Consecutive Elementary Reactions

1. 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,

2. Integration of these ordinary differential equations gives:

3. 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!

4. 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)

5. 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:

6. 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.

7. 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.