Chemistry - Why does free chlorine in the stratosphere lose its ozone-depleting potential after about 100,000 reactions?

Solution 1:

Since the stratosphere is nowhere near a closed system, a chlorine atom will eventually leave it. Look at the phrasing again:

It is estimated that one chlorine atom can destroy over 100,000 ozone molecules before it is removed from the stratosphere.

It is not stated, that it looses its potential, it just leaves the region, where there is sufficient ozone concentration.

In a closed system, the catalytic cycle would continue until the ozone concentration is small enough, that the chance of chlorine atoms recombining is bigger.

Thanks to Nicolau's comment I decided to further look into the issue. Also qwersjc gave some valuable insights. For further reading I suggest, the following sources:

• http://www.nobelprize.org/nobel_prizes/chemistry/laureates/1995/ (overview)
• Nobel Lecture by S. Rowland (Free Access)
• Stratospheric Chlorine: a Possible Sink for Ozone. R. S. Stolarski, R. J. Cicerone; Canadian Journal of Chemistry, 1974, 52(8): 1610-1615. (Open access)
• Original Paper by M. J. Molina and F. S. Rowland; Nature 249, 810 - 812 (28 June 1974) (Might not be free), reprint on ozone.unep.org

The Ozon Cycle

The ozone cycle is what protects us from quite dangerous UV-B radiation ($M$ is an inert Air molecule like $\ce{N2}$): $$ \ce{O2 ->[h\nu] O + O} \\ \ce{O + O2 ->[<M>] O3}\\ \ce{O3 ->[h\nu] O + O2} $$

The Troublemakers

The main reason for chlorine atoms in the stratosphere is man made. Chlorofluorocarbons were very common in many products. These molecules are colourless and water-insoluble. Diffusion taking its course the end up in the stratosphere, where they may undergo dissociation. $$\ce{CCl3F ->[h\nu] Cl + CCl2F}$$ So the main problem is, that free chlorine radicals are produced in the stratosphere. Also these CFCs have a lifetime in the stratosphere of up to 150 years.

There are some natural sources (of close to insignificant importance) that also produces free Chloride Radicals, i.e. volcanic eruptions. Those may transport Hydrochloride into the stratosphere, where it can react with the Hydroxide radical: $$\ce{HCl + OH -> Cl + H2O}$$

Removal of Chlorine

There are several steps involved, that lead to the removal of Chlorine from the stratosphere. Basically it will stay there for quite a while and cause significant damage. The stratosphere is very dry and water-soluble compounds, like HCl, will not be washed out quickly. In order to leave the stratosphere, the chlorine atoms or compounds therefore have to be near the troposphere.

Probably the most important reaction is with methane forming Hydrochloride, which may the be washed out by water (causing at least a part of acid rain nevertheless). $$\ce{Cl + CH4 -> HCl + CH3}$$ The likeliness of this event is about 1000 times smaller than colliding with another ozone.

However eventually, after about two years (a number I picked up on the way), a chlorine will leave the stratosphere. In the troposphere is more water present, so Hydrochloric acid will be formed and washed out.

In our estimates, termination of the Cl--ClO chain results from a downward diffusion of the longer lived species in the chain (HCl, ClO) and eventual removal by tropospheric process. From: Nature 249, 810-812 (28 June 1974).

There are also a number of reactions that decrease the potential of Chlorine radicals. $$\ce{ClO + NO2 -> ClONO2}\\ \ce{ClO + O2H -> ClOH + O2}\\ ...$$

However these also form reservoir molecules that might diffuse back to the stratosphere.

The calculations behind this are rather complex and use a wide variety of empiric data along with complex models.

I think there is still a lot of research going on in this area, considering more molecules like $\ce{CO2}$ and other greenhouse gases, as well as global climate change.

The Nobel lecture (1995) closes with the following remarks and we can only hope that this holds true:

However, with the limitations just expressed, the threat of extensive further stratospheric ozone depletion during the 21st century appears to be under control.

Solution 2:

According to Wikipedia, Martin is correct; a chlorine molecule, being slightly heavier than oxygen, will eventually be transported out of the ozone layer back to the troposphere (taking approximately 2 years to do so). Additionally, presence of other atoms in the ozone layer have a small chance of destroying the radical chlorine, causing it to form $\ce{HCl}$ or $\ce{ClONO2}$.

So most likely this estimate is based on some math crunching between the time-frame that the chlorine is in the ozone, the probabilities of chance reactions, and the rates/probabilities of these reactions.