Activation Energy

Question

The rate constant for the reaction of ozone with oxygen atoms was determined at four temperatures. Calculate the activation energy and frequency factor A for the reaction O(g) + O3(g) -> 2 O2(g) given the following data:

T (K) k(M^-1 s^-1)

250 1.72 x 10^6

275 2.69 x 10^6

300 5.02 x 10^6

325 8.51 x 10^6

Answer 1

We need to use the Arrhenius equation k = Ae^-Ea/RT, where k = rate constant, Ea = activation energy, R the gas constant in joules/mole-K., and T = absolute temperature.

As we are given the rate constant for several different temperatures, and we have two unknowns, we can get two equations with two unknowns and solve for them.

1.72 x 10^6 = A e^-Ea/8.314 x 250 and

2.69 x 10^6 = A e^-Ea / 8.314 x 275

Take the natural log of both sides for each equation. to get

14.35 = lnA x -Ea/ 2078.5

14.81 = lnA x -Ea/ 2286.4

Solve for lnA in the first equation and put the result into the second equation.

The resulting equation will have only one unknow, Ea, that can be solved for.

Once having Ea,use any equation and solve for lnA then take the antilog of both sides to determine A.

I will leave the rest for you to do.