Value of mixing ratio and rate constant in Chapman mechanisn

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?

• 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. – Martin - マーチン Apr 22 '16 at 12:22