DEDUCING MECHANISMS FROM RATE DATA

1. DEDUCING MECHANISMS FROM RATE DATA

2. COMPLEX REACTIONS (combinations of elementary steps) Reversible unimolecular K = k1/k-1 ; “principle of microscopic reversibility” Parallel unimolecular Consecutive unimolecular Consecutive reversible unimolecular

3. PARALLEL UNIMOLECULAR 1. The rate laws Integrated form A disappears with first order kinetics, with a rate constant k = k1 + k2. The overall rate is determined by the fastest step. At the completion of the reaction, the ratio of products is

4. CONSECUTIVE UNIMOLECULAR 1.Integration of the rate laws The rate laws A disappears in a first-order process

5. The solution to this differential equation is At time = 0, [A] = [A]o, [B] = 0, [C] = 0 [C] = [A]o - [B] - [A].

6. (equal rate constants) The form of an empirical rate law for this reaction would be From the rate law:

7. Using the equation for [B] obtained earlier from integration Comparing with the empirical rate law For a complex reaction, the rate measured by product production may not be represented by a simple empirical rate law. (however, the rate with respect to reactant is)

8. 2. The rate limiting step approximation. If k2 >> k1 Simple empirical rate law The overall rate of a series of consecutive steps can be no faster than the slowest step, the “rate limiting step”. The rate of product production is just the rate of the slow step. No steps in a mechanism after the rate-limiting step will appear in a rate law.

9. CONSECUTIVE REACTIONS WITH A REVERSIBLE STEP The rate laws

10. 1. The pre-equilibrium approximation Suppose that each time a B is formed, the probability of it returning to A is much greater than that for conversion to C ie, k-1>>k2

11. 2. The steady-state approximation The intermediate, B, is reactive, in low concentrations throughout the reaction, and d[B]/dt  0; k-1, k2 >> k1

12. The steady-state solution Note that if k-1 >> k2, The pre-equilibrium solution If k2 >> k-1 The rate-limiting step solution The steady-state approximation is the most general.

13. k1 k-1 EVALUATING MECHANISMS USING EMPIRICAL RATE DATA: EXAMPLE 1 2NO + O2 → 2NO2 (stoichiometric) empirical rate law suggested mechanism (note: stoichiometric reaction could also be a mechanism, but improbable because termolecular). Is this a possible mechanism? To answer, derive rate law and compare with experimental result.

14. K1 K-1 Deduce the rate law from the mechanism using approximate solutions Rate of product production NO3 is an intermediate which must be eliminated from the rate law. This can be accomplished by either of two approximations, namely (i) pre-equilibrium (first step) (ii) steady-state approximation applied to NO3 Try pre-equilibrium first, since it is easiest.

15. K1 K-1 Pre-equilibrium Solution Fast equilibrium Eliminating the intermediate NO3 Pre-equilibrium solution Empirical rate law Agrees with empirical rate law where k2K = kexp, and the suggested mechanism is possible

16. K1 K-1 Steady State Solution For practice, look at s.s. solution, and compare it with pre-equilibrium. Steady state approximation is only applied to intermediates; here NO3

17. k1 k-1 Now, from final step of the mechanism Steady-state solution Pre-equilibrium solution If k-1 >> k2(NO), the steady-state and pre-equilibrium solutions are the same! This is as expected from the mechanism.

18. K1 K-1 The steady-state solution explains an unexpected effect of NO concentration Steady-state solution If high concentrations of (NO) are employed, k2(NO) may become sufficiently large to be such that k2(NO) >> k-1 The rate law has changed! This effect is observed experimentally, and accounted for by the steady-state solution, but not the pre-equilibrium solution.

19. Note that k2(NO) >> k-1 is equivalent to the first step being rate limiting: rate limiting Summary for deducing rate laws from suggested mechanisms. • Express the rate as the production of product from the last step. • Eliminate the intermediate. • a) If there is a preceding reversible step, try the pre-equilibrium approximation; usually this is stated as part of the mechanism • NO + O2 NO3 (fast, eq’m) • NO3 + NO → 2NO2 • b) if not specified as an equilibrium, try the steady-state approximation.