What is the activation energy of this reaction?

Question

A student collected time (t) and concentration ([A]) data at 295 K for the reaction 2A→B.

The student ran the same reaction at a different temperature and measured a different reaction rate, with the following results:

T (K)	k (s^-1)
295	0.0125
325	0.0357

I used The Arrhenius Equation (k=Ae^(−Ea/RT)) to solve for this problem, but I am not sure what to plug in for the frequency factor (A).

Answer 1

When you have two sets of data (k1, T1 and k2, T2) you don't need the frequency factor as you can use a modification of the Arrhenius equation, as follows:

ln (k2/k1) = - Ea/R (1/T2 - 1/T1)

ln (0.0357 / 0.0125) = -Ea / 0.008314 (1/325 - 1/295) ... note to change R to units of kJ/Kmol

1.0494 = -Ea / 0.08314 (0.003077 - 0.003390)

1.0494 = 3.13x10^-4Ea / 0.08314

Ea = 2.79 kJ/mol

(be sure to check of of the math)