chemical kinetics1
TRANSCRIPT
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ChemicalKinetics
Chapter I
Peter Atkins, Physical Chemistry, 7th editionJeffrey I. Steinfeld et al, Chemical Kinetics and Dynamics, 2nd edition
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Basic concepts of kinetics
Thermodynamics• First law• Second law• Third law
Kinetics
Deal with changes of the system properties in time.
(Physical-Chemical)
Feasibility of any process or reacction to take place
(DSUniv. > 0, DG < 0)
a) Rate of a chemical reaction:
Chemical kinetics: Study chemical systems whose composition changes with time
!Gas, liquids, solid• Homogeneous: Single-phase
• Heterogeneous: Multi-phase
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Stoichiometric representation
aA + bB + … cC + dD …
a and b: # of moles of A and B, i.e. the reactants
c and d: # of moles of C and D, i.e. the products
IrreversibleChemical reaction
ReversibleChemical reaction
2H2 +O2 2H2O H2 + I2 2HI
Type of reactions:• Elementary: One step
• Complexes: Multi-steps
Rate of reaction: Change in composition of the reaction mixtures
dtDd
ddtCd
cdtBd
bdtAd
aR 1111
Reac. [i] (-) Prod. [j] (+)
I2 + hn I2*I2* 2I
2I + M I2 + MH2 + 2I 2HI
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b) Order and Molecularity of a chemical reaction:
• One or more reactants[i]’s
• One or more intermadiates[E]’s
• One or more species that do not appear in the reaction
[C]
Reaction rate
R = f([A], [B])
R a [A]m [B]n
• m and n: Integer, fractional or negative
R = k [A]m [B]n
Rate equation!
Rate constant(Proportionality constant)
• m: Order of reaction with respect to A.
• n: Order of reaction with respect to B
• p = m + n : Overall order of reaction
http://www.chem.uci.edu/education/undergrad_pgm/applets/sim/simulation.htm
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General expression
k
i
ni
ickR1
• ni: Reaction order with respect to i’s component.
*Units of K : [i]-(p-1)t-1
k
iinp
1
Elementary reactions are described by their molecularity
Molecularity: # of reactants involved in the reaction step! (always an integer)
Spontaneousdecomposition
A and B reactwith each other
Three reactantsthat comes together
A Products Unimolecular
A + B Products Bimolecular
A + B + C Products Termolecular
http://www.chm.davidson.edu/ChemistryApplets/kinetics/ReactionRates.html
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Elementary reaction rate lawsTime behavior Integrating the rate law
a) Zero-Order reaction:
ktAAktAA
t
dtkAdkdtAd
Aa
AkdtAd
aR
tt
t
t
A
A
t
00
0
][
][
0
0
][][][][
0
][][
1][,1
][][1
00
t
[A]t
[A]0
m = -K
a) A productsHeterogeneous reactions
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b) First-Order reaction:
ktt
t
eAA
ktAA
0
0
][][
][][ln
303.2]log[]log[
]ln[]ln[][][
][][][][1
0
00
][
][
1
0
ktAA
ktAAdtkAAd
kdtAAdAk
dtAd
aR
t
t
tA
A
t
a = 1
t0=0
t
log[A]t
log[A]0
m = -k/2.303
t
[A]t
[A]0
t
e-1[A]0
k-1 = t (Decay time)[A]t = [A]0/ee=2.7183
b) A productsCH3NC CH3CN
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(CH3)3CBr + H2O (CH3)3COH + HBr[90% acetone & 10% water]T (min) [C] (mol/L)
0 0.1056
9 0.0961
18 0.0856
24 0.0767
40 0.0645
54 0.0536
72 0.0432
105 0.0270
0 20 40 60 80 100 120
0.04
0.05
0.06
0.07
0.08
0.09
0.10
0.11
[C] (
mol
/L)
t (min)
KtAA t 0][][
0 20 40 60 80 100 120
0.1
log[
C] (
mol
/L)
t (min)
303.2]log[]log[ 0
KtAA t
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c) Second-Order reaction:
c1) A + A products
ktAA
dtkA
AdktAA
xxdx
kdtA
AdAkdtAdR
t
tA
At
t
2][
1][
1
2][
][2][
1][
1
1
2][
][][][21
0
0
][
][2
0
2
22
0
t
[A]t-1
[A]0-1
m = 2k
2CH3 C2H6b
a
b
a
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c2) A + B products
kt
BABA
BA
baxabax
dx
xABAdx
xBBAdx
xBxAdx
xBxAkdtdx
BBAAx
BAkdtAdR
t
t
tt
][][][][ln
][][1
)ln(1
][][][][][][][][
][][
][][][][
][][][
0
0
00
00000000
00
00
11
H2 + O OH + H
b
a
b
a
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d) Third-Order reaction:
d1) A + A + A products
ktAA
dtkA
AdktAA
xnxdx
kdtA
AdAkdtAdR
t
tA
At
n
b
an
t
6][1
][1
3][
][3][1
][1
21
1)1(
1
3][
][][][31
20
2
0
][
][32
02
1
33
0
t
[A]t-2
[A]0-2
m = 6k
b
a
I + I + M I2 + M
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d2) A + A + B products
kt
BABA
BAAABA
kdtyByA
dy
yByAkdtdy
BAyBB
yAA
BAkdtAdR
t
t
t
t
t
][][][][ln
][2][1
][1
][1
][2][1
][2][
][2][
][,][][][
2][][
][][][21
0
02
00000
02
0
02
0
00
0
0
2
Partial fractions!
