Question

ClO is a reactive gas that is involved in the destruction of the ozone layer in the stratosphere. The rate constant, k, for the decomposition of the gas into Cl2 and O2 at 298 K is 7.2 x 109 M-1 s-1and the activation energy is 13.2 kJ/mol.

1. Write the balanced equation for the decomposition reaction.

2. Write the rate law for the reaction and explain how you determined the order of the reaction.

3. What is the rate constant of this reaction at 217 K, the temperature in the lower stratosphere?

4. Does the value of the rate constant at 217 K compared to the value of the rate constant at 298 K make sense? Explain.

Answer 1

The reaction for the decomposition of ClO gas is

Now, there are one Cl and one O on the left and two Cl and two O on the right. Hence, to balance the reaction, we multiply 2 on ClO.

Hence, the balanced reaction for the decomposition is

The rate law for the reaction can be written as

Where at  

We know that rate of the reaction has a unit of . In our case the rate constant has a unit of .

Hence, the unit cancellation for the rate equation will be

Hence, clearly, the order of the reaction is 2.

We already know that the activation energy of the reaction is .

We can take the rate constant at as

To find the rate constant () of the reaction at , we can use the Arrhenius equation of the following form

Hence, the rate constant of the reaction at the lower atmosphere at T = 217 K is about .

Yes, the value of rate constant at T=217 K does make sense because, as the temperature has dropped from T = 298 K to T = 217 K, the rate constant has also dropped by a factor of about 7. It is because at lower temperature, less fraction of the reactants have enough kinetic energy to overcome the activation energy barrier as predicted by the Arrhenius equation.