Past exam of the chemistry course of the year 4 of the natural sciences course of the University of Cambridge / 2022 / Interdisciplinary paper IDP1 / 1

Prefer a replacement that releases little reactive chlorine or bromine into the stratosphere: ideally omit those elements, or give the parent gas a short troposphere removal time compared with transport to the stratosphere. A carbon–hydrogen bond can permit rapid attack by the hydroxyl radical; other readily oxidized functionality can also shorten the atmospheric residence time. The degradation products must themselves avoid transporting long-lived reactive halogen to altitude. Merely retaining fewer chlorine atoms is less effective than preventing their delivery altogether.

Both chlorine and bromine participate in catalytic ozone destruction. Bromine is much more effective per delivered atom, by a factor of roughly 60 in the usual lower-stratospheric comparison; the precise effectiveness depends on chemical partitioning and location. Fluorine is largely trapped in very stable hydrogen fluoride and does not sustain an analogous ozone-destroying cycle. Thus short-lived gases without chlorine or bromine have the smallest direct ozone-depletion potential. Fluorination alone does not ensure a small climate impact.^[ref]

A small global warming potential requires both a small greenhouse gas radiative efficiency per unit emitted mass and a short atmospheric lifetime. Weak absorption in the terrestrial atmospheric window is desirable, particularly where absorption by existing gases is weak; strong carbon–fluorine vibrational bands can make even an ozone-safe substitute an efficient greenhouse gas. Rapid removal by lower-atmospheric chemistry limits the integrated burden, provided it does not generate abundant, long-lived radiatively active products. The atmospheric residence time and the absorption spectrum must therefore be assessed separately.

In a vertical-beam, effective-wavelength Beer-Lambert law approximation, the optical depth above altitude $z$ is $\tau (z)={\sigma }_{{\mathrm{O}}_2}{N}_{{\mathrm{O}}_2}(z)+{\sigma }_{{\mathrm{O}}_3}{N}_{{\mathrm{O}}_3}(z)$. Using centimetres consistently givesThe transmitted photon flux is proportional to $e^{-\tau }$. If the parent-gas absorption cross section and photodissociation yield are otherwise the same, they cancel in the ratio of photolysis rate coefficients:The corresponding fractions of the unattenuated beam are about $7.52\times 10^{-7}$ and $0.654$. Strong shielding by the overlying oxygen and especially ozone therefore makes destruction vastly faster higher in the stratosphere, even though the molecular absorption properties have not changed.

This numerical ratio uses the intended simplified radiation model. A real photolysis rate coefficient integrates wavelength-dependent actinic flux, absorption cross section and quantum yield. A nonvertical direct beam would use slant optical depth $\tau /\cos \theta$; diffuse scattering and the true solar spectrum would also matter. The supplied effective cross sections do not specify a unique broadband radiative-transfer calculation.

The global warming potential compares equal-mass pulses, while the tabulated greenhouse gas radiative efficiencies are per ppb. For a fixed emitted mass, the initial mixing ratio is inversely proportional to molar mass. The molecular formulas give approximately $M_r=151.39\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ for ${\mathrm{C}}_2{\mathrm{H}}_2\mathrm{C}{\mathrm{l}}_3\mathrm{F}$ and $M_{11}=137.36\mathrm{g}\mathrm{mo}{\mathrm{l}}^{-1}$ for $\mathrm{CC}{\mathrm{l}}_3\mathrm{F}$. Thus the ratio of mass-based greenhouse gas radiative efficiencies is $(0.24/0.26)(M_{11}/M_r)$.

In the standard one-box interpretation, the two quoted removal times represent independent first-order sinks acting on the burden. Their rates add, givingFor exponential pulse removal, the time-integrated abundance is proportional to $\tau (1-e^{-H/\tau })$. Dividing the replacement's forcing integral by the CFC-11 integral cancels the unknown carbon-dioxide reference integral:The finite-horizon factor for CFC-11 is important: $1-e^{-100/55}=0.8377$, not one. Omitting the molar-mass correction would incorrectly compare equal-ppb rather than equal-mass pulses.

This is about 76 times smaller than the stated CFC-11 value, because rapid tropospheric removal outweighs the fairly similar per-ppb greenhouse gas radiative efficiencies. It still represents appreciable warming per emitted mass. If the shorter lifetime alone is used as the troposphere-dominated approximation, the result is ${\mathrm{GWP}}_{100}\simeq 70.4$, close to the combined-rate result. If the two given lifetimes instead describe separate local compartments, an exact two-box calculation would also require exchange rates and burden partitioning; those are not supplied. The boxed result states the usual one-box assumption explicitly.

TODO: user-deferred biological component. Biological carbon uptake, storage and release are outside the current scope. The physical and ocean-chemistry explanation is given here; the deferred component means this is not a complete all-process answer.

There is no single first-order atmospheric lifetime for an added carbon dioxide pulse. Air–sea gas exchange and adjustment of the surface mixed layer act on years-to-decades scales; redistribution into the ocean interior takes centuries to millennia. These transfers partition carbon between atmosphere and ocean rather than making the entire added carbon inventory disappear. Dissolution also changes the ocean's carbonate speciation: conversion among dissolved carbon dioxide, bicarbonate and carbonate buffers the uptake, but provides a finite capacity at a given alkalinity. A substantial perturbation therefore remains airborne after the faster exchanges have adjusted.

Further removal involves dissolution of carbonate sediments and carbonate compensation over several thousand years, followed by the much slower silicate-weathering and burial pathway, typically tens to hundreds of thousands of years. The exact fractions and times depend on pulse size and model conditions. A thousand years exceeds the fast exchange times but not the complete ocean–solid-Earth adjustment time, so a residual atmospheric perturbation is expected. An intercomparison found a substantial long tail after ocean equilibration, with further carbonate neutralization on roughly 3–7 kyr scales.^[ref]

For a gas whose lifetime is much less than the selected horizon, the numerator of its global warming potential has nearly saturated: ${\int }_0^H{a}_i{m}_i(t)dt\simeq a_i{m}_i(0){\tau }_i$. The carbon-dioxide denominator continues to accumulate because of its long-lived response. Consequently a shorter horizon usually gives a larger GWP for this short-lived substitute; a longer horizon gives a smaller GWP. If the horizon becomes comparable to, or shorter than, the substitute's lifetime, the numerator also depends strongly on the horizon and cannot be replaced by its infinite-time limit.

The horizon is a value choice, and integrated forcing is not the same as temperature at a chosen future date. Equal-GWP pulses can therefore have different near-term warming and long-term temperature paths. The result also depends on greenhouse gas radiative efficiency, background concentrations, lifetime estimates and which indirect chemical effects or feedbacks are included. A pulse-based metric does not by itself describe a continuing emissions trajectory, nor does it measure ozone depletion or local air-pollution impacts. Comparisons should state the horizon, the emission scenario and the chosen climate outcome.^[ref]