1. §10.1 Typical complex reactions
Chapter X
Kinetics of Complex Reactions
§10.1 Typical complex reactions
Levine: p

2. Typical complex reactions
reaction contains more than one elementary reaction
Typical complex reactions
1) Opposing Reaction :
2) Parallel Reaction:
3) Consecutive Reaction:

3. 1.1 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. therefore
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.

5. t = 0 a t = t a-x x t = te a-xe xe
(2) rate equation
For first-first order
opposing reaction:
t = 0 a
t = t
a-x x
t = te
a-xe xe
The total rate is
Under equilibrium conditions

6. Principle of relaxation method for studying fast reaction
which suggests that k+ and k can be determined by measuring x at t and at equilibrium concentration. Relaxation method.
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

7. 1.2 Parallel reaction / Competing reaction
When
When
The rate of parallel reaction is determined mainly by the faster one.

8. t x = y + z a For production of B and C: A B C a a-x y z
Integration of the equation yields:
For production of B and C: A B C a
a-x y z
x = y + z

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

10. Optimum temperature for better selectivity
Example
A  B A1
Ea, 1
A  C A2
Ea, 2
logA2
1/T
logA1
log k B C
logA2
1/T
logA1
logk B C

11. Using catalyst to better selectivity
The selectivity of the parallel reaction can be improved by adoption of appropriate catalyst.

12. Selectivity: 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:

13. 1.3 Consecutive reaction a = x + y + z CH4 + Cl2 CH3Cl CH2Cl2 CHCl3
Some reactions proceed through the formation of intermediate.
CH4 + Cl2
CH3Cl
CH2Cl2
CHCl3
CCl4
General reaction A B C
t = 0 a
t = t x y z
a = x + y + z

14. C
tmax t A B

15. At tmax, the concentration of B = ?
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., tmax.
At tmax, the concentration of B = ?

17. k2/k1
1/5 5 10
100
103
108
tmax
2.01
0.40
0.25
0.047
710-3
10-7
ymax/a
0.67
0.13
0.08
7 10-3
10-3
Ea,1Ea,2
-0.4
4.0
5.7
11.5
17.2
46.1 t y
k1/k2
When k2 >> k1, ymax would be very small, and the tmax would be very short.

18. Steady-state approximation
Physical meaning of k2 >> k1
B is a active intermediate (Such as active atom: Cl, H, etc., radicals: CH3•, H2C:, C+, C-, etc., activated molecules: A*), it is difficult to form but easy to decompose to product.
For consecutive reaction with large k2/k1 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

19. When k2 >> k1
The total rate is determined mainly by k1
When k2 << k1
The total rate is determined mainly by k2
The rate of the overall consecutive reaction depends only on the smaller rate constant (rate-determining step).

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

21. Rate-determining step approximation
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.
What is a eligible r. d. s.?
Its activation energy should be 10 kJmol-1 more than that of other steps.