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Nonelementary Reaction Kinetics

ITK-329 Kinetika & Katalisis

Dicky Dermawanwww.dickydermawan.net78.net

dickydermawan@gmail.com

Chapter 4

2

Historical PerspectiveDobereiner (1829), Wilhelmy (1850) supposed that reaction rates

would be simply related to the stoichiometry of the reaction1878: Van’t Hoff showed that the rate equation had little

correlation to stoichiometry.

Reaction Rate Equation 4 PH3 P4 + 6 H2 ]PH[kr 33PH3

2 AsH3 As2 + 3 H2 ]AsH[kr 34AsH3

2 PH3 + 4 O2 P2O5 + 3 H2O 2/1235PH ]O[]PH[kr

3

C12H22O11 + H2O H C6H12O6 + C5H9O5CH2OH ]H[]suksrose[kr 6S

CH3COOR + H2O H CH3COOH + ROH ]H[]COORCH[kr 37Ac

CH3COOH + ROH H CH3COOR + H2O ]H[]ROH[]COOHCH[kr 38Ac

ClCH2COOH + H2O HOCH2COOH + HCl ]ClOHC[kr 2329ClOHC 232

2 FeCl3 + SnCl2 FeCl2 + SnCl4 ]Sn[]Fe[kr 22310Fe3

KClO3 + 6 FeO KCl + 3 Fe2O3 ]ClO[]Fe[kr 32

11Fe3

3

Historical PerspectiveVan’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?4 PH3 P4 + 6 H2 ]PH[kr 33PH3

4

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:

CH3CHO CH4 + COAt +/- 500oC: -rCH3CHO = k.CCH3CHO

3/2

H2 + I2 2 HI

(CH3)2N2 C2H6 + N2 At low pressures below 50 mmHg:

-rN2 ~ CAZO

2

At high pressures greater than 1 atm:-rN2

~ CAZO

2

22

H32

HI31HI Ckk

CCkkr

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

5

Reactive Intermediates

David Chapman (1913), Muriel Chapman & Max Bodenstein (1907):H2 + Cl2 2 HCl Cl • as reactive intermediates

H

Mechanism:

CH3CH2HC CH2

H +CH3HC=CHCH3 + H+

CH3CH2HC CH2

H +CH3CH2HC=CH2 + H+

CH3CH2HC CH2

H +CH2 =CHCH2CH3 + H+

CH3CH2HC=CH2 + H+ CH3CH2HC CH2

H +

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

CH3CH2HC=CH2 CH3HC=CHCH3

Reactive Intermediates are by definition reactive. The undergo many reactions

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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

Incorrect:A —1 P -rA = k1 [A]

Correct:A + X—1 P + X -rA = k1 [A] [X]

Collosion Partner

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Rates of Overall Reaction

HPIHA 3

2

1

A P

3P321I

321H

21A

rrrrrr

rrrrrrr

]I[kr]I[kr

]H[]A[kr

3322

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For each reaction: For each species:

In a constant volume batch reactor:

]I[kdt

]P[d

]I[k]I[k]H[]A[kdt

]I[d

]I[k]I[k]H[]A[kdt

]H[d

]I[k]H[]A[kdt

]A[d

3

321

321

21

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Pseudo-Steady-State Hypothesis

HPIHA 3

2

1

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.

0]I[k]I[k]H[]A[kdt

]I[d

0]I[k]I[k]H[]A[kdt

]H[d

321

321

]H[]A[kk

k]I[

32

1

]H[]A[kk

kk]I[k

dt

]P[d

32

313 ]H[]A[kr op

According to stoichiometry: ]H[]A[krr opA

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Another Example:Rates of Overall Reaction

(CH3)2N2 C2H6 + N2

AZO C2H6 + N2

At low pressures below 50 mmHg : -rN2 ~ CAZO2At 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.CAZO

2

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

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

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

Then, 3AZO2

2AZO31

*AZO3N kCk

CkkCkr

2

3AZO2

2AZO1

*AZO kCk

CkC

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H4.1.3Find Rate Expression of Overall Reaction….

2 N2O5 4 NO2 + O2

Mechanism:

2k

3

22k

32

32k

k

52

NO 2NONO

NOONONONO

XNONOONX

4

3

2

1

What rate expression is consistent with this mechanism?