tkAA
orderpseudoBkk
AkdtAdR
t
nd
'2][
1][
1
2],['
]['][21
0
2
[B]>>[A][B] = const.
O + O2 + M O3 + M
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d3) A + B + C products
]][][[][ CBAkdtAdR
Reaction rate for n order respect with only one reactant
ktnnAA
nktAAn
dtnkA
Ad
AkdtAd
nR
nnt
nnt
A
A
t
n
n
t
)1(][1
][1
][1
][1
)1(1
][][
][)(
1
)1(0
)1()1(0
)1(
][
][ 00
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e) Reaction half-lives: Alternative method to determine the reaction order
2][
][ 0
21
21
AAt
2ln1
][2/][ln
2/][][
][][ln
2/1
2/1
0
0
0
0
kt
ktA
A
AA
ktAA
t
t
First-order reaction
For a reaction of order n>1 in a single reactant
Independent of [A]0
1
0
1
21 ])[1(
12
n
n
Ankt
This is function of [A]0
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1st order reaction half-lives:
0 10 20 30 40 500
0.2
0.4
0.6
0.8
11
6.738 10 3
A t( )
500 t
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T dependence of the rate constant, kThe Arhenius equation:
k(T):
• [i]• t• pH (only in solution) T! (Strongly)
TkE
TB
Act
Aek )(
1/T
ln[k(T)]lnA
m = -EAct/kB
Chemical coordinates
E
EAct(F)EAct(R)
Reac
Prod.
DH0Rxn
A :Frequency factor
0Re
0Pr
0
0 )()(
acodRxn
ActActRxn
HHH
FEREH
DDD
D
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Ineffective Effective
Determinant Parameters
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Catalysis
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Complex reactionsa) Reversible reactions:
A1 A2kf
kr
12
2
211
AkAkdtAd
AkAkdtAd
fr
rf
If @ t=0[A1] = [A1]0
[A2] = [A2]0
[A1] + [A2] = [A1]0 + [A2]0[A2] = [A1]0 + [A2]0 - [A1]
020111
1020111
AAkkkAdtAd
AkAAkAkdtAd
rrf
rrf
(Mass conservation law)
ClCl
Cl
Cl
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102011 A
kkAAk
kkdtAd
rf
rrf
Introducing the variable m
tkk
AkAkAkAk
dtkkAm
AdAmkk
dtAd
kkAAk
m
rfrf
rf
t
trf
A
Arf
rf
r
0201
21
1
11
1
0201
ln
0
1
01
tkkAk
AkAkrf
f
rf
01
21ln
If @ t=0[A2]0=0
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tkk
rf
f
tkkfr
rf
rf
rf
ekk
AkA
AAA
ekkkk
AA
1012
1012
011
When the equilibrium is reached
eq
eq
eq
r
f
eqreqf
eqreqf
KA
A
kk
AkAk
AkAk
dtAd
dtAd
1
2
21
21
21
0
0
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b) Consecutive reactions:
A1 A2 A3k1 k2
223
22112
111
AkdtAd
AkAkdtAd
AkdtAd
b1) First:
tkeAA 1011
b2) Second:
For [A2] Linear differential equation of first order
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tktk
tktktktk
eekk
AkA
eekk
AkeAAeAkAk
dtAd
AkAkdtAd
21
2121
12
0112
12
01102201122
2
11222
Standardmethods
b3) Third:
If @ t=0[A2]0=0
[A1]0 = [A1] + [A2] + [A3] [A3] = [A1]0 - [A1] - [A2]
tktktktktk e
kkk
ekk
kAAee
kkk
eAA 21211
12
1
12
2013
12
1013 11
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0 2 4 6 8 100
0.2
0.4
0.6
0.8
11
0
A t( )
A 0( )
B t( )
A 0( )
C t( )
A 0( )
100 t0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
11
0
A t( )
A 0( )
B t( )
A 0( )
C t( )
A 0( )
100 t
K1 = 1K2 = 100
K1 = 1K2 = 0.1
A B C CBA
