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Write the reacting terminus as $R-\mathrm{C}{\mathrm{H}}_2-\mathrm{CH}=\mathrm{C}{\mathrm{H}}_2$, where $R$ includes the pre-existing stereocentres and the intact $\mathrm{OC}{\mathrm{H}}_2\mathrm{C}(=\mathrm{O})\mathrm{NM}{\mathrm{e}}_2$ substituent. ozone undergoes 1,3-dipolar cycloaddition across the terminal alkene to give a molozonide. In a resonance description of ozone as ${\mathrm{O}}^{-}-{\mathrm{O}}^{+}=\mathrm{O}$, the alkene pi pair bonds to one terminal oxygen while the other terminal oxygen forms the second C–O bond and the ozone pi bond shifts onto its central oxygen. Cleavage of this unstable primary ozonide produces a carbonyl compound and a carbonyl oxide, which recombine to form the secondary ozonide. Reductive workup breaks the peroxide bonds and gives the carbonyl fragments $R-\mathrm{C}{\mathrm{H}}_2\mathrm{CHO}$ and formaldehyde.

Excess sodium borohydride also reduces the newly formed aldehyde: hydride attacks its carbonyl carbon, shifting the pi electrons onto oxygen, and the final acidic workup protonates the alkoxide. Thus the retained chain becomes $R-\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2\mathrm{OH}$. The terminal alkene carbon becomes formaldehyde and can be reduced to methanol; it is no longer part of the main product. This accounts for the one-carbon shortening of the retained skeleton.

The original amide carbonyl is present in both H and I and is not reduced under the ordinary borohydride workup. The existing stereocenters and benzyl ether are retained. Stopping the mechanism at an aldehyde, or deleting the amide C=O when reading the smaller printed scheme, would give the wrong product. The new terminal alcohol carbon is CH2 and therefore adds no stereocenter.

Ozone is bent, with two equivalent O–O bonds of approximate bond order $1.5$. Its useful localized orbital hybridization description is $s{p}^2$ at all three oxygens. Two hybrids at the central oxygen form sigma bonds and a third contains a lone pair; the three perpendicular p orbitals form a three-centre four-electron pi bond.

The three pi orbitals are bonding, nonbonding and antibonding, filled as ${\pi }_{\mathrm{b}}^2{\pi }_{\mathrm{nb}}^2{\pi }_{\ast }^0$. The terminal-centred nonbonding orbital is the Homo, conventionally $1a_2$; the delocalized antibonding orbital is the LUMO, $2b_1$. The two principal resonance structures, ${}^{-}\mathrm{O}-{\mathrm{O}}^{+}=\mathrm{O}$ and $\mathrm{O}={\mathrm{O}}^{+}-{\mathrm{O}}^{-}$, distribute the extra pi bond across the two links.

The 18 valence electrons comprise four sigma-bond electrons, ten in five sigma-framework lone pairs, and four in the pi system. This gives a paired ground-state model. More accurate treatments include electron correlation; the simple bond-order picture is not an exact charge-density calculation.^[ref]

The central carbon in carbon dioxide has two bonding directions and no lone pair, whereas the central oxygen in ozone has two bonding directions and one lone pair. In the VSEPR model, carbon dioxide therefore has a linear arrangement; ozone has an approximately trigonal-planar electron-domain arrangement but a bent atomic skeleton. Multiple bonding occupies one direction for this geometrical count. The extra central-oxygen lone pair, rather than a different number of atomic nuclei, creates the difference.

A warmer troposphere does not imply a warmer stratosphere: increased carbon dioxide can cool the middle and upper stratosphere by enhancing infrared emission. One direct kinetic effect is slower temperature-dependent destruction in the Chapman cycle, tending to increase upper-stratospheric ozone. Two indirect chemical effects can have the opposite sign. If the entry atmospheric cold trap warms, it can admit more water; reaction with an electronically excited oxygen atom then supplies more of the HOx family, enhancing catalytic ozone loss. In cold polar air, changes in water and temperature can favour polar stratospheric clouds, whose surfaces activate halogen reservoirs and can enhance ozone destruction when sunlight returns. These are conditional pathways, not a universal sign for total ozone: cold-trap temperature and circulation, halogen abundance and altitude all matter. Methane oxidation can also supply stratospheric water.^[ref]

For one specified channel, the photolysis rate coefficient isIt depends on spectral actinic flux, absorption cross section, and channel quantum yield. Solar zenith angle, season, overhead absorbers, clouds and aerosol scattering affect the photon field; branching and collisional quenching affect the chemical yield. Absorption alone does not guarantee the desired dissociation.

