Past exam of the chemistry course of the year 1 of the natural sciences course of the University of Cambridge / 2023 / Paper 1 / 5 / c / iv / Solution

Let $r_i$ be the event rate for step $i$, soThe free radical balances, including the factors of two for initiation and termination, areThus $r_2=r_3$ and $r_1=r_4$, givingBoth propagation events form hydrogen chloride, soThe orders are one in hydrogen, one half in chlorine and three halves overall, with $k_{\mathrm{obs}}=2k_2\sqrt{k_1/k_4}$ when the observed rate is HCl formation. If the rate is instead defined as the stoichiometrically normalized reaction rate, half that formation rate, the prefactor lacks the factor two. The bath concentration cancels because the same M-assisted initiation and recombination control the free radical pool. The result does not require $k_2=k_3$; different free radical concentrations make their steady fluxes equal. For molar concentration, $k_{\mathrm{obs}}$ has units $\mathrm{d}{\mathrm{m}}^{3/2}\mathrm{mo}{\mathrm{l}}^{-1/2}{\mathrm{s}}^{-1}$.