ITK-329 Kinetika & Katalisis
Chapter 4
Dicky Dermawan www.dickydermawan.net78.net
dickydermawan@gmail.com
65

Historical Perspective
Dobereiner (1829), Wilhelmy (1850) supposed that reaction rates would be simply related to the stoichiometry of the reaction
1878: Van’t Hoff showed that the rate equation had little correlation to stoichiometry.
Reaction
4 PH
3

P
4
+ 6 H
2
2 AsH
3

As
2
+ 3 H
2
Rate Equation r
PH
3
  k
3

[ PH
3
] r
AsH
3
  k
4

[ AsH
3
]
2 PH
3
+ 4 O
2

P
2
O
5
+ 3 H
2
O
C
12
H
22
O
11
+ H
2
O  H


CH
3
COOR + H
2
O  H


C
6
H
12
O
6
+ C
5
H
9
O
5
CH
2
OH
CH
3
COOH + ROH
CH
3
COOH + ROH  H

 CH
3
COOR + H
2
O
ClCH
2
COOH + H
2
O

HOCH
2
COOH + HCl
2 FeCl
3
+ SnCl
2

FeCl
2
+ SnCl
4
KClO
3
+ 6 FeO

KCl + 3 Fe
2
O
3 r
PH
3
  k
5

[ PH
3
]

[ O
2
]
1 / 2 r
S
  k
6

[ suksrose ]

[ H

] r
Ac
  k
7

[ CH
3
COOR ]

[ H

] r
Ac
  k
8

[ CH
3
COOH ]

[ ROH ]

[ H

] r
C
2
H
3
ClO
2 r
Fe
3

  k
9

[ C
2
H
3
ClO
2
]
  k
10

[ Fe
3

]
2 
[ Sn
2

]
66 r
Fe
3

 k
11

[ Fe
2

]

[ ClO
3

]

Historical Perspective
Van’t Hoff: the kinetics of a reaction related to molecularity, i.e. the number of molecules participating in some critical step in the reaction
Unimolecular reaction:
Cyclopropane  Propylene
Bimolecular reaction:
*OH + C
2
H
6
 H
2
O + C
2
H
5
*
Termolecular reaction:
CH
3
* + CH
3
* + N
2
 C
2
H
6
+ N
2
: all first-order reactions are unimolecular
: all second-order reactions are bimolecular
: all third-order reactions are termolecular
Critical step : what about?
4 PH
3

P
4
+ 6 H
2 r
PH
3
  k
3

[ PH
3
]
67

When a reaction involves the formations and subsequent reactions of intermediate species , it is not uncommon to find a non-integer order or other type of kinetic expression:
At +/- 500 o C: -r
CH3CHO
= k.C
CH
CH3CHO
3
CHO
3/2
 CH
4
+ CO
H
2
+ I
2
 2 HI  r
HI
 k
1 k

2 k
3

 k
C
3
I
2


C
C
H
2
H
2
(CH
3
At low pressures below 50 mmHg:
)
2
N
2
-r
N2
At high pressures greater than 1 atm:
-r
N2
 C
2
H
6
~ C
AZO
2
~ C
AZO
+ N
2
An elementary reaction is defined as a chemical reaction going from reactants to products without going through any stable intermediates.
In this context, a species is said to be stable if it has lifetime longer than ~10 -11 sec
68

Reactive Intermediates are by definition reactive. The undergo many reactions
David Chapman (1913), Muriel Chapman & Max Bodenstein (1907):
H
2
+ Cl
2
 2 HCl Cl • as reactive intermediates
Every overall chemical reaction can be divided into a sequence of elementary reaction.
Every reaction has a mechanism, defined as the sequence of elementary reactions that occur at appreciable rates when the reactants come together and react to form products
Mechanism:
CH
3
CH
2
HC=CH
2
H

