,

,

where is the conversion fraction, is the inlet concentration (taken to be 10 moles/liter), is the universal gas constant (1.987 cal/mol K), and is the temperature (in kelvin).

Use the sliders to vary the activation energies for the forward () and reverse () reactions. Both of these activation energies are expressed in cal/mol.

This Demonstration plots the contour lines for the reaction rate either for exothermic reactions or for endothermic reactions . The equilibrium conversion is plotted versus the temperature (see the black curve, for which we have ). It can be easily shown that . Thus, for endothermic reactions, and , so and will increase monotonically with if you move along a horizontal line (i.e. at a constant conversion fraction). On the other hand, for exothermic reactions we have , thus we have along a horizontal line (i.e. at a constant value of ): (1) at low temperature and ; and (2) at higher temperature and . In conclusion, for an exothermic reaction, the reaction rate initially increases with increasing , reaches a maximum value when , then starts to decrease until it reaches the equilibrium conversion curve where . The loci of the points where are indicated by the gray dots and curve.