In the Chapman mechanism (which tells about the activities of ozone in the stratosphere), there is a equation for the lifetime ($\tau_{\ce{O}}$) of an oxygen atom, $\ce{O}$ against conversion to ozone, $\ce{O3}$, through a certain reaction is given as $$\tau_{\ce{O}} = \frac{1}{k_2 C_{\ce{O_2}}n_a^2},$$ where $k_2$ is the rate constant of a reaction involving consumption of $\ce{O2}$ to form $\ce{O3}$, $$\ce{O + O2 + M -> O3 + M},$$ $\ce{M}$ is a third body present during the reaction. $C_{\ce{O2}}$ is the mixing ratio of $\ce{O2}$ (which is given as $0.21~\mathrm{mol/mol}$), $n_a$ is the air number density.
Source: Daniel J. Jacob: Introduction to atmospheric Chemistry. 1999, To be published. Chapter 10.

I am confused regarding this mixing ratio of $\ce{O2}$. Shouldn't be this value in the stratosphere different from that in troposphere?

Also, regarding $k_2$, nothing is mentioned about how and where this was measured. I mean if the value of $k_2$ is derived through laboratory experiments, then how reliable is this value for the reactions happening in the stratosphere?

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    $\begingroup$ 1. The calculations you refer to are only valid within the "low-pressure limit". 2. The steady state approximation fails, as it overestimates the density of the ozone layer by at least a factor of two. 3. It is explicitly stated that "in the lower stratosphere, a steady state solution [...] would not [...] be expected [...]". 4. The kinetics of certain reactions are probably not so much influenced by gravity as some of the other necessary simplifications, so conducting the experiments in a lab probably yields very reliable results as opposed to the theory. $\endgroup$ – Martin - マーチン Apr 22 '16 at 12:22

The entire stratosphere lies within the "homosphere", where the composition of gases is dominated by mixing processes and the atmosphere is thus homogenous. This reaches up to about 100 km, whereas the stratosphere doesn't go any higher than about 50 km.

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