reaction kinetics(5)

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Reaction Kinetics (5)

Xuan ChengXiamen University

Physical Chemistry

2

Key Words

Pyrolysis Acetaldehyde Methane Polymerization Monomer Initiator Relaxation

高温分解乙醛甲烷聚合单体引发剂迟豫

Physical Chemistry

Reaction Kinetics

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Physical Chemistry Rice-Herzfeld Mechanisms

Simple rate laws can follow from quite complex chain mechanisms.

(a) Initiation: CHOCHCHOCH ak 33 ][ 3CHOCHkr a

(b) Propagation:

COCHCHCHCHOCH bk3433

]][[ 33 CHCHOCHkr b

(c) Retardation: COCHCOCH ck 33 ][ 3 COCHkr c

(d) Termination: 3333 CHCHCHCH dk 23][ CHkr d

The Rice-Herzfeld mechanism for the pyrolysis of acetaldehyde is

A chain reaction can lead to a simple rate law.

Pyrolysis of acetaldehyde )()()( 43 gCOgCHgCHOCH

2/33

4 ][][

CHOCHkdt

CHd

Reaction Kinetics

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Physical Chemistry Rice-Herzfeld Mechanisms

The net rates of the formation of the two intermediates are

0][][]][[][][ 2

333333

CHkCOCHkCHCHOCHkCHOCHk

dt

CHddcba

0][]][[][

3333

COCHkCHCHOCHk

dt

COCHdcb

0][][ 233 CHkCHOCHk da

CHOCHCHOCH ak 33 ][ 3CHOCHkr a

COCHCHCHCHOCH bk3433

]][[ 33 CHCHOCHkr b

COCHCOCH ck 33 ][ 3 COCHkr c

3333 CHCHCHCH dk 23][ CHkr d

The sum of the two equation is

Reaction Kinetics

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Physical Chemistry

The rate of formation of CH4 is

2/13

2/1

3 ][][ CHOCHk

kCH

d

a

2/33

2/1

334 ][]][[

][CHOCH

k

kkCHCHOCHkb

dt

CHd

d

ab

Rice-Herzfeld Mechanisms0][][ 2

33 CHkCHOCHk da

in agreement with the three-halves order observed experimentally.

However, the true mechanism is more complicated than R-H mechanism.

Other products (acetone, CH3COCH3, and propanaldehyde, CH3CH2CHO) can be formed.

Prob. 17.81

Reaction Kinetics

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Free-Radical PolymerizationsPhysical

Chemistry

Let I and M stand for the initiator and monomer

RI ik2

RMMR ak

211 MMM pk

nmk

mn MMM t ,,2,1,0 m ,2,1,0n

Chain polymerizationResults in the rapid growth of an individual polymer chain for each activated monomer, and often occurs by a radical chain process.

(a) Initiation

(b) Propagation

(c) Termination

322 MMM pk

nk

n MMM np

1,1

Reaction Kinetics

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Chemistry

RI ik2

RMMR ak

(a) Initiation

(b) Propagation

][Ikr i

(fast)

211 MMM pk

322 MMM pk

nk

n MMM np

1,1

]][[ MMkr p

The rate-determining step is the formation of the radicals R.

The chain of reactions propagates quickly,

f is the yield of the initiation step, the fraction of radicals that R successfully initiate a chain. 8.03.0 f

][2][

Ifkdt

Mdi

(17.99)

Reaction Kinetics

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Chemistry

nmk

mn MMM t ,,2,1,0 m ,2,1,0n(c) Termination

2][ Mkr t

Assume that the rate of termination is independent of the length of the chain,

the rate of change of radical concentration by this process is

The total radical concentration is approximately constant throughout the main part of the polymerization.

(the rate at which radicals are formed by initiation the rate at which they are removed by termination)

2][2][

Mkdt

Mdt

(17.101)

Reaction Kinetics

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Chemistry

0][2][2][ 2

MkIfk

dt

Mdti

Applying the steady-state approximation

The steady-state concentration of radical chains

The rate of propagation of the chains (the monomer is consumed)

]][[][

MMkdt

Mdp

2/12/1

][][ Ik

fkM

t

i

(17.102)

][][][ 2/1

2/1

MIk

fkk

dt

Md

t

ip

(17.103)

The rate of polymerization is proportional to the square root of the initiator concentration.

