You are working for a manufacturer of cleaning supplies and are investigating the use of hydrogen peroxide, H₂O₂, as a stain removal agent in laundry detergent. However, the water available in the market test region contains an iron oxide component and you want to know if this will interfere with the use of hydrogen peroxide. The activation energy for the decomposition of hydrogen peroxide is 75.3 kJ · mol^–1. In the presence of an iron oxide catalyst the activation energy for decomposition was found to be 32.8 kJ · mol^–1. By what factor does the rate of decomposition increase at 25°C in the presence of the catalyst if all other factors are equal?

ANTICIPATE Because the activation energy for the catalyzed reaction is much lower, you should expect a large increase in the decomposition rate.

PLAN Because the rate constant is related to the activation energy according to Eq. 1b of Topic 7D (k_r = Ae^–E_a/RT), write an expression for the ratio of the rate constants at the two temperatures, k_r2/k_r1, and solve the expression for k_r2 in terms of k_r1.

What should you assume? Assume that the pre-exponential factor for decomposition with and without catalyst is the same.