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Two Proposed Mechanismcan give rise to the same rate expression

2 NO + 2 H2 N2 + 2 H2O

OH 2HOH

OHNH NO 2 : A Mechanism

2k

222

222k

2

2

1

OH 2HOH

OH 2NHON

ON NO 2 : B Mechanism

2k

222

222k

222

22k

k

2

5

4

3

What rate expression is consistent with these mechanism?

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H4.2.1Example of Chain Reaction:Free Radical as Active Intermediate

H2+ Br2 2 HBr

Mechanism:Initiation X + Br2 —

1 2 Br• + X

Propagation Br • + H2 —2 HBr + H •

H • + Br2 —3 HBr + Br •

Terminatiion X + 2 Br • —4 Br2 + XH • + HBr —5 H2 + Br •

What rate expression is consistent with this mechanism?

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Chain ReactionsH-Il4.3Mekanisme berantai di bawah ini diusulkan untuk reaksi dekomposisi ozon:Inisiasi :

2k

32 ClOClOOCl 1

Propagasi :

22k

33

23k

32

O2ClOOClO

OClOOClO3

2

Terminasi :

22k

22k

33

OClClOClO

O3ClClOClO5

4

Bagaimana persamaan laju reaksi dekomposisi ozon menurut mekanisme ini?

Hasil percobaan pada suhu rendah menunjukkan bahwa persamaan laju dekomposisi ozon mengikuti persamaan:

23

21

]O[]Cl[kdt

]O[d32

3

Apakah mekanisme yang diusulkan konsisten dengan hasil percobaan ini?

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Chain Reactions

H4.1Houser & 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?

252k

252 NOOHCONOHC 1

OHCNOCHONOHCCH

OCHCHOHC

5223k

2523

23k

52

3

2

OHHCCHOCHOHC2 523k

524

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Chain Reactions:Thermal Cracking of Ethane

Ex.7-2The 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

104k

52

252k

62

42k

52

524k

623

3k

62

HCHC2

:ationminTer

HHCHCH

HHCHC

HCCHHCCH

:opagationPr

CH2HC

:Initiation

5

4

3

2

1

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Chain Reactions: Flame Retardants

P7-3BHydrogen 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:

OOHOH

HCOOHCO

OH2OOH

OOO

2

2

2

2

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

HClClH

ClHHClH 2

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

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Chain Reactions:The Pyrolysis of Acetaldehyde

P7-4AThe pyrolysis of acetaldehyde is believed to take place according to the following sequence:

Derive the rate expression for the rate of disappearance of acetaldehyde

62k

3

23k

3

43k

33

3k

3

HCCH 2

HCO 2CHCHOCHCHO

CHCOCHCHOCHCH

CHOCHCHOCH

4

3

2

1

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Chain Reactions in TribologyEngine Oil Degradation

P7-7COne 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:

inactiveROO 2

RROOHRHROO

ROOOR

HIRRHI

I2I

t

2p

1p

i

0

k

k

k2

k

k2

ROHRHHO

RROHRHRO

HOROROOH

2k

k

k

5p

4p

3p

Derive the rate expression for the degradation of the uninhibited motor oil:

a. At low temperature (25oC)b. At high temperature (100oC)

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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:

inactiveROOA

AROOHAHROO

4A

1A

k

k

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

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Free Radical Polymerization1. The ReactionINITIATION                     This reaction produces the formation of the Primary Radical                       PROPAGATION

                   

TERMINATIONTransfer

To solvent                    

To monomer                      

To chain transfer agent                    

To initiator                    

Addition                    Disproportionation                       

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Rate-determining (-limiting) Step

Using PSSH:

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:

BA

XAXA

3#

#

2

1

32

13B k]X[k

]X[]A[kkr

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

]A[k

kkr

3

13B

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2 N2O5 4 NO2 + O2

Mechanism:

2k

3

22k

32

32k

k

52

NO 2NONO

NOONONONO

XNONOONX

4

3

2

1

What rate expression is consistent with this mechanism?

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

Fast

Slow

Fast

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(P7-11.3)

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).

Or he may expire

The ill person may become healty

Or he may become ill through contact with another ill personH I

k1(P7-11.1)

I + H 2Ik2 (P7-11.2)

I Hk3

I Dk4 (P7-11.4)

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,