TEMPERATURES OF THE MAXIMUM REACTION-RATE AND THEIR RELATION TO THE EQUILIBRIUM TEMPERATURES

This paper derives the relationship between the temperatures of maximu m reaction rate and the equilibrium temperatures for exothermic reacti ons. For a reversible reaction described by Arrhenius type rate coeffi cients the relation is found to be (1/T-r,T- max) - (1/T-eq) (R/(E-2 - E-1)) ln(E-2/E-1), where R is the gas constant and E-1 and E-2 are th e activation energies of the forward and backward reaction. The result implies that the operating Line of the maximum reaction rate will be parallel to the equilibrium line in a 1/T versus conversion diagram wh en the activation energies (or enthalpy change of reaction) are consta nt. For systems with constant pressure, the constant distance between the two curves is then equivalent to a constant driving force of the r eaction, Delta G/T. Thus, we have shown that a recently developed prin ciple for an energy efficient process design, called equipartition of forces, can be applied also near the maximum reaction rate for element ary, exothermic reactions with Arrhenius' type kinetics at constant pr essure.