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0 2 4 6 8 100
0.2
0.4
0.6
0.8
11
0
A t( )
A 0( )
B t( )
A 0( )
C t( )
A 0( )
100 t
K1 = 1K2 = 0.01
0 2 4 6 8 100
0.2
0.4
0.6
0.8
11
0
A t( )
A 0( )
B t( )
A 0( )
C t( )
A 0( )
100 t
K1 = 1K2 = 0.1
0 2 4 6 8 100
0.2
0.4
0.6
0.8
11
0
A t( )
A 0( )
B t( )
A 0( )
C t( )
A 0( )
100 t
K1 = 1K2 = 10
0 2 4 6 8 100
0.2
0.4
0.6
0.8
11
0
A t( )
A 0( )
B t( )
A 0( )
C t( )
A 0( )
100 t
K1 = 1K2 = 100
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c) Parallel reactions:(First order decay to different products)
A1 A2
A3
k2
k3
133
122
13121
AkdtAd
AkdtAd
AkAkdtAd
c1) First:
tkk
t
t
A
A
eAAdtkkAAd
AkkdtAd
32
0
1
01
011321
1
1321
32' kkk
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c2) Second:
tkk
atat
ttkk
A
tkk
ekk
AkA
ea
dte
dteAkAd
eAkdtAd
32
32
2
32
1
1
32
0122
0012
02
0122
[A2]0 = 0
c3) Third:
tkk
atat
ttkk
A
tkk
ekk
AkA
ea
dte
dteAkAd
eAkdtAd
32
32
3
32
1
1
32
0133
0013
03
0133
[A3]0 = 0
b
a
b
a
b
a
b
a
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0 0.5 1 1.5 20
0.5
11
0
A1 t( )
A2 t( )
A3 t( )
20 t
k2= 1, k3=10
0 0.5 1 1.5 20
0.5
11
0
A1 t( )
A2 t( )
A3 t( )
20 t
k2= 1, k3=1
0 0.5 1 1.5 20
0.5
11
0
A1 t( )
A2 t( )
A3 t( )
20 t
k2= 1, k3=0.1
A1 A2
A3
k2
k3
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d) Parallel reactions:
A1 A2
A3
k1
k3
333
33112
111
AkdtAd
AkAkdtAd
AkdtAd
0
0
2
033
011
A
AAAA
t
tktk
tk
tk
eAkeAkdtAd
eAA
eAA
31
3
1
0330112
033
011
tktk
ttk
ttk
A
eAAeAAA
dteAkdteAkAd
31
31
2
030301012
0033
0011
02
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0 1 2 3 40
0.5
1
1.51.311
0
A1 t( )
A2 t( )
A3 t( )
40 t0 1 2 3 4
0
0.5
1
1.5
21.963
0
A1 t( )
A2 t( )
A3 t( )
40 t0 1 2 3 4
0
0.5
1
1.5
21.982
0
A1 t( )
A2 t( )
A3 t( )
40 t
k1= 1, k3=10k1= 1, k3=1k1= 1, k3=0.1
A1 A2
A3
k1
k3
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Steady-State approximation
This method is very usefulwhen intermediates are presentin small amount [Ai]
0
dtAd i
If we take the case b2) of Consecutive reactions(k1 << k2)
12
12
11222 0
Akk
A
AkAkdtAd
SS
tkSS eA
kk
A 101
2
12
tkSS eAA 11013
A1 A2 A3
k1 k2
A1 A2 A3
k1
K-1
k2
Home work!0 2 4 6 8 10
0
0.2
0.4
0.6
0.8
11
0
A t( )
A 0( )
B t( )
A 0( )
C t( )
A 0( )
100 t
0
0
0302
011
AAAA
t
)1( 1013
tkSS eAA
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The Michaelis-Menten mechanism(Enzyme action)
+ +
S (Substrate)E (Enzyme) X(Enzyme-Substrate
complex)
E (Enzyme)
P1 & P2
(Products)
True chemical Intermediate
[ES] << 1K2 > k1
0dtESd
Another Initial condition is:
[E]0 = [E] + [ES][S]0 = [S] + [P] SEES
E + S ES E + Pk1
K-1 K-2
K2
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12
2
12
1
2112
11
0
kkPEk
kkSEk
ES
PEkSEkESkkdtESd
ESkSEkdtPd
dtSd
SS
SS
2121
02121
kkPkSkEPkkSkk
dtSd
E + S ES E + Pk1
K-1 K-2
K2
Considering[S] >> [P] @ t = 0
SEES
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SK
vvEkv
kkk
K
Skkk
EkdtSdv
Sk
kkSkESkk
dtSd
M
SS
M
1
1
02
1
21
1
21
02
1
211
021
Michaelis-Mentenconstant
KM
vS
[S]
v
vS
2
t 0
t 0