Nonelementary Reaction Kinetics

65Nonelementary Reaction KineticsITK-329 Kinetika & KatalisisDicky Dermawanwww.dickydermawan.net78.netdickydermawan@gmail.com

Chapter 466Historical PerspectiveDobereiner (1829), Wilhelmy (1850) supposed that reaction rates would be simply related to the stoichiometry of the reaction1878: Vant Hoff showed that the rate equation had little correlation to stoichiometry.

67Historical PerspectiveVant 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?

68Historical FindingsWhen 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.CCH3CHO3/2

H2 + I2 2 HI

(CH3)2N2 C2H6 + N2 At low pressures below 50 mmHg:-rN2 ~ CAZO2At 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 sec69Reactive IntermediatesDavid Chapman (1913), Muriel Chapman & Max Bodenstein (1907):H2 + Cl2 2 HCl Cl as reactive intermediates

Mechanism:

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 productsCH3CH2HC=CH2 CH3HC=CHCH3 Reactive Intermediates are by definition reactive. The undergo many reactions70Kinetic of Elementary ReactionsA + 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 +Qr4 = 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 + X1 P + X -rA = k1 [A] [X] Collosion Partner 71Rates of Overall Reaction

A P

For each reaction: For each species: In a constant volume batch reactor:

72Pseudo-Steady-State Hypothesis

A PAccording 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:

73Another Example:Rates of Overall Reaction(CH3)2N2 C2H6 + N2AZO 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.CAZO2

(CH3)2N2* + (CH3)2N2 k2 (CH3)2N2 + (CH3)2N2rAZO*= -k2.CAZOCAZO*

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

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

Then,

74H4.1.3Find Rate Expression of Overall Reaction.2 N2O5 4 NO2 + O2

Mechanism:

What rate expression is consistent with this mechanism?

75Two Proposed Mechanismcan give rise to the same rate expression2 NO + 2 H2 N2 + 2 H2O

What rate expression is consistent with these mechanism?

76H4.2.1Example of Chain Reaction:Free Radical as Active Intermediate H2+ Br2 2 HBr

Mechanism:InitiationX + Br2 1 2 Br + X

PropagationBr + H2 2 HBr + H H + Br2 3 HBr + Br

TerminatiionX + 2 Br 4 Br2 + XH + HBr 5 H2 + Br

What rate expression is consistent with this mechanism?

77Chain ReactionsH-Il4.3Mekanisme 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?78Chain ReactionsH4.1Houser & 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?

79Chain Reactions:Thermal Cracking of EthaneEx.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

80Chain Reactions: Flame RetardantsP7-3BHydrogen 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:

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

81Chain Reactions:The Pyrolysis of AcetaldehydeP7-4AThe pyrolysis of acetaldehyde is believed to take place according to the following sequence:Derive the rate expression for the rate of disappearance of acetaldehyde

82Chain Reactions in TribologyEngine Oil DegradationP7-7COne 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:

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

83Engine Oil Degradation:The Role of AntioxidantP7-7C (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)

84Free Radical Polymerization

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

TERMINATIONTransferTo solvent To monomer To chain transfer agent To initiator Addition Disproportionation

85Rate-determining (-limiting) StepUsing 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:

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

862 N2O5 4 NO2 + O2

Mechanism:

What rate expression is consistent with this mechanism?

Rate-determining (-limiting) StepWhen 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

87(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 expireThe ill person may become healtyOr he may become ill through contact with another ill personH Ik1(P7-11.1)I + H 2Ik2(P7-11.2)I Hk3I Dk4(P7-11.4)Example : P7-8AConsider 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,CH3CH2HC=CH2 + H+

CH3CH2HC CH2

H

+

CH3CH2HC CH2

H

+

CH3HC=CHCH3 + H+

CH3CH2HC CH2

H

+

CH3CH2HC=CH2 + H+

CH3CH2HC CH2

H

+

CH2 =CHCH2CH3 + H+