 Solution

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.