= Solution
Under the proposed steady balance,
$$
k_9[\mathrm{Cl}][\mathrm{CH_4}]=k_{10}[\mathrm{OH}][\mathrm{HCl}],
\qquad
[\mathrm{OH}]=\frac{k_9[\mathrm{Cl}]x_{\mathrm{CH_4}}}{k_{10}x_{\mathrm{HCl}}}.
$$
The air <number density> cancels from the ratio. Therefore
$$
\boxed{[\mathrm{OH}]=\frac{(10^{-14})(1.2\times10^5)(0.6\times10^{-6})}
{(4.5\times10^{-13})(1.1\times10^{-9})}
=1.45\times10^6\ \mathrm{molecules\,cm^{-3}}.}
$$
The <reservoir relaxation test for a chemical steady state> gives a <hydrogen chloride> relaxation time of $1/(k_{10}[\mathrm{OH}])=1.53\times10^6\ \mathrm s\simeq17.7$ days. <Hydrogen chloride> is a reservoir rather than a rapidly equilibrating <radical>. A steady state is plausible only if <chlorine> abundance, <methane>, <hydroxyl radical> and transport vary slowly compared with several weeks. \b[It is doubtful during rapid vortex breakdown and reservoir reformation], precisely when production and mixing are changing. The numerical <hydroxyl radical> value is conditional on the steady-state hypothesis, not an independent measurement of <hydroxyl radical>.
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