Curve A is oxygen photodissociation; curve B is ozone photodissociation. Molecular oxygen needs relatively short-wavelength ultraviolet photons, which are strongly screened at lower altitudes, so its rate increases steeply with height. Ozone can dissociate using longer wavelengths that penetrate much further, producing the much larger, less height-sensitive rate shown by B. The plotted quantity is a first-order coefficient with units ${\mathrm{s}}^{-1}$, rather than a bimolecular rate constant.

With $[{\mathrm{H}}_2]=5\times 10^{-6}[\mathrm{M}]$, a reaction of an electronically excited oxygen atom with hydrogen gives one OH and, after rapid H conversion, one HO${}_2$. The radical source becomesThis is about 4.75 times the original source. Holding water, oxygen, NO and radiation fixed keeps the fast radical partition approximately unchanged, while bimolecular termination makes total radical abundance scale as $\sqrt{S}$. Thusabout 2.18 times the original catalytic loss. This predicts a stronger ozone-loss tendency within the specified stationary box model, not a numerically determined percentage change in the ozone layer. The latter requires coupled odd-oxygen production, changing ozone concentrations, transport and the longer-term water budget; those have been held fixed here.

The fast family is NO${}_3$ plus N${}_2$O${}_5$. Put $x=[\mathrm{N}{\mathrm{O}}_3]$, $y=[{\mathrm{N}}_2{\mathrm{O}}_5]$, and freeze the supplied parent concentrations while definingThe two equations are $\dot{x}=S-(a+d)x+by$ and $\dot{y}=ax-(b+c)y$. Their stationary solution isHere $a=15.67$, $b=0.0690$, $c=3.84\times 10^{-7}$ and $d=1.919$ in inverse seconds; $S=5.93\times 10^6\mathrm{molecules}\mathrm{c}{\mathrm{m}}^{-3}{\mathrm{s}}^{-1}$. Reversible storage must not be counted as permanent family loss: only the $ac/(b+c)$ term represents the association route followed by hydrolysis.

Closed-family interconversion has ${\tau }_{\mathrm{eq}}=1/(a+b)=0.0635\mathrm{s}$. Including the supplied losses, the two linear relaxation times are approximately $0.0566\mathrm{s}$ and $133\mathrm{s}$, from the eigenvalues of $\left(\begin{array}{cc}a+d& -b\\ -a& b+c\end{array}\right)$. Fast exchange is therefore well separated from the slower total-family adjustment. However, NO is consumed by ozone on $1/(k_1[{\mathrm{O}}_3])\simeq 59.8\mathrm{s}$, comparable to and shorter than the family relaxation. Thus the quoted stationary concentration is justified for a maintained background or a sufficiently slowly varying quasi-stationary environment; it is not automatically reached in an isolated parcel initialized with the supplied composition. NO auto-oxidation is negligible at this concentration. Additional organic losses of NO${}_3$, if present, would need to be added to the model.

At night, nitrate radical addition and ozone attack are relevant oxidations of isoprene; direct daytime photochemistry is absent, though small OH sources can still exist. The nitrate-containing products identify the NO${}_3$-addition route. Add NO${}_3$ to the terminal carbon next to the methyl-substituted alkene carbon, producing a nitrooxy substituent and an allylic radical. Resonance moves the radical to the far terminal carbon while shifting the double bond. Oxygen trapping gives a peroxy radical with the carbon skeletonA nitrate-forming termination branch, for example the organic-nitrate branch of reaction with NO, replaces the terminal peroxyl group by a nitrate ester, giving ${\mathrm{O}}_2\mathrm{NOC}{\mathrm{H}}_2-\mathrm{C}(\mathrm{C}{\mathrm{H}}_3)=\mathrm{CH}-\mathrm{C}{\mathrm{H}}_2\mathrm{ON}{\mathrm{O}}_2$. An alternative branch forms an alkoxy radical, such as peroxy-radical reaction with NO${}_3$ producing RO${}^{\bullet }$, NO${}_2$ and O${}_2$. Reaction of the terminal CH${}_2$O${}^{\bullet }$ group with O${}_2$ then gives an aldehyde plus HO${}_2$, producing ${\mathrm{O}}_2\mathrm{NOC}{\mathrm{H}}_2-\mathrm{C}(\mathrm{C}{\mathrm{H}}_3)=\mathrm{CH}-\mathrm{CHO}$. These are covalent O–NO${}_2$ ester groups, not C–NO${}_2$ nitro groups. The delocalized radical can be trapped after conformational change, so this mechanism does not require one universal alkene geometry for both product channels. Product structures alone do not fix a unique branching ratio.

