§9. 3 The rate equation of reaction with simple order

1. §9.3 The rate equation of reaction with simple order

2. Reaction with simple order H2 + I2 = 2 HI Reaction with definite order Overall reactions H2 + Cl2 = 2 HCl Reaction without definite order H2 + Br2 = 2 HBr

3. It was found that reactions with same reaction order are usually of same kinetic characteristics, therefore, reactions are usually classified on the basis of reaction order.

4. Reaction with simple order: The reaction whose rate only depends on the concentration ofreactants, and both the partial order and the reaction order is zero or plus integer is called reaction with simple order. r = kcn

5. Comparison between reactions with different reaction orders

6. 3.1 First-order reaction: Reaction: A  P at t = 0c0 at t = tc Differential rate equation: can be rearranged into: Which can be integrated directly

7. c~t curve of first-order reaction Only when t , can c  0, which suggests that, the first-order reaction can not complete. Half-life

8. lnc ~ t curve of the first-order reaction The slope of the lnc ~ t curve is the k1

9. Characteristics of the first-order reaction 1) Unit of k is s-1 2) lnc is in linear proportion to t 3) can not complete 4) Half-life does not depend on c0

10. Example: • Decay of isotopes 2) Decomposition 3) Isomerization

11. Example: The half-life of the first-order decay of radioactive 14C is about 5720 years. The natural abundance of 14C isotope is 1.1  10-13 mol% in living matter. Radiochemical analysis of an object obtained in an archeological excavation shows that the 14C isotope content is 0.89  10-14 mol%. Willard F. Libby 1960 Noble Prize USA 1908/12/17 ~1980/09/08 Application of 14C for age determinations (radiocarbon dating)

12. 3.2 Second-order reaction 2A  P; A + B  P A + B  P a b cA= axcB =bx Differential rate equation:

13. When a = b

14. c~t curve of second-order reaction When c  0,t  , which suggests that, the pure second-order reaction can not complete, either. Half-life

15. 1/c ~ t curve of second-order reaction For pure second-order reaction

16. Characteristics of second-order reaction 1) Unit of k is mol-1dm3s-1 2) 1/c is in linear proportion to t 3) can not complete 4) Half-life Increasing the initial concentration of the reactant will shorten the reaction time.

17.  Example: • dimerization 2) decomposition 3) recombination 4) esterification C12H22O11 + H2O  C6H12O6 + C6H12O6 5) hydrolysis

18. C12H22O11 + H2O  C6H12O6 + C6H12O6 In 1850, experiment done by Wilhelmy suggested that the rate equation of the reaction is: Because the amount of water keeps nearly unchanged during the reaction, [H2O] keeps nearly constant, and the rate equation can be then simplified as Pseudo first-order reaction

19. 3.3 third-order reaction 3A  P A + B + C  P 2A + B  P 3A  P

20. For A + B + C  P with same initial concentration Differential rate equation Integrated rate equation

21. Only five third-order gaseous reactions have been observed. 2NO + X2 N2O + X2O; X = H, D 2NO + O2 2NO2; 2NO + X2 2NOX; X = Br, Cl Are these true third order reactions ?

22. r = k [C6H5CHO]2[CN-] r = k [C2H4O][H+][Br-]

23. 3.4 Zeroth-order reaction A  P Differential rate equation When c = 0, the reaction completes, the reaction time is: The zero-order reaction can complete.

24. c ~ t curve for zero-order reaction

25. Characteristics of zeroth-order reaction 1) Unit of k is mol dm-3s-1 2) c is in linear proportion to t 3) can complete 4) When c increases, reaction time will be prolonged.

26. Examples: Decomposition over catalysts: 1) 2N2O  2N2 + O2 over Pt wire 2) 2NH3  N2 + 3H2 over W wire Photochemical reaction: r = kI I: intensity of radiation

27. 5.5 for nth-order reaction For n 1