high pressures). 

The coupling takes may forms. Velocity appears in every equation, so that coupling is always present. Density usually depends on pressure, temperature, and composition through an equation of state and density appears in every equation. Thermodynamic properties (e.g., cp and h) and transport properties (e.g., p, X, D km) also depend on pressure, temperature, and composition. Chemical reaction rates depend on composition and temperature. All in all it is clear that this system is highly coupled. 

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