§9.4 Determination of the reaction order

cc0,1

t

c0,2

c0,3

r0,1

r0,2

r0,3

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.

Methods for determination of reaction order

1) Integration method

2) Differential method

3) Partial order method

4) Isolation method

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

1) 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.

A + B P

C2H5ONa + C2H5(CH3)2SI

NaI + C2H5O C2H5 + S(CH3)2

r = k[C2H5ONa][C2H5(CH3)2SI]

r = k [A][B]

t/s 102[A]/ moldm-3 102[B] / moldm-3

0 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

Table 1 kinetic data for C2H5ONa + C2H5(CH3)2SI reaction

at 337.10 K

=0 =1 =0 =2 =0 =1

=0 =0 =1 =0 =2 =1

105 104 104 103 103 103

0 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 1.042 13.32 3.729

Table2 k of the reaction of different order

r = k[C2H5ONa][C2H5(CH3)2SI]

Therefore, the rate equation is:

kkt

,

1) The attempt method is a laborious method

2) For reaction without simple order, it is impossible

to ascertain reaction order using this method.

3) the experimental error may cause confusion

sometimes.

Comment:

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

t / s c / moldm-3 t / s c / moldm-3

0 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

Table 3 kinetic data for A P.

The rate equation of A P can be expressed as

r = k[A]

0 1000 2000 3000 4000 5000

0.0

0.2

0.4

0.6

0.8

1.0

C /

mol

dm

-3

t / s

0 1000 2000 3000 4000 5000

-5

-4

-3

-2

-1

0

ln (

C /

mol

dm

-3)

t / s

0 1000 2000 3000 4000 5000

0

40

80

120

160

1/ C

(/ m

ol d

m-3

)

t / s

0 1000 2000 3000 4000 5000

0

20

40

60

80

100

1 / C

2

t / s

3) half-life method

the half-life of a reaction is proportional to the initial concentration of the reactant

11/ 2 0

nt kc 1/ 2 0ln ln (1 ) lnt k n c

-5 -4 -3 -2 -1 0 13

4

5

6

7

8

9

10

ln t 1

/2

lnC0

S = 1

Graphic method

(1n) = 1, n = 2

Therefore, the reaction is of second order.

1/ 2 0ln ln (1 ) lnt k n c

Calculation method

1/ 2 0ln ' ln (1 ) ln 't k n c

1/ 2

1/ 2

0

0

ln'

1ln

'

t

tn

c

c

c0/moldm-3 0.05 0.10 0.20

t1/2/h 37.03 19.15 9.45

NH4OCN CO(NH2)2

n1 = 2.051, n2 = 2.019

n = 2.035 2

4.2 differential method

Use the differential form of the rate equation to determine the order of the reaction.

ndcr kc

dt ln ln lnr k n c

Graphic method

Decomposition % 0 5 10 15 20

r / Pamin-1 1137 998.4 898.4 786.5 685.2

Decomposition % 25 30 35 40 45

r / Pamin-1 625.2 574.5 500.0 414.6 356.0

Table 4 decomposition of CH3CHOCH4+CO.

3.8 4.0 4.2 4.4 4.6 4.8

5.5

6.0

6.5

7.0

lnr

/ P

a m

in-1

lnC / mol dm-3

3.8 4.0 4.2 4.4 4.6 4.8

5.5

6.0

6.5

7.0

lnr

/ P

a m

in-1

lnC / mol dm-3

Linear fitting results:

ln r = -1.593+1.865 lnc

Linear correlation coefficient: 0.998

Therefore, the order of the reaction is 2.

ln ln lnr k n c

0 0ln ln lntr k n c

Determination of reaction order through several parallel experiments.Reaction order with respect to concentration: nC

cc0,1

t

c0,2

c0,3

r0,1

r0,2

r0,3

Determination of reaction order through one experiment.

Reaction order with respect to time: nt

c

c1

c2

c3c4

t1 t2 t3 t4 tt4

r1

r2

r3 r4

ln ln lnr k n c 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.

calculation method

ln ' ln ln 'r k n c

ln ln lnr k n c ln'

ln'

t

rrncc

0

0

0

0

ln'

ln'

C

r

rn

c

c

Decomposition % 0 5 10 15 20

r / Pa min-1 1137 998.4 898.4 786.5 685.2

Decomposition % 25 30 35 40 45

r / Pa min-1 625.2 574.5 500.0 414.6 356.0

nt= 2.534; 1.952; 2.327; 2.274

nt = 2.272 2

nc

= ntBoth intermediate and product do not affect the reaction

> ntIntermediate or product catalyze the reaction

< ntIntermediate or product inhibit the reaction

Table 5 relationship between nC and nt.

r = k[A][B] n = +

r = k[A][B][M] n = + +

4.3 Partial order method

A B Car kc c c

A B Cln ln ln ln lnr k c c c

A B Cln ln (ln ln ln )r k c c c

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.

4.4 Isolation method

A B Cln ln ln ln lnr k c c c 'A B Cln ' ln ln ln lnr k c c c

ln ln' '

A

A

cr

r cWhen cB and cC were controlled

Three methods:

1) Fixation of concentration method;

2) Excess concentration method;

3) Application of stoichiometric ratio

1) Fix the concentration of other reactants

Rate equation of 2NO + 2H2 N2 + 2H2O is

r = k[NO] [H2].

No.

Initial pressure / Pa

Initial rateNO H2

1 50662.5 20265 486.36

2 50662.5 10132.5 243.18

3 25331.25 20265 121.59

2) Excess concentration

C12H22O11 + H2O C6H12O6 + C6H12O6

12 22 11 2[C H O ][H O]r k 12 22 11'[C H O ]r k

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.

3) Using stoichiometric ratio

aA + bB P

Initial concentration 1 b/a

Conversion concentration x bx/a

Residual concentration 1-x (b/a)(1-x)

r = k[A] [B] = k (b/a)(1-x)+ = k(b/a)(1-x)n

Other methods:1) Unit of k

2) Dependence of t1/2 on c0