How do I solve this AP Chemistry problem on catalysts?

Question

 A famous chemical demonstration is the "magic genie" procedure, in which hydrogen peroxide decomposes to water and oxygen gas with the aid of a catalyst. The activation energy of this (uncatalyzed) reaction is 70 kJ/mol. When the catalyst is added, the activation energy (at 20°C) is 42 kJ/mol. Theoretically, to what temperature (°C) would one have to heat the hydrogen peroxide solution so that the rate of the uncatalyzed reaction is equal to the rate of the catalyzed reaction at 20°C? Assume the frequency factor A is constant and assume the initial concentrations are the same.

Answer 1

Maria,

The relevant equation (a mathematical form you will see lots more, the exponential) is:

R = A exp (-.delta.H/RT) where R is overall rate, A is the frequency factor, .delta.H is the activation energy , R is the Universal gas constant, and T is temperature in K (please note, NOT in .degrees.C !).

So, set your two expressions of .delta.H/RT equal to each other, and solve for the missing T (then convert it back to .degrees.C).

Myself, I wouldn't want to be in the lab with you, if you were trying to determine the temperature experimentally. 215C for your solution will likely convert you into one of the reactants!