1. Chapter X Kinetics of Complex Reactions Levine: p.559 17.9

2. In this section we are to consider some examples of reactions more complex than A + B  P, and see how the integrated rate laws are modified. complex reactions: reaction contains more than one elementary reaction typical complex reactions 1) Opposing Reaction 2) Parallel Reaction 3) Consecutive Reaction §1. Typical complex reactions

3. 1) Opposing Reaction / reversible reaction majority of the reactions are reversible, i.e., the forward and the backward / reverse reaction take place simultaneously. (1) kinetic equilibrium constant for opposing reaction consisting of elementary reactions: As reaction proceeds, r + increases while r  decreases. When r + becomes equal to r , equilibrium is reached.

4. In this way we arrive at a very important connection between the equilibrium constant and the rate coefficients of simple reactions. This relation, named as kinetic equilibrium constant, is correct only for elementary reactions. therefore

5. For first-first order opposing reaction: (2) rate equation t = 0a0 t = ta-xa-xx t = t e a-xea-xe xexe The change rate of [A] has two contributions: A is depleted by the forward reaction at a rate k + [A], but is replenished by the reverse reaction at a rate k - [B]. The total rate of change of the concentration of A is therefore

6. Under equilibrium conditions which suggests that k + and k  can be determined by measuring x at t and equilibrium concentration.

7. Similar to the rate equation of first-order reaction 1-2 opposing reaction 2-2 opposing reaction Principle of relaxation method for studying fast reaction

8. 2) parallel reaction / Competing reaction When The rate of parallel reaction is determined mainly by the faster one.

9. Integration of the equation yields: ABC a00 a-xa-xyz x = y + z a t For production of B and C:

10. The composition of the final products is fixed. selectivity of the reaction. A B C t c

11. Optimum temperature for better selectivity Example A  B A1A1 E a, 1 A  C A2A2 E a, 2 When A 1 >A 2, E a,1 >E a,1, to increase the ratio of B in the products, should higher temperature or lower temperature be chosen? logA 2 1/T logA 1 log k B C

12. When A 1 > A 2, E a,1 <E a,2, to increase the ratio of B in the products, should higher temperature or lower temperature be chosen? logA 2 1/T logA 1 logk B C The selectivity of the parallel reaction can be improved by adoption of appropriate catalyst. Using catalyst to better selectivity

13. Main reaction and Side reaction: reaction with higher k is taken as the main reaction, while others side reactions. Reaction that produces the demanded product is the main reaction. Selectivity:

14. 3 Consecutive reaction Some reactions proceed through the formation of intermediate. CH 4 + Cl 2 CH 3 ClCH 2 Cl 2 CHCl 3 CCl 4 ABC t = 0a00 t = txyz a = x + y + z General reaction

15. C t max t A C B

16. shows that the intermediate’s concentration rises from zero to a maximum and then drops back to zero as A is depleted and C dominates in the mixture. If C is the demanded product, the reaction time should be prolonged. If B is the demanded product, the reaction should be interrupted at optimum time, i.e., t max. At t max, the concentration of B = ? C t max t A C B

18. k2/k1k2/k1 1/551010010 3 10 8 t max 2.010.400.250.047 7  10 -3 10 -7 y max /a 0.670.130.08 7  10 -3 10 -3 0 E a,1  E a,2 -0.44.05.711.517.246.1 When k 2 >> k 1, y max would be very small, and the t max would be very short. t y 0 k 1 /k 2

19. Physical meaning of k 2 >> k 1 B is a active intermediate (Such as active atom: Cl, H, etc., radicals: CH 3, H 2 C:, C +, C -, etc., activated molecules: A * ), it is difficult to form but easy to decompose to product. For consecutive reaction with large k 2 /k 1 ratio, once the reaction take place, the active intermediate (B) rapidly attains its maximum concentration and its concentration keeps nearly unchanged during the whole reaction. Steady-state approximation

20. When k 2 >> k 1 The total rate is determined mainly by k 1 When k 2 << k 1 The total rate is determined mainly by k 2 The rate of the overall consecutive reaction depends only on the smaller rate constant (rate-determining step).

21. rate-determining step (r. d. s.): the step with the slowest rate. ?? !!  It’s a r.d.s     patient !

22. The rate of the elementary step with the lowest rate constant, i.e., r.d.s., can be used to express the actual rate of the overall reaction. Its activation energy should be 10 kJ  mol -1 more than that of other steps. What is a eligible r. d. s.? Rate-determining step approximation

23. Procedure for synthesis of ammonia: 1) diffusion; 2) absorption; 3) activation; 4) reduction; 5) protonation; 6) desorption; 7) diffusion. which step is the r.d.s? Key step for optimization of the reaction conditions

24. Electrocatalytic degradation of p-nitrophenol