This Demonstration shows the temperature trajectory that maximizes the reaction rate of a reversible reaction.
are the pre-exponential Arrhenius constants for the forward and reverse reactions,
are the energies of activation,
is the universal gas constant,
is the absolute temperature,
are the initial concentration of the reactants, and
is the conversion of species
. The temperature function that gives the maximum reaction rate satisfies the condition
at each point in time; this function has an analytical solution for this reaction 
the initial concentrations of
are taken equal to 0.5, and 1.0.
One complication can occur: for low conversions,
may have a value sufficiently small enough to make
; then the equation for
gives a value
(or negative); in practice the temperature is limited by the reactor materials or the catalyst's physical properties. The optimum temperature profile and the concentration of the reactants as a function of time are shown for user-set values of reaction time, maximum allowable temperature, and parameters