Radical clock reactions involve a competition between a unimolecular radical reaction with a known rate constant and a bimolecular radical reaction with an unknown rate constant to produce unrearranged and rearranged products. The rearrangement of an unrearranged radical, U•, proceeds to form R• (the clock reaction) with a known rate constant (k). These radicals react with a trapping agent, AB, to form the unrearranged and rearranged products UA and RA, respectively.
The yield of the two products can be determined by gas chromatography (GC) or nuclear magnetic resonance (NMR). From the concentration of the trapping agent, the known rate constant of the radical clock, and the ratio of the products, the unknown rate constant can be indirectly established.
If a chemical equilibrium exists between U• and R•, the rearranged products are dominant. Because the unimolecular rearrangement reaction is first order and the bimolecular trapping reaction is second order (both irreversible), the unknown rate constant (k) can be determined by: