Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Interdisciplinary paper IDP1 / 3 / b

The profile shows a low-ozone mixed layer up to approximately 2 km, with roughly 30 ppb ozone, and an overlying free-tropospheric value of roughly 50 ppb. The rise occurs through a transition layer extending to about 2.8 km, so these are approximate regime readings, not exact values for every altitude. The horizontal axis is already a mixing ratio; it does not provide a number density without additional air-density information.

Excited $\mathrm{O}({}^{1}D)$ has two competing fates. Collisional deactivation returns ground-state oxygen, which reforms ozone rapidly; reaction with water instead gives net ozone loss and two OH radicals. The chemical branching fraction for the latter isThus only about 4.92% of these ozone photolyses directly lead to the specified net chemical loss; treating every photodissociation as permanent removal would overestimate the sink. The corresponding first-order rate is $J_1{f}_w=9.8361\times 10^{-7}{\mathrm{s}}^{-1}$. Converting the given hydroperoxyl mixing ratio to a concentration gives $[\mathrm{H}{\mathrm{O}}_2]=20\times 10^{-12}[\mathrm{M}]=4.4\times 10^8\mathrm{c}{\mathrm{m}}^{-3}$, so $k_4[\mathrm{H}{\mathrm{O}}_2]=9.6800\times 10^{-7}{\mathrm{s}}^{-1}$.

For a well-mixed marine atmospheric boundary layer of depth $H=2\times 10^5\mathrm{cm}$, the downward surface flux is $v_{\mathrm{dep}}[{\mathrm{O}}_3]$. Dividing by the layer volume per unit area gives a first-order dry deposition rate $v_{\mathrm{dep}}/H=7.5\times 10^{-7}{\mathrm{s}}^{-1}$. The air density cancels on expressing the entire balance in ozone mixing ratio $\chi$:At steady state, with $P_{\chi }=0.25/3600\mathrm{ppb}{\mathrm{s}}^{-1}$,The effective removal time is about 4.28 days. This calculation assumes a uniform layer of the diagnosed depth, fixed chemical conditions and a local time-independent balance.

The observed value is about 4 ppb higher than the local chemical–dry deposition balance predicts. Entrainment from the ozone-richer free troposphere adds a term $(w_e/H)({\chi }_{\mathrm{FT}}-{\chi }_{\mathrm{BL}})$; horizontal Advection can likewise import ozone or longer-lived precursors from other regions. Time dependence, including the day–night cycle of photodissociation and changes in mixing depth, is also omitted. The approximately four-day model adjustment time means that air arriving at the measurement location need not have attained the assumed local steady state. These transport and history terms can raise ozone without changing the given local chemical constants.