Central feature

Reaction Kinetics

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Physical Chemistry Free-Radical

PolymerizationsThe degree of polymerization (DP)

The number of monomers in the polymer

dtPd

dtMd

Pd

MdDP

tottot /][

/][

][

][

(17.104)

][][][

2

1/][ 2 IfkRk

dt

RddtPd itott

tottot

(17.105)

][][][ 2/1

2/1

MIk

fkk

dt

Md

t

ip

(17.103)

for termination by combination2/12/1 ][)(

][

Ikfk

MkDP

ti

p (17.104)

Reaction Kinetics

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Physical Chemistry Fast Reactions

Experimental methods for fast reactions

Rapid-flow method

Pistons Mixing chamber

Movable spectrometer

The reactants are mixed as they flow together in a chamber. The reaction continues as the thoroughly mixed solutions flow through the outlet tube, and observation of the composition at different positions along the tube is equivalent to the observation of reactant mixture at different times after mixing.

Disadvantage:

A large volume of reactant solution

Reaction Kinetics

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Stopped-flow method

Pistons Mixing chamber

Movable spectrometer

The two solutions are mixed very rapidly by injecting them into a tangential mixing chamber. Beyond the mixing chamber there is an observation cell fitted with a stopping syringe, when a required volume (1 mL) has been injected. The reaction continues in the thoroughly mixed solution and is monitored.

Reaction Kinetics

Stopping syringe

Disadvantage:

A large volume of reactant solution

Small samples

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Flash photolysis method

The gaseous or liquid sample is exposed to a brief photolytic flash of light and then the contents of the reaction chamber are monitored. Both emission and adsorption spectroscopy may be used to monitor the reaction, and the spectra are observed electrochemically or photographically at a series of times following the flash.

Reaction Kinetics

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Physical Chemistry Fast ReactionsTemperature-jump relaxation methods

Relaxation

The return of a system to equilibrium

Time, t

T2

T1

Exponential relaxation

[A]

Temperature jump

Consider the reversible reaction

CBA fk kb

]][[ BAkr ff

][Ckr bb

For all times after the T jump ][]][[ CkBAkdt

dAbf (17.107)

Equilibrium concentrations at T2 eqeqeq CBA ][,][,][

let ][][ AAx eq ][][ BBx eq ][][ CCx eq dt

dx

dt

Ad

][

Reaction Kinetics

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Time, t

T2

T1

Exponential relaxation

[A]

At equilibrium

][]][[ CkBAkdt

dAbf (17.107)

The perturbation is small eqeq BAx ][][

0][

dt

Ad

)]([)])([]([ xCkxBxAkdt

dxeqbeqeqf

(17.108)

)

][]([][][][

1 xkk

BAxkCkBAkdt

dx

fb

eqeqfeqbeqeqf

0][][][ eqbeqeqf CkBAk (17.109)

xdt

dx 1 1][]([ beqeqf kBAk (17.110)

Reaction Kinetics

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eqeq CCAAx ][][][][

texx

0

xdt

dx 1 1][]([ beqeqf kBAk (17.110)

t

eqeq eAAAA

)][]([][][ 0

Where x is the departure from equilibrium at the new temperature and x0 is the departure from equilibrium immediately after the temperature jump.

1)][]([ beqeqf kBAk

The concentration of A (and of B) relaxes into the new equilibrium at a rate determined by the sum of the two new rate constants.

Reaction Kinetics

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Physical Chemistry Fast ReactionsAnalyzing a temperature-jump experiment

)()()(2 aqOHaqHlOH ][ 2OHkr ff

The H2O(l) H+(aq) + OH-(aq) equilibrium relaxes in 37 s at 298K and pH7, pKw=14.01. Calculate the rate constants for the forward and reverse reactions.

]][[ OHHkr br

])[]([1 OHHkk bf

The equilibrium condition is eqeqbeqf OHHkOHk ][][][ 2

1

22 6.55][][

]][[

molLk

OH

k

OH

OHH

k

k ww

b

f

172/12/1 )100.2()(])[][(1 molLkKKKkOHHKk bwwbb

16108.16.55

wKK

Reaction Kinetics

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Physical Chemistry Fast ReactionsAnalyzing a temperature-jump experiment

The H2O(l) H+(aq) + OH-(aq) equilibrium relaxes in 37 s at 298K and pH7, pKw=14.01. Calculate the rate constants for the forward and reverse reactions.

