By Claude F. Bernasconi
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Additional info for Relaxation Kinetics
3 (1-3). By using Castellan's determinant as the starting point it is also relatively easy to obtain explicit expressions for the 1/T values if some steps equilibrate much more rapidly or much more slowly than others. The mathematically unsophisticated reader may, however, feel more comfortable with the procedures outlined in the following section, which are based directly on the principles outlined in Chapter 3. 8) *-l ® ® serves well to illustrate how the principles discussed in Chapter 3 can be applied and extended to systems comprising more than three states.
Both schemes are of such general interest that a detailed discussion is amply justified. T h e following treatment is to a large extent based on a paper by Eigen (9) but is somewhat more detailed and explicit where this was felt desirable for the sake of understanding and clarity. , H + is merely a "spectator," not a catalyst. 64 is a three-state system and thus is characterized by two relaxation times. They are derived in the usual way, that is, by setting u p two linearized rate equations and solving for Eqs.
15). However, Eq. 56 provides J_ T 2 Π* = *l(^A + *ι*2(*Α + CB) = ^B) + *-l *-l + *l(*A + + k_ "2 ^B) which is equivalent to Eq. 15. B. k2 + k_2 » kx(cA + cB), k_x In analogy to case A we use Eq. 49 to obtain 1/ Tl = k2 + * . 58) Λ2 ~T Λ _ 2 Needless to say Eqs. 1. C. £_! + k2 » kx(cA + cB), k_2 In this common situation C is frequently referred to as a "steady state" or "stationary state" intermediate. 59) Again applying Eq. 60) Λ2 which can also be obtained directly by means of the steady state assumption.