   CH
3
HC=CHCH
3
H
CH
3
CH
2
HC CH
2
+
CH
3
CH
2
HC=CH
2
+ H
+
H
CH
3
CH
2
HC CH
2
+
CH
3
HC=CHCH
3
+ H
+
H
CH
3
CH
2
HC CH
2
+
H
CH
3
CH
2
HC CH
2
+
CH
3
CH
2
HC=CH
2
+ H
+
CH
2
=CHCH
2
CH
3
+ H
+
69

A + B — 2  P +Q
-r
A
= -r
B r
2
= k
2
= +r
P
[A] [B]
-
r r
A
= k
2
B
= k
= +r
Q
2
[A] [B]
[A] [B]
2 A — 4  P +Q
-
+ r
+ r
P
= k
2
Q
= k
2
[A] [B]
[A] [B] r
4
= k
4
+ r
[A] [A] = k
4
P
= k
4
[A] 2
+ r
Q
= k
4
[A] 2
[A] 2 r
A
/2 =
+ r
P
/1 =
+ r
Q
/1 = k
4
[A] 2
-r
A
= 2k
4
[A] 2
Collosion Partner
Incorrect:
A — 1  P
Correct:
A + X— 1  P + X
-r
A
= k
1
[A]
-r
A
= k
1
[A] [X]
70

A  P
A

H
 

1

2
I
 
P

H

For each reaction: r
1 r
2 r
3


 k k
1
2 k
3


[

[
A
I
[ I ]
]
]

[ H

]
For each species: r r
A r
H r
I
P



 r

 r

1 r
3

1 r
1
 r
2
 r

2 r
2 r
3
 r
3
In a constant volume batch reactor: d [ A ] dt
  k
1

[ A ]

[ H

]
 k
2

[ I ] d [ H

] dt
  k
1

[ A ]

[ H

]
 k
2

[ I ]
 k
3

[ I ] d [ I ] dt
 k
1

[ A ]

[ H

]
 k
2

[ I ]
 k
3

[ I ] d [ P ] dt
 k
3

[ I ]
71

A

H
 

1

2
I
 
P

H

A  P
According to pseudo-steady-state approximation, one can compute accurate values of the concentrations of all of the intermediates in a reaction by assuming that the net rate of the intermediates is negligible.
d [ H

] dt
  k
1

[ A ]

[ H

]
 k
2

[ I ]
 k
3

[ I ]

0 d [ I ]
 k
1

[ A ]

[ H

]
 k
2

[ I ]
 k
3

[ I ]

0 dt

[ I ]
 k
2 k
1
 k
3

[ A ]

[ H

] d [ P ] dt
 k
3

[ I ]
 k k
1
2

 k
3 k
3

[ A ]

[ H

]

According to stoichiometry: r p
 k o

[ A ]

[ H

]
 r
A
 r p
 k o

[ A ]

[ H

]
72

(CH
3
)
2
N
2
AZO  C
2
 C
2
H
6
H
6
+ N
2
+ N
2
At low pressures below 50 mmHg :
At high pressures greater than 1 atm :
-r
N2
-r
N2
~ C
AZO
2
~ C
AZO
Reaction mechanism [F.A. Lindemann,Trans. Faraday Soc., 17, 598 (1922)]
(CH
3
)
2
N
2
+ (CH
3
)
2
N
2
— k1  (CH
3
)
2
N
2
+ [(CH
3
)
2
N
2
]*
(CH
3
)
2
N
2
* + (CH
3
)
2
N
2
— k2  (CH
3
)
2
N
2
+ (CH
3
)
2
N
2 r r
AZO*
AZO*
= k
1
.C
AZO
2
= -k
2
.C
AZO
C
AZO*
(CH
3
)
2
N
2
* — k3  C
2
H
6
+ N
2 r
AZO*
= -k
3
.C
AZO*

C
AZO *
 k
2 k
1


C
C
AZO
2
AZO
 k
3
PSSH: r
AZO*
= k
1
.C
AZO
2 - k
2
.C
AZO
C
AZO*
-k
3
.C
AZO*
 0
Then, r
N
2
 k
3