172/12/1 )100.2()(])[][(1 molLkKKKkOHHKk bwwbb

1111176

104.1)100.2()1037(

1

sLmol

molLskb

15104.2 sKkk bf

K and Kw are dimensionless

kf and kb are expressed in different units

Reaction Kinetics

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Physical Chemistry Reactions in Liquid

SolutionsSolvent Effects on Rate Constants

gas-phase reaction

liquid-phase reactionsolvent

Ionic Reactionsgas-phase reaction

liquid-phase reactionsolvent

ions

solvation oH

oG

Encounters, Collisions, and the Cage Effectgas-phase reaction

liquid-phase reactionMolecules are far apart and move freely between collisions

Little empty space between molecules and can’t move freely

Reaction Kinetics

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SolutionsEncounters, Collisions, and the Cage Effect

Encounters

Collisions A process in which B and C diffuse together to become neighbors

Each encounter in solution involves many collisions between B and C

B

C

B

C

Cage effect for B and C

Reaction Kinetics

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SolutionsDiffusion-controlled Reactions

Gas-phase

Liquid-phaseMore encounters, shorter time together

Less encounters but stay near each other for much longer than in a gas

B

C

B

C

Cage effect for B and CEncounter pair

Reaction Kinetics

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Suppose the rate of formation of an encounter pair BC is

The steady-state concentration of BC

BCCB dk ]][[ CBkr d

PBC ak ][BCkr a

CBBC dk '

][' BCkr d

0]BC[]BC[]B][C[d

][d ' add kkkt

BC

']B][C[

][da

d

kk

kBC

The overall rate law for the formation of products

Reaction Kinetics

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The overall rate law for the formation of products

]B][C[]BC[d

][d2kk

t

Pa '2

da

da

kk

kkk

']B][C[

][da

d

kk

kBC

If the rate of separation of the unreacted encounter pair is much slower than the rate at which it forms products

ad kk '

BCCB dk

PBC ak

CBBC dk '

da

da kk

kkk 2

(1) diffusion-controlled reaction

The rate of reaction is governed by the rate at which the reactant particles diffuse through the medium.

Reaction Kinetics

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SolutionsDiffusion-controlled ReactionsThe overall rate law for the formation of products

]B][C[]BC[d

][d2kk

t

Pa '2

da

da

kk

kkk

']B][C[

][da

d

kk

kBC

If the rate of separation of the unreacted encounter pair is much faster than the rate at which it forms products

'da kk

BCCB dk

PBC ak

CBBC dk '

Kkk

kkk a

d

da '2

(2) activation-controlled reaction

The reaction proceeds at the rate at which energy accumulates in the encounter pair from the surrounding solvent.

'd

d

k

kK

Reaction Kinetics

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SolutionsDiffusion-controlled ReactionsThe rate of a diffusion-controlled reaction is calculated by considering the rate at which the reactants diffuse together.

PCB dk

))((4 CBCBAD DDrrNk where B C, nonionic (17.111)

))((2 CBCBAD DDrrNk where B = C, nonionic (17.112)

1))((4

WCBCBADe

WDDrrNk where B C, ionic (17.113)

)(4 0

2

CBr

CB

rrkT

ezzW

Reaction Kinetics

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SolutionsDiffusion-controlled ReactionsWhen apply the Stokes-Einstein equation (16.37)

))((4 CBCBAD DDrrNk where B C, nonionic (17.111)

B

C

C

B

CB

CBD r

r

r

rRT

rr

rrRTk 2

3

2)(

3

2 2

(17.114)

BB r

kTD

6

CC r

kTD

6

where B C, nonionic

if rB = rC

Dk3

8RT

34RT

where B C, nonionic

where B = C, nonionic (17.115)

Is the solvent’s viscosity

Reaction Kinetics

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SolutionsActivation Energies

Gas-phase reactions: high temperature (up to 1500K)

Liquid-phase reactions: relatively lower temperature (up to 500K)

Liquid-phase reactions: activation energy range 235 kcal/mol

Gas-phase reactions: activation energy range -3100 kcal/mol

Home Work

17.67 17.70 17.77

17.83 17.87 17.89

Reaction Kinetics

reaction kinetics(5)

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