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.

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.

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.

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.

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]

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.

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.

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]

Methane reaching the stratosphere is oxidized and is an important source of stratospheric water vapor. That water can feed HOx radical family chemistry and alter radiative cooling and polar-cloud conditions. Methane also converts chlorine atoms into hydrogen chloride, opposing some chlorine-driven ozone loss. These effects compete: increasing methane does not have one universal ozone sign at every altitude and latitude.

Methane consumes hydroxyl radicals during its initial oxidation and therefore influences atmospheric oxidative capacity and the removal of other trace gases. Subsequent oxidation generates peroxy radicals. In the presence of sufficient nitrogen monoxide, these convert nitrogen monoxide to nitrogen dioxide without consuming ozone, allowing net photochemical ozone production. At low nitrogen monoxide, peroxide formation and ozone-destroying radical reactions compete. Methane oxidation ultimately produces carbon monoxide and carbon dioxide; the sign and rate of the associated ozone response depend on the radical/nitrogen oxides regime, not methane alone.

A humidity assumption is necessary: warming does not by itself specify how much water is available. At fixed relative humidity, the Clausius-Clapeyron equation gives the first-order vapor pressure responseIf water abundance is approximated as proportional to $e_s$, the usual first-order estimate is a $26.7\%$ increase in hydroxyl radical production. Integrating the constant-latent-heat expression instead of linearizing gives $e_s(289)/e_s(285)=\exp [(45050/8.314)(1/285-1/289)]=1.3010$.

There is a small but explicit concentration correction when the square brackets are literal molecules per volume. Since $[{\mathrm{H}}_2\mathrm{O}]=\varphi e_s/(k_{B}T)$ and $P_{\mathrm{OH}}=2k[\mathrm{O}({}^{1}D)][{\mathrm{H}}_2\mathrm{O}]$,The corresponding finite-change concentration result is $(285/289)(1.3010)-1=0.2830$. The $25.3\%$ linear concentration estimate and the $26.7\%$ vapor pressure approximation express different stated approximations; neither follows without a humidity condition.

Extra water increases the fraction of oxygen singlet D atoms reacting to form hydroxyl radicals rather than being collisionally quenched and recycled into ozone. In clean, low-nitrogen oxides air this tends to increase ozone loss. In nitrogen oxides-rich air, increased hydroxyl radical can accelerate precursor oxidation and ozone production, while radical termination also changes. Greater hydroxyl radical production therefore does not imply a universally positive or negative ozone response.

The lost ozone-column photolysis shielding is $\Delta N=20(2.69\times 10^{16})=5.38\times 10^{17}\mathrm{molecules}\mathrm{c}{\mathrm{m}}^{-2}$, so its optical-depth decrement is $\sigma \Delta N=0.0538$. Under the stipulated effective-cross-section Beer-Lambert model, the transmitted photodissociation flux increases by $\exp (0.0538)$.

The short-lived oxygen singlet D atom satisfies $[\mathrm{O}({}^{1}D)]\simeq J_{{\mathrm{O}}_3}[{\mathrm{O}}_3]/(k_q[M])$ when quenching dominates. At fixed local ozone, water and air density, hydroxyl radical production is proportional to $J_{{\mathrm{O}}_3}$. ConsequentlyA linear optical-depth approximation would give $5.38\%$. A realistic calculation integrates the wavelength-dependent absorption cross section, quantum yield and actinic flux; clouds and multiple scattering modify the simple transmitted-beam model.

Ozone change can also alter the radiative temperature structure, water vapor and circulation, thereby changing the water reaction channel and the supply of ozone/precursors to the troposphere. If the held-fixed tropospheric ozone assumption is relaxed, altered ozone itself changes the photochemical source of oxygen singlet D atom. These are additional feedbacks, distinct from the isolated UV-transmission calculation above.