1. Nano Catalysis & Materials Lab.1 6. Kinetics of overall reactions

2. Nano Catalysis & Materials Lab.2 6.1 Introduction Adsorption equilibrium constant Entropy decreases upon adsorption exothermic Two basic assumption All surface sites are identical ( uniform surface ) No interactions between adsorbed species

3. Nano Catalysis & Materials Lab.3 6.2 Kinetics of single reactions : uniform species 4.2.1 Single path reactions : General equations (one overall rxn, one path ) O 2 + 2* SO 2 + O* 2O* SO 3 + * 1212 SO 2 + O 2 SO 3 N (1)

4. Nano Catalysis & Materials Lab.4 1 2 0 0 2 O 2 + 2* H 2 + 2* H* + O* OH* + H* H 2 + O* 2O* 2H* OH* + * H 2 O + 2* H 2 O + * 2H 2 + O 2 2H 2 O Multiple – path reaction (only one overall rxn, but multiple path ) N (1) N (2)

5. Nano Catalysis & Materials Lab.5 1 1 0 0 1 C* + H 2 O CO* + C CO* + CO C + H 2 O CO + H 2 O CO* + H 2 CO + C* CO 2 + C* CO + H 2 CO 2 + H 2 Reaction networks (multiple overall rxns, multiple rxn paths ) N (1) N (2) N (1) N (2)

6. Nano Catalysis & Materials Lab.6 a ) Quasi-Stationary State Approximation n-elementary steps ( general relation between overall rate and rates of elementary steps) quasi-Stationary State Approximation (v 1 -v -1 )v 2 v 3 …v n + v -1 (v 2 -v -2 )v 3 v 4 …v n + v -1 v -2 (v 3 -v -3 ) …v n + … + v -1 v -2 v -3 …(v n – v -n ) = v 1 v 2 v 3 …v n – v -1 v -2 v -3 … – v -n ----------- (1) ------------------------------- (2) v : overall rxn rate (2) (1) ------------ (3)

7. Nano Catalysis & Materials Lab.7 ------------ (5) ------------ (4) General relations for elementary steps and for the overall rxn

8. Nano Catalysis & Materials Lab.8 i) Relations with affinity A + B C + D (elementary step) net where Affinity of the elementary step (-Gibbs free energy) ------------ (6)

9. Nano Catalysis & Materials Lab.9 ------------ (7) ------------ (8) ------------ (9) net ------------ (10) From eq.(8) ------------ (11)

10. Nano Catalysis & Materials Lab.10 (12) For overall reaction Eq (11) gives (13)

11. Nano Catalysis & Materials Lab.11 If there is a (rds), A i =0, v i =-v -I except for i=d ∴ Eq (13) becomes (14) (A from thermodynamic data, v and v measurable )

12. Nano Catalysis & Materials Lab.12 Average Stoichiometric number (15) From eq(11) and (5) (16) (17) (18)

13. Nano Catalysis & Materials Lab.13 ⅱ ) Equilibrium constants and rate constants of an overall reaction

14. Nano Catalysis & Materials Lab.14 The affinity A is given by

15. Nano Catalysis & Materials Lab.15 b) Exchange rates or rates at equilibrium m

16. Nano Catalysis & Materials Lab.16

17. Nano Catalysis & Materials Lab.17

18. Nano Catalysis & Materials Lab.18 2. Definition of the rds and of at equilibrium

19. Nano Catalysis & Materials Lab.19

20. Nano Catalysis & Materials Lab.20 (C) Identification of the rate determining step 1. Rate measurements near equilibrium

21. Nano Catalysis & Materials Lab.21 2. General method (Tempkin Int. Chem. Eng. 11, 709) Example ammonia synthesis Step 1 N 2 + 2* 2 N* + H* 3 NH* + H* 4 NH 2 * + H* 5 H 2 + 2* 2N* NH* + * NH 2 * + * NH 3 + 2* 2H* i12223i12223 N 2 + 3H 2 2NH 3 Step 5 is very fast, for steps 1 to 4, we assume that equilibrium is not reached (v i  v -i ) 15 N is transferred from the reactant N 2 to the product NH 3 at a net rate

22. Nano Catalysis & Materials Lab.22

23. Nano Catalysis & Materials Lab.23 If  A and  B are the molar fractions of the tracer atom in the reactant N 2 and the product NH 3,

24. Nano Catalysis & Materials Lab.24 can be determined from the net overall rate v and from the net rate of tracer transfer . If the steps through which the tracer does not pass are equilibrated, In conclusion, the stiochiometric number determined from the transfer of tracer is also that of the overall rxn and of the rds. (43)

25. Nano Catalysis & Materials Lab.25 6. 2. 2. Rate Expression for overall reaction : Two – Step Sequences S 1 + A 1 S 2 + A 2 A 1 + A 2 B 1 + S 2 B 2 + S 1 B 1 + B 2 k1k1 k -1 k2k2 k -2 Overall rxn (1) (2) ( * Homework)