1. §9.4 Determination of the reaction order

2. r = k [A][B] [C] 
Whenever we determine the order of a reaction, we can write out the rate equation of the reaction and tell the detail of the kinetic characteristics of the reaction according to the rate equation.
Otherwise, the rate equation can provide useful information about the mechanism of the reaction. Therefore, determination of the order of the reaction is a work of great importance.
Integration method
Differential method
Partial order method
Isolation method
Methods for determination of reaction order

3. 4.1 Integration methods
The integration methods are to use the integrated rate equation to determine the order of the reaction.
Integration methods includes:
1) attempt method (trial-and–error )
2) graphic method
3) half-life method

4. r = k[C2H5ONa][C2H5(CH3)2SI]
The attempt method:
the values of k can be calculated from the selected integrated equation from a knowledge of initial concentration (c0) and the concentration at various time intervals (c). If the reaction is of the selected order of reaction, the k at different intervals thus obtained should be the same.
C2H5ONa + C2H5(CH3)2SI 
NaI + C2H5O C2H5 + S(CH3)2
r = k[C2H5ONa][C2H5(CH3)2SI]
A + B  P
r = k [A][B]

5. Table 1 kinetic data for C2H5ONa + C2H5(CH3)2SI reaction at 337.10 K
t/s
102[A]/ moldm-3
102[B] / moldm-3
9.625
4.920
720
8.578
3.878
1200
8.046
3.342
1800
7.485
2.783
2520
6.985
2.283
3060
6.709
2.005
3780
6.386
1.682 
4.704

6. r = k[C2H5ONa][C2H5(CH3)2SI]
Table2 k of the reaction of different order
, 
=0
=1
=2
=0
=1
=2
105
104
103
1.454
1.599
3.313
1.764
7.579
3.642
720
1.108
1.143
3.088
1.604
7.357
3.678
1200
0.935
1.205
3.051
1.550
10.02
3.760
1800
1.042
0.960
2.751
1.333
10.93
3.773
2520
0.511
0.747
2.405
1.093
11.11
3.731
3060
0.449
0.685
2.440
13.32
3.729 k t
Therefore, the rate equation is:
r = k[C2H5ONa][C2H5(CH3)2SI]

7. Comment: The attempt method is a laborious method
For reaction without simple order, it is impossible to ascertain reaction order using this method.
the experimental error may cause confusion sometimes.

8. 2) The graphic method
The linear relationship of reaction with different order is different.
order
Linear relationship
zeroth
c ~ t
first
lnc ~ t
second
1/c ~ t
third
1/c2 ~ t

9. r = k[A] The rate equation of A  P can be expressed as
Table 3 kinetic data for A  P.
t / s
c / moldm-3
1.000
3000
0.050
500
0.606
3500
0.030
1000
0.368
4000
0.018
1500
0.223
4500
0.011
2000
0.135
5000
0.007
2500
0.082

11. 3) half-life method S = 1 (1n) = 1, n = 2
the half-life of a reaction is proportional to the initial concentration of the reactant
Graphic method
S = 1
(1n) = 1, n = 2
Therefore, the reaction is of second order.

12. Calculation method NH4OCN  CO(NH2)2 n1 = 2.051, n2 = 2.019
c0/moldm-3
0.05
0.10
0.20
t1/2/h
37.03
19.15
9.45
n1 = 2.051, n2 = 2.019
n =  2

13. 4.2 differential method Graphic method
Use the differential form of the rate equation to determine the order of the reaction.
Graphic method
Table 4 decomposition of CH3CHOCH4+CO.
Decomposition % 5 10 15 20
r / Pamin-1
1137
998.4
898.4
786.5
685.2 25 30 35 40 45
625.2
574.5
500.0
414.6
356.0

14. ln r = -1.593+1.865 lnc Linear fitting results:
Linear correlation coefficient: 0.998
Therefore, the order of the reaction is 2.

15. c c1 c2 c3 c4 t1 t2 t3 t4 t r1 r2 r3 r4 c
c0,1 t
c0,2
c0,3
r0,1
r0,2
r0,3
Determination of reaction order through several parallel experiments.
Determination of reaction order through one experiment.
Reaction order with respect to time: nt
Reaction order with respect to concentration: nC
The method of initial rates is applicable of a wide variety of reactions and is particularly useful in reactions that are complicated by processes involving intermediate or products.

16. Calculation method nt= 2.534; 1.952; 2.327; 2.274  nt = 2.272  2
Decomposition % 5 10 15 20
r / Pa min-1
1137
998.4
898.4
786.5
685.2 25 30 35 40 45
625.2
574.5
500.0
414.6
356.0
nt= 2.534; 1.952; 2.327; 2.274
 nt =  2

17. r = k[A][B][M] n = + + 
Table 5 relationship between nC and nt. nc
= nt
Both intermediate and product do not affect the reaction
> nt
Intermediate or product catalyze the reaction
< nt
Intermediate or product inhibit the reaction
r = k[A][B] n = + 
r = k[A][B][M] n = + + 

18. 4.3 Partial order method
To plot lnr versus lncA, if a linear relation can obtained,  = 0,  = 0.
If no linear relation can be observed, adjust the value of  and  until a line can be obtained. The slope of this line is , and the corresponding value of  and  can be obtained simultaneously.

19. 4.4 Isolation method Three methods: When cB and cC were controlled
Fixation of concentration method;
Excess concentration method;
Application of stoichiometric ratio

20. 1) Fix the concentration of other reactants
Rate equation of 2NO + 2H2  N2 + 2H2O is r = k[NO] [H2].
No.
Initial pressure / Pa
Initial rate NO H2 1
20265
486.36 2
243.18 3
121.59

21. 2) Excess concentration
C12H22O11 + H2O  C6H12O6 + C6H12O6
In excess concentration method, the concentration of B and C is made very much larger than that of A。
This technique is particularly useful in determining rate constants for reactions involving water in aqueous solution.
Pseudo order reaction.

22. 3) Using stoichiometric ratio
aA bB  P
Initial concentration b/a
Conversion concentration x bx/a
Residual concentration x (b/a)(1-x)
r = k[A] [B] = k (b/a)(1-x)+ = k(b/a)(1-x)n
Other methods:
Unit of k
Dependence of t1/2 on c0