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 / a / i / Solution

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.