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Consecutive Elementary Reactions. When proposing a reaction sequence, or mechanism, it is important to derive a rate expression that can be tested against experimental data. If we consider the simplest elementary sequence:

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consecutive elementary reactions
Consecutive Elementary Reactions
  • When proposing a reaction sequence, or mechanism, it is important to derive a rate expression that can be tested against experimental data. If we consider the simplest elementary sequence:
  • the question is how would reaction products evolve from a system that abides by this mechanism?
  • The differential equations governing the rate of formation and/or decomposition of the components of the system are:
  • For A,
  • For B,
  • For C,
slide3
Defining the dynamics of this simplest of reaction sequences is relatively challenging
    • How would you approach the following catalytic reaction sequence?
    • The concentration of most reaction intermediates cannot be measured!
    • The rate constants for each elementary step in the sequence cannot be estimated independently!
slide4
Simplifications are available when the decomposition of B (r2) is rapid, relative to the decomposition of A (r1).
    • In this example, rate comparisons are made on the basis of first-order rate constants i.e. k2 relative to k1
  • If r2 is “quick” (k2 = 2 k1) If r2 is “fast” (k2 = 10 k1)
steady state approximation
Steady-State Approximation
  • The steady-state hypothesis (SSH) is an important technique of applied chemical kinetics.
    • If an intermediate compound in a reaction sequence is very reactive, its concentration reaches a plateau after a short period, called the relaxation time.
  • The analytical expression of the SSH: the derivative with respect to time of the concentration of reactive intermediates is equal to zero.
  • If compound B was highly reactive, meaning k1/k20, our rate expressions and their solutions are greatly simplified:
steady state approximation1
Steady-State Approximation
  • Steady-State Hypothesis
  • In a sequence of elementary steps going through reactive intermediates, the rates of the steps in the sequence are equal.
  • In our consideration of the sequence ABC, the SSH applied to B reduced the rate expressions to:
  • This suggests that the rate of decomposition of A (-d[A]/dt) equals the rate of formation of C (d[C]/dt) when the intermediate is sufficiently reactive.
rate determining step
Rate Determining Step
  • Another set of simplifying techniques can be applied when one reaction of a sequence can be identified as rate limiting.
    • The dynamics of the overall sequence are dominated by the kinetics of this single rate determining step
    • All other elements of the sequence affect the overall dynamics by supplying the reagents that are needed by the rate limiting reaction.

In this ABC example, r1 is much faster than r2, making a rate determining step assignment a useful simplifying assumption.