C
AZO *
 k
1 k
2

 k
C
3

C
AZO
AZO
2
 k
3
73

Mechanism:
2 N
2
O
5
 4 NO
2
+ O
2
X

N
2
O
5
 
 k 
  k

2
NO
2

NO
3

X
NO
2

NO
3
 k 
NO

NO
3
 k 
NO

2 NO
2
O
2

NO
2
 What rate expression is consistent with this mechanism?
74

2 NO + 2 H
2
 N
2
+ 2 H
2
O
Mechanism A : 2 NO

H
2
 
N
2

H
2
O
2
H
2
O
2

H
2
 k 
2 H
2
O
Mechanism B : 2 NO
  
   k

4
N
2
O
2
N
2
O
2

H
2
 k 
N
2

2 H
2
O
2
H
2
O
2

H
2
 k 
2 H
2
O
 What rate expression is consistent with these mechanism?
75

H
2
+ Br
2
 2 HBr
Mechanism:
Initiation X + Br
2
— 1  2 Br• + X
Propagation Br • + H
2
H • + Br
2
— 2
— 3
 HBr + H •
 HBr + Br •
Terminatiion X + 2 Br • — 4
H • + HBr — 5
 Br
2
 H
2
+ X
+ Br •
 What rate expression is consistent with this mechanism?
76

H-Il4.3
Mekanisme berantai di bawah ini diusulkan untuk reaksi dekomposisi ozon:
Inisiasi :
Cl
2

O
3
 
ClO
 
ClO
2

Propagasi :
ClO
ClO
3
2

 
O
3

O
3
 
 
ClO
ClO
2
3

 
O
2

2 O
2
Terminasi :
ClO
3
ClO



ClO

ClO
3

  
 
Cl
Cl
2
2


3 O
O
2
2
 Bagaimana persamaan laju reaksi dekomposisi ozon menurut mekanisme ini?
 Hasil percobaan pada suhu rendah menunjukkan bahwa persamaan laju dekomposisi ozon mengikuti persamaan:
 d [ O
3
] dt
 k

[ Cl
2
]
1
2

[ O
3
]
3
2
Apakah mekanisme yang diusulkan konsisten dengan hasil percobaan ini?
77

H4.1
Houser & Lee [J. Phys. Chem., 71 (3422), 1967] have studied the pyrolysis of ethyl nitrate using a stirred flow reactor. They have proposed the following mechanism for the reaction.
Initiation :
C
2
H
5
ONO
2
 
C
2
H
5
O
 
NO
2
Propagation :
C
2
H
5
O
   
CH
3
 
CH
2
O
CH
3
 
C
2
H
5
ONO
2
  
CH
3
NO
2

C
2
H
5
O

Termination : 2 C
2
H
5
O
  k 
CH
3
CHO

C
2
H
5
OH
 What rate expression is consistent with this mechanism?
78

Chain Reactions:
Thermal Cracking of Ethane
Ex.7-2
The thermal decomposition of ethane to ethylene, methane, butane, and hydrogen is believed to proceed in the following sequence:
Initiation :
C
2
H
6
 
2 CH
3

Pr opagation :
CH
3
 
C
2
H
6
 
CH
4

C
2
H
5

C
2
H
5
  
C
2
H
4

H

H
 
C
2
H
6
 
C
2
H
5
 
H
2
Ter min ation :
2 C
2
H
5
  
C
4
H
10
Use PSSH to derive a rate law for the formation of ethylene
79

Chain Reactions: Flame Retardants
P7-3B
Hydrogen radicals are important to sustaining combustion reactions. Consequently, if chemical compounds that can scavenge the hidrogen radicals are introduced, the flame can be extinguished. While many reactions occur during the combustion process, we shall choose CO flames as a model system to ilustrate the process [S.
Senkan et al., Combustion and Flame, 69, p. 113 (1987)] . In the absence of inhibitors: O
2
O
 
O

H
2
O

O

2 OH

The last two reactions are rapid compared to the firs two. When HCl is introduced to the flame, the following additional reactions occur:
CO

