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Nonelementary Reaction Kinetics. ITK-329 Kinetika & Katalisis. Chapter 4. Dicky Dermawan Historical Perspective. Dobereiner (1829), Wilhelmy (1850) supposed that reaction rates would be simply related to the stoichiometry of the reaction

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nonelementary reaction kinetics

Nonelementary Reaction Kinetics

ITK-329 Kinetika & Katalisis

Chapter 4


historical perspective
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.

historical perspective3
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 + C2H6  H2O + C2H5*

Termolecular reaction:

CH3* + CH3* + N2  C2H6 + N2

: all first-order reactions are unimolecular

: all second-order reactions are bimolecular

: all third-order reactions are termolecular

Critical step: what about?

historical findings
Historical Findings

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 +/- 500oC: -rCH3CHO = k.CCH3CHO3/2

H2 + I2 2 HI

(CH3)2N2 C2H6 + N2

At low pressures below 50 mmHg:

-rN2 ~ CAZO2

At high pressures greater than 1 atm:

-rN2 ~ CAZO

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

reactive intermediates
Reactive Intermediates

Reactive Intermediates are by definition reactive. The undergo many reactions

David Chapman (1913), Muriel Chapman & Max Bodenstein (1907):

H2 + Cl2 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



kinetic of elementary reactions
Kinetic of Elementary Reactions

A + B —2 P +Q r2 = k2 [A] [B]

-rA = k2 [A] [B] +rP = k2 [A] [B]

-rB = k2 [A] [B] +rQ = k2 [A] [B]-rA = -rB = +rP = +rQ

2 A —4 P +Q r4 = k4 [A] [A] = k4 [A]2 +rP = k4 [A]2

+rQ = k4 [A]2 -rA = 2k4 [A]2

- rA/2 = +rP/1 = +rQ/1 = k4 [A]2

Collosion Partner


A—1 P -rA = k1 [A]


A + X—1 P + X -rA = k1 [A] [X]

rates of overall reaction
Rates of Overall Reaction

A  P

For each reaction:

For each species:

In a constant volume batch reactor:

pseudo steady state hypothesis
Pseudo-Steady-State Hypothesis

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.

According to stoichiometry:

another example rates of overall reaction
Another Example:Rates of Overall Reaction

(CH3)2N2 C2H6 + N2

AZO C2H6 + N2

At low pressures below 50 mmHg : -rN2 ~ CAZO2

At high pressures greater than 1 atm : -rN2 ~ CAZO

Reaction mechanism [F.A. Lindemann,Trans. Faraday Soc., 17, 598 (1922)]

(CH3)2N2+ (CH3)2N2 —k1 (CH3)2N2+ [(CH3)2N2]* rAZO*= k1.CAZO2

(CH3)2N2* + (CH3)2N2 —k2 (CH3)2N2+ (CH3)2N2 rAZO*= -k2.CAZOCAZO*

(CH3)2N2* —k3C2H6+ N2rAZO*= -k3.CAZO*

PSSH: rAZO*= k1.CAZO2 - k2.CAZOCAZO* -k3.CAZO* 0


h4 1 3 find rate expression of overall reaction
H4.1.3Find Rate Expression of Overall Reaction….

2 N2O54 NO2+ O2


  • What rate expression is consistent with this mechanism?
two proposed mechanism can give rise to the same rate expression
Two Proposed Mechanismcan give rise to the same rate expression

2 NO+ 2 H2  N2 + 2 H2O

  • What rate expression is consistent with these mechanism?
h4 2 1 example of chain reaction free radical as active intermediate
H4.2.1Example of Chain Reaction:Free Radical as Active Intermediate

H2+ Br22 HBr


Initiation X + Br2—12 Br• + X

Propagation Br • + H2—2HBr + H •

H • + Br2—3HBr + Br •

Terminatiion X + 2 Br • —4Br2 + X

H • + HBr —5H2 + Br •

  • What rate expression is consistent with this mechanism?
chain reactions
Chain Reactions


Mekanisme berantai di bawah ini diusulkan untuk reaksi dekomposisi ozon:

Inisiasi :

Propagasi :

Terminasi :

  • Bagaimana persamaan laju reaksi dekomposisi ozon menurut mekanisme ini?
  • Hasil percobaan pada suhu rendah menunjukkan bahwa persamaan laju dekomposisi ozon mengikuti persamaan:

Apakah mekanisme yang diusulkan konsisten dengan hasil percobaan ini?

chain reactions14
Chain Reactions


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 :

Propagation :

Termination :

  • What rate expression is consistent with this mechanism?
chain reactions thermal cracking of ethane
Chain Reactions:Thermal Cracking of Ethane


The thermal decomposition of ethane to ethylene, methane, butane, and hydrogen is believed to proceed in the following sequence:

Use PSSH to derive a rate law for the formation of ethylene

chain reactions flame retardants
Chain Reactions: Flame Retardants


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:

The last two reactions are rapid compared to the firs two. When HCl is introduced to the flame, the following additional reactions occur:

Derive a rate law for consumption of CO for both when no retardant present and when HCl is introduced

chain reactions the pyrolysis of acetaldehyde
Chain Reactions:The Pyrolysis of Acetaldehyde


The pyrolysis of acetaldehyde is believed to take place according to the following sequence:

Derive the rate expression for the rate of disappearance of acetaldehyde

chain reactions in tribology engine oil degradation
Chain Reactions in TribologyEngine Oil Degradation


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 I2 is an initiator and RH is the hydrocarbon in the oil.

When the temperature is raised to 100oC, the following additional reaction occurs as a result of the decomposition of the unstable ROOH:

  • Derive the rate expression for the degradation of the uninhibited motor oil:
  • At low temperature (25oC)
  • At high temperature (100oC)
engine oil degradation the role of antioxidant
Engine Oil Degradation:The Role of Antioxidant

P7-7C (cont’)

When an antioxidant is added to retard degradation at low temperatures, the following additional termination step occur:

  • Derive the rate expression for the degradation of the uninhibited motor oil:
  • At low temperature (25oC)
  • At high temperature (100oC)

Free Radical Polymerization

1. The Reaction


This reaction produces the formation of the Primary Radical






rate determining limiting step
Rate-determining (-limiting) Step

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:

Using PSSH:

If it is known that reaction (3) is much slower than (1) & (2) reactions, it is easily derived that:


Rate-determining (-limiting) Step

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 N2O54 NO2+ O2


  • Fast
  • Slow
  • Fast
  • What rate expression is consistent with this mechanism?

Example : P7-8A

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,



Or he may become ill through contact with another ill person


I + H 2I





The ill person may become healty



Or he may expire


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).