Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2021 / Interdisciplinary paper IDP1 / 1

Write $D=[\mathrm{C}{\mathrm{l}}_2{\mathrm{O}}_2]$ and $c=[\mathrm{ClO}]$. In the steady-state approximation for the dimer, chlorine peroxide chlorine peroxide formation is balanced by its two competing removal channels:The association event rate is $k_1[M]c^2$; the associated disappearance rate of chlorine monoxide is twice that value. Each successful photodissociation event produces two chlorine atoms after the subsequent fast fragmentation, and their return to chlorine monoxide consumes two ozone molecules. Thermal dissociation instead returns the dimer to two chlorine monoxide radicals without destroying ozone. Thus the chemical branching fraction for an ozone-destroying event is $f=J_2/(J_2+k_3[M])=0.7$, givingThis is the sunlit chlorine monoxide dimer cycle, with net conversion $2{\mathrm{O}}_3\to 3{\mathrm{O}}_2$. It assumes that the dimer relaxes rapidly, downstream fragmentation and chlorine–ozone reactions are sufficiently fast, and competing chlorine sinks can be neglected. Counting the formation event twice and then multiplying by two again would overestimate loss by a factor of two.

Low temperature favours association into the dimer and, especially, suppresses its thermally activated dissociation back to chlorine monoxide. More of the dimer can therefore follow photodissociation instead of the chemically unproductive thermal return. The supplied branching fraction is a local condition, not a temperature-independent universal yield.

Cold polar air also permits polar stratospheric clouds and efficient heterogeneous conversion of chlorine reservoirs into photolabile forms. The stratospheric polar vortex isolates and cools that air. Darkness permits activation and storage, but rapid catalytic ozone loss requires the return of sunlight. These chemical and meteorological conditions explain the springtime maximum; low temperature alone does not supply the photodissociation photons.

The two initial reservoirs each contain one chlorine atom, so complete activation supplies a total chlorine mixing ratio of $2.2\times 10^{-9}$. Under the specified approximation that active chlorine in sunlight is predominantly chlorine monoxide,The daytime loss is consequentlyFor twelve sunlit hours per day, the daily ozone decrement isThe full-day mean concentration loss is $5.269\times 10^5\mathrm{molecules}\mathrm{c}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$. Maintaining that rate would consume the initial ozone in about $79.1$ days. This is a fixed-active-chlorine estimate: reservoir reformation, transport and chlorine partitioning change during a real depletion event, and the approximation fails when insufficient ozone remains to recycle chlorine rapidly.

The initial ozone concentration is $(3\times 10^{-6})[M]=3.60\times 10^{12}\mathrm{molecules}\mathrm{c}{\mathrm{m}}^{-3}$. Over fifty days with twelve active hours per day, the required combined daytime rate isThe mixed chlorine-bromine ozone-loss cycle also consumes two ozone molecules per radical-pair reaction, so $L_{\mathrm{Br}}=2k_6[\mathrm{ClO}][\mathrm{BrO}]$. Subtracting the dimer contribution yieldsThe same result follows by assigning the dimer $1.897$ ppm of the fifty-day loss and the mixed cycle the remaining $1.103$ ppm. This uses the same daylight fraction for both cycles and retains the earlier fixed-ClO approximation. It estimates a sunlit BrO abundance, not the total inventory of bromine in all reservoirs.

Under the proposed steady balance,The air number density cancels from the ratio. ThereforeThe reservoir relaxation test for a chemical steady state gives a hydrogen chloride relaxation time of $1/(k_{10}[\mathrm{OH}])=1.53\times 10^6\mathrm{s}\simeq 17.7$ 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. 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.

Cooling can increase springtime ozone destruction by extending cold conditions favourable for polar stratospheric clouds, stratospheric chlorine activation and dimer stability. Removal of reactive nitrogen into settling particles can delay chlorine nitrate reformation. With sunlight and substantial available chlorine, the active period can become longer or stronger. Vortex breakup, transport and the declining halogen inventory also matter, so a colder year does not determine the ozone loss by temperature alone.

Outside the cold polar activation regime, cooling generally slows temperature-activated gas-phase ozone destruction and can increase ozone if other conditions are held fixed. This is a weaker, less universal conclusion in the lower stratosphere because transport and imported ozone are important. Enhanced sulfate-surface activation or unusually cold cloud-forming air can instead activate chlorine and reverse the purely gas-phase tendency. Distinguish a local chemical cooling effect from the dynamical response of the midlatitude ozone-column photolysis shielding.

In the upper stratosphere, cooling slows temperature-dependent odd-oxygen destruction, including $\mathrm{O}+{\mathrm{O}}_3\to 2{\mathrm{O}}_2$ and important catalytic reactions. With photochemical production otherwise fixed, the local steady ozone abundance tends to rise. This chemical response is one reason increasing carbon dioxide can enhance upper-stratospheric ozone while cooling that region. It is compatible with enhanced chemical depletion in cold activated polar air; the controlling regimes differ.^[ref]

For fluorine, the key is chemical sequestration, not an inability of free F to react. Fluorine atoms readily form very stable hydrogen fluoride through reaction with hydrogen-containing gases. Breaking hydrogen fluoride or regenerating a sustained free-fluorine radical population under ordinary stratospheric conditions is difficult, so an efficient analogous catalytic family is not maintained.

For iodine, the traditional approximation is limited delivery to the stratosphere. Many iodine source gases are short lived in the troposphere, and their reactive products are efficiently taken up or removed before slow large-scale ascent. This historically motivated omitting iodine from the major stratospheric chlorine/bromine budget. It does not establish that iodine atoms are intrinsically ineffective catalysts, or that stratospheric iodine is exactly zero.

Indeed, the blanket omission needs qualification even for this exam's date. Aircraft observations published in 2020 detected both IO and particulate iodine in stratospheric air and inferred continuing multiphase recycling and ozone loss. Gas/particle partitioning and measurement sensitivity must be considered together; a small gas-phase concentration alone can miss an active reservoir. Thus the traditional supply argument is the intended contrast with fluorine's stable-HF sink, but zero stratospheric iodine chemistry is not supported by those observations.^[ref]