Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2022 / Paper 3 / 42 / c / i

The dominant OH-to-HO${}_2$ pseudo-first-order rate is $k_5[{\mathrm{O}}_3]=90{\mathrm{s}}^{-1}$, corresponding to $0.0111\mathrm{s}$. Recycling HO${}_2$ through atomic oxygen and NO has rate $k_6[\mathrm{O}]+k_8[\mathrm{NO}]=0.0218{\mathrm{s}}^{-1}$, corresponding to $45.9\mathrm{s}$ for an individual HO${}_2$ radical. A fixed-total two-state exchange relaxes at the sum of forward and reverse rates, giving about $0.0111\mathrm{s}$ for the partition perturbation. Its fast partition is thereforeThis supports a steady-state approximation in chemical kinetics for rapidly recycled intermediates if the parent concentrations vary slowly. It does not by itself establish stationarity of the entire HOx family. The later source–termination estimate gives a family turnover time of about 16 hours, far longer than partition relaxation; a stationary absolute abundance additionally assumes sufficiently persistent radiation and background conditions. This is the distinction between fast family partition and slow family balance.