OH

H
 
O
2
CO
2

H

OH
 
O

H
 
HCl H
2

Cl

H
 
Cl

HCl
Derive a rate law for consumption of CO for both when no retardant present and when HCl is introduced
80

Chain Reactions:
The Pyrolysis of Acetaldehyde
P7-4A
The pyrolysis of acetaldehyde is believed to take place according to the following sequence:
CH
3
CHO
 
CH
3
 
CHO

CH
3
 
CH
3
CHO
 
CH
3
 
CO

CH
4
CHO
 
CH
3
CHO
 
CH
3
 
2 CO

H
2
2 CH
3
  
C
2
H
6
Derive the rate expression for the rate of disappearance of acetaldehyde
81

Chain Reactions in Tribology
Engine Oil Degradation
P7-7C
One of the major reasons for engine oil degradation is the oxidation of the motor oil. To retard the degradation process, most oils contain an antioxidant [see Ind. Eng. Chem.
26, 902 (1987)].
Without an inhibitor to oxidation present, the suggested mechanism at low temperature is:
Where I
2 the oil.
is an initiator and RH is the hydrocarbon in
When the temperature is raised to 100 o C, the following additional reaction occurs as a result of the decomposition of the unstable ROOH:
ROOH
 k 
RO
 
HO

RO
 
RH
 k 
ROH

R

HO
 
RH
 k 
H
2
O

R

I
2
 
2 I

I
 
RH
 
R
 
HI
R
 
O
2
 k 
ROO

ROO
 
RH
 k 
ROOH

R

2 ROO
   inactive
Derive the rate expression for the degradation of the uninhibited motor oil: a. At low temperature (25 o C) b. At high temperature (100 o C)
82

Engine Oil Degradation:
The Role of Antioxidant
P77C (cont’)
When an antioxidant is added to retard degradation at low temperatures, the following additional termination step occur:
ROO
 
AH
 k 
ROOH

A

A
 
ROO
    inactive
Derive the rate expression for the degradation of the uninhibited motor oil: a. At low temperature (25 o C) b. At high temperature (100 o C) 83

Free Radical Polymerization
1. The Reaction
INITIATION
This reaction produces the formation of the Primary Radical
PROPAGATION
TERMINATION
Transfer
To solvent
To chain transfer agent
Addition
Disproportionation
To monomer
To initiator
84

When one of the steps is much slower than all of the other steps in the mechanism, the rate of this step is fully control the overall rate, thus considerable simplification can be gained:
A

 1
X

2
A
# 
X
A
#  3
B
Using PSSH: r
B
 k
3 k

2 k
1

[

[ A
X ]

]

[ X ] k
3
If it is known that reaction (3) is much slower than (1) & (2) reactions, it is easily derived that: r
B
 k
3
 k
1 k
3

[ A ]
85

When one of the steps is much slower than all of the other steps in the mechanism, the rate of this step is fully control the overall rate, one can often derive a suitable rate equation for the reaction using somewhat less algebra
2 N
2
O
5
 4 NO
2
+ O
2
Mechanism:
X

N
2
O
5
 
 k 
  k

2
NO
2

NO
3

X
NO
2

NO
3
 k 
NO

NO
3
 k 
NO

2 NO
2
O
2

NO
2



Fast
Slow
Fast
 What rate expression is consistent with this mechanism?
86

Example : P7-8
A
Consider the application of the PSSH to epidemology. We shall treat each of the following steps as elementary in that the rate will be proportional to the number of people in a particular state of health. A healthy person, H, can become ill, I, spontaneously, k
1
H I (P7-11.1
)
Or he may become ill through contact with another ill person
The ill person may become healty k
3
I H
Or he may expire k
2
I + H 2I k
4
I D
(P7-11.2
)
(P7-11.3
)
(P7-11.4
)
The reaction given in equation (P7-11.4) is normally considered completely ireversible, although the reverse reaction has been reported to occur :
(a) Derive an equation for death rate.
(b) At what concentration of healty people does the death rate become critical?
(c) Comment the validity of the PSSH under the condition of part (b).
87