Question

1. The rate constants for the reactions of atomic chlorine and of hydroxyl radical with ozone are given by 3 x 10^-11 e-^250/T and 2 x 10^-12 e^-940/T, where T is the Kelvin temperature. Calculate the ratio of ozone destruction by these catalysts at 20 km, given that at this altitude the average concentration of OH is about 100 times that of Cl and that the temperature is about -50°C. Calculate the rate constant for ozone destruction by chlorine under conditions in the Antarctic ozone hole, when the temperature is about -80°C and the concentration of atomic chlorine increases by a factor of one hundred to about 4 x 10⁵ moleccm^-3.

Answer 1

The reaction rate of atomic chlorine with O3 is given by Rate = [Cl][O3]3x10- 11e -250/223 = 9.78-12[Cl][O3]. The reaction rate of OH with O3 is given by Rate = [OH][O3]2x10-12e -940/223 = 2.95-14[OH][O3]. If we take the ratio of these two rates, we get that the ratio of the reaction with Cl to the reaction with OH is given by 330x[Cl]/[OH]. We are told that the concentration of OH is approximately 100x that of Cl, so the end result is that the reaction with Cl is 3.3 times faster than the reaction with OH.

The reaction rate constant  of atomic chlorine with O3 is given by Rate constant = 3x10- 11e -250/193.