Physical Chemistry Third Edition

506 11 The Rates of Chemical Reactions

to obtain the result

kt

(

1

[B] 0 −[A] 0

)(

1

[A]

−

1

[A] 0

)

+

1

([B] 0 −[A] 0 )^2

ln

(

[B] 0 [A]

[A] 0 [B]

)

11.22For the reaction

aA+bB+cC−→products

assume that the rate law is third order overall:

rate−

1

a

d[A]

dt

kf[A][B][C]

Integrate the rate law for the case of a stoichiometric

mixture, such that

[A]:[B]:[C]a:b:c

11.23For the reaction of the previous problem, integrate the
rate law for the case of a nonstoichiometric mixture,
using the method of partial fractions.

11.24For the hypothetical reaction

A+2B+2C−→products

assume that the following initial-rate data were obtained:

Run[A] 0 /mol L−^1 [B] 0 /mol L−^1 [C] 0 /mol L−^1 −d[A]/dt/

mol L−^1 min−^1

1 0.635 0.985 0.985 1. 23 × 10 −^5

2 0.635 0.985 0.635 7. 93 × 10 −^6

3 0.635 0.438 0.635 1. 57 × 10 −^6

4 0.438 0.438 0.635 1. 08 × 10 −^6

Find the order with respect to each reactant and find the

value of the rate constant.

11.25Methyl acetate was hydrolyzed using HC1 as a catalyst.
The reaction is monitored by titrating aliquots of the
reaction solution with base.

Time/s (Volume of base−volume of base

at end of reaction)/mL

339 13. 47

1242 12. 01

2745 10. 11

4546 8. 00

Find the pseudo order of the reaction, the apparent rate

constant, and the volume of base that would have been

required att0. Remember that the apparent rate

constant depends on the concentration of the catalyst.

11.26The reaction

2H 2 O 2 −→2H 2 O+O 2

is catalyzed by iodide ions. Since the iodide ions are not

consumed, we can determine the order with respect to

H 2 O 2 in the same way as for a reaction with a single

reactant. The following data were obtained for the

decomposition of hydrogen peroxide in 0.02 mol L−^1 KI

at 25◦C:

Time/minutes Volume of O 2 evolved/mL

00

5. 00 7. 50

10. 00 14. 00

25. 00 28. 80

45. 00 41. 20

65. 00 48. 30

∞ 57. 90

a.Determine the order with respect to H 2 O 2 and find the

value of the apparent rate constant at this temperature.

Assume that the reverse reaction can be neglected.

b.Find the volume of O 2 evolved at a time of 35.00 s.

11.27The decomposition of benzenediazonium chloride in

water is given by the reaction equation

C 6 H 5 N+ 2 +2H 2 O−→C 6 H 5 OH+N 2 +H 3 O+

Since the concentration of water is nearly fixed, we can

determine the pseudo order with respect to the diazonium

ion as with a reaction having a single reactant.

Moelwyn-Hughes and Johnson followed the reaction at

40 ◦C by monitoring the pressure of the nitrogen evolved

by the reaction. The following data were taken, with the

pressure in arbitrary units:

Time/s P∞−P Time/s P∞−P

0 22.62 900 15. 49

60 22.08 1200 13. 62

120 21.55 1800 10. 54

240 20.47 2400 8. 15

360 19.45 3000 6. 34

480 18.48 3600 4. 88

600 17.60 4800 2. 98

a.Determine the pseudo order with respect to the

diazonium ion and find the value of the apparent rate

constant for this temperature.

b.Find the pressure of the evolved nitrogen gas at 1500 s.