Optimal Temperature Policy for a Reversible Reaction

Initializing live version
Download to Desktop

Requires a Wolfram Notebook System

Interact on desktop, mobile and cloud with the free Wolfram Player or other Wolfram Language products.

This Demonstration shows the temperature trajectory that maximizes the reaction rate of a reversible reaction.


For the reaction

, the rate is


with and ,

where and are the pre-exponential Arrhenius constants for the forward and reverse reactions, and are the energies of activation, is the universal gas constant, is the absolute temperature, , , , and 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 [1]




, and


the initial concentrations of and 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 and .


Contributed by: Clay Gruesbeck (December 2013)
Open content licensed under CC BY-NC-SA




[1] G. F. Froment, K. B. Bischoff, and J. de Wilde, Chemical Reactor Analysis and Design, 3rd ed., Hoboken, NJ: Wiley, 2011.

Feedback (field required)
Email (field required) Name
Occupation Organization
Note: Your message & contact information may be shared with the author of any specific Demonstration for which you give feedback.