reaction kinetics(5)
TRANSCRIPT
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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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Free-Radical PolymerizationsPhysical
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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Free-Radical PolymerizationsPhysical
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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Free-Radical PolymerizationsPhysical
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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Physical Chemistry Fast Reactions
Experimental methods for fast reactions
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
13
Physical Chemistry Fast Reactions
Experimental methods for fast reactions
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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Physical Chemistry Fast ReactionsTemperature-jump relaxation methods
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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Physical Chemistry Fast ReactionsTemperature-jump relaxation methods
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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Physical Chemistry Reactions in Liquid
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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Physical Chemistry Reactions in Liquid
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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Physical Chemistry Reactions in Liquid
SolutionsDiffusion-controlled Reactions
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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Physical Chemistry Reactions in Liquid
SolutionsDiffusion-controlled Reactions
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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Physical Chemistry Reactions in Liquid
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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Physical Chemistry Reactions in Liquid
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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Physical Chemistry Reactions in Liquid
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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Physical Chemistry Reactions in Liquid
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