= Solution
Assume a hydrogen-helium <perfect gas> with mean particle mass $2.3m_H$, <Jupiter> gravity $g\simeq24.8\,\mathrm{m\,s^{-2}}$, and mixing over one <atmospheric scale height>. At $T=1000\,\mathrm K$,
$$
H=\frac{k_BT}{2.3m_Hg}\simeq1.45\times10^5\,\mathrm m.
$$
The <eddy mixing time> is $\tau_{\rm mix}\simeq H^2/K_{zz}$. A <chemical quench level> at one bar requires $\tau_{\rm mix}\lesssim\tau_{\rm chem}=10^5\,\mathrm s$, hence the <vertical eddy diffusion coefficient> must be of order
$$
\boxed{K_{zz}\gtrsim2.1\times10^5\,\mathrm{m^2\,s^{-1}}=2.1\times10^9\,\mathrm{cm^2\,s^{-1}}.}
$$
The number depends quadratically on the assumed mixing length; using a fraction of $H$ reduces it accordingly.
Above the <chemical quench level>, neglect photochemistry, condensation, and molecular diffusion. The <quenched atmospheric mixing ratio> $f_A=n_A/n$ is approximately constant, while the <number density> is
$$
\boxed{n_A(z)=f_A\frac{p_q}{k_BT}e^{-(z-z_q)/H}.}
$$
Thus the abundance fraction is frozen, but the absolute <number density> falls with <pressure> and altitude. Examples are <carbon monoxide–methane quenching>, through $\mathrm{CO}+3\mathrm H_2\rightleftharpoons\mathrm{CH}_4+\mathrm H_2\mathrm O$, and <nitrogen–ammonia quenching>, through $\mathrm N_2+3\mathrm H_2\rightleftharpoons2\mathrm{NH}_3$.
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