558 12 Chemical Reaction Mechanisms I: Rate Laws and Mechanisms
which reproduces the empirical rate law with the following expressions for the empirical
parameters:kak 2(
k 1
k′ 1) 1 / 2
(12.5-8a)kbk′ 2
k 3(12.5-8b)Exercise 12.18
Verify Eqs. (12.5-6) and (12.5-7).Photochemical Chain Reactions
The energy to break the Br–Br bond in the initiation step of a chain reaction can be
supplied by ultraviolet light instead of by an inelastic molecular collision.Exercise 12.19
The Br–Br bond energy in Table A.9 of Appendix A is 193 kJ mol−^1. Calculate the minimum
frequency and maximum wavelength of light with sufficient energy per photon to break a
Br–Br bond.The initiation step and the termination step of the photochemically initiated reaction
of H 2 and Br 2 are(1) Br 2 +hν−→2Br
(1′) 2Br−→Br 2(12.5-9)
where we use the expression for the energy of a photon,hν, as a symbol for the photon.
The rest of the mechanism is just as in Eq. (12.5-3). The termination reaction is the
same as before.The Laws of Photochemistry
Photochemical reactions are described by two empirical laws. The first is theGrotthuss–
Draper law, which states that only absorbed radiation is effective in producing a pho-
tochemical change. A large intensity of incident light will not produce a photochemical
effect if none of it is absorbed. The second law is theStark–Einstein law of photochem-
ical equivalence, which states that for each photon absorbed, one molecule undergoes
the initial photochemical process. With high-intensity laser light a molecule can absorb
several photons in a single photochemical process, and this provides an exception to
the Stark–Einstein law.^20(^20) See, for example, L. Li, M. Wu, and P. M. Johnson,J. Chem. Phys., 86 , 1131 (1987).