chbe 452 lecture 15
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CHBE 452 Lecture 15. Theory Of Activation Barriers. Last Time Found Barriers To Reaction Are Caused By. Uphill reactions Bond stretching and distortion Orbital distortion due to Pauli repulsions Quantum effects Special reactivity of excited states. Today Models. Polanyi - PowerPoint PPT PresentationTRANSCRIPT
CHBE 452 Lecture 15 Theory Of Activation Barriers
1
Last Time Found Barriers To Reaction Are Caused By
Uphill reactions Bond stretching and distortion Orbital distortion due to Pauli
repulsions Quantum effects Special reactivity of excited states
2
Today Models
Polanyi Bond stretching + Linearization
Marcus Bond stretching + parabola
Blowers Masel Bond streching + Pauli repulsions
3
Polayni's Model
4
Ener
gy
E a
rBH
B RHr
BHr
RH
Figure 10.3 A diagram illustrating how an upward displacement of the B-H curve affects the activation energy when the B-R distance is fixed.
Ener
gy
rBH
B RHr
BHr
RH
Reactants
Products
Figure 10.4 A diagram illustrating a case where the activation energy is zero.
Derivation Of Polayni Equation
5
En
erg
y
rAB
Ea
Actual
PotentialLinear
Fit
Line 1
Line 2r
1r
2
BCAB
Figure 10.6 A linear approximation to the Polanyi diagram used to derive equation (10.11).
E E + Sl r - r (reactants)1 Reactant 1 ABC 1
E E + Sl r - r (products)2 product 2 2 ABC
(10.9)
(10.10)
Case Where Polayni Works (Over A Limited Range Of ΔH)
6
-20 -15 -10 -5 0 5 10 15 20
-20 -15 -10 -5 0 5 10 15 20
0
5
10
15
20
25
, kcal/molerH
, k
cal/
mo
lea
E
Figure 10.7 A plot of the activation barriers for the reaction R + H R RH + R with R, R = H, CH3, OH plotted as a function of the heat of reaction Hr.
Equation Does Not Work Over Wide Range Of H
7
-2.4 -4.8 -7.2 -9.6
-6
-4
-2
0
2
Log kac
, kcal/molerH
MarcusEquation
Figure 10.11 A Polanyi plot for the enolization of NO2(C6H4)O(CH2)2COCH3. Data of Hupke and Wu[1977]. Note Ln
(kac) is proportional to Ea.
Seminov Approximation: Use Multiple Lines
8
-40 -20 0 20 400
0
10
20
30
40
Heat Of Reaction, kcal/mole
Act
ivat
ion
Bar
rier,
kcal
/mol
e Seminov
-100 -50 0 50 1000-20
0
20
40
60
80
100
Heat Of Reaction, kcal/moleA
ctiv
atio
n B
arrie
r, kc
al/m
ole Seminov
Figure 11.11 A comparison of the activation energies of a number of hydrogen transfer reactions to those predicted by the Seminov relationships, equations (11.33) and (11.34)
Figure 11.12 A comparison of the activation energies of 482 hydrogen transfer reactions to those predicted by the Seminov relationships, over a wider range of energies.
Equation Does Not Work Over A Wide Data Set
9
-30 -20 -10 0 10 20 300
-30 -20 -10 0 10 20 300
0
5
10
15
20
25
30
, kcal/molerH
, kca
l/m
ole
aE
Figure 10.10 A Polanyi relationship for a series of reactions of the form RH + R R + HR. Data from Roberts and Steel[1994].
Key Prediction Stronger Bonds Are Harder To Break
10
En
erg
y
rAB
Weak Bond
rAB
EaEa
Bond E
nerg
y
Strong Bond
Figure 10.8 A schematic of the curve crossing during the destruction of a weak bond and a strong one for the reaction AB + C A + BC.
Experiments Do Not Follow Predicted Trend
11
50 60 70 80 90 100 110 12030
35
40
45
50
55
60
65
70
75
, k
cal/
mo
lea
E
Predicted Trend
Experimental Trend
Figure 10.9 The activation barrier for the reaction X- +CH3X XCH3 +
X-. The numbers are from the calculations of Glukhoustev, Pross and Radam[1995].
Marcus: Why Curvature?
12
-2.4 -4.8 -7.2 -9.6
-6
-4
-2
0
2
Log kac
, kcal/molerH
MarcusEquation
Figure 10.11 A Polanyi plot for the enolization of NO2(C6H4)O(CH2)2COCH3. Data of Hupke and Wu[1977]. Note Ln
(kac) is proportional to Ea.
Derivation: Fit Potentials To Parabolas Not Lines
13
Figure 10.13 An approximation to the change in the potential energy surface which occurs when Hr changes.
Ener
gy
rX
E a
ApproximationActual
Potential
r1
r2
E1
E2
Eleft E
right
1
Derivation
14
Figure 10.13 An approximation to the change in the potential energy surface which occurs when Hr changes.
Ene
rgy
rX
E a
ApproximationActual
Potential
r1
r2
E1
E2
Eleft
Eright
1
E (r ) SS (r r ) Eleft X 1 X 1
21
(10.21)
E (r ) SS (r r ) H Eright X 2 X 22
r 2
(10.22)
Solving
15
r22
2
‡
212
1‡
1H+E+)r(rSS=E+)r(rSS
SS SS1 2
Result
E 1H
4EE wA
r
a0
2
a0
r
(10.23)
(10.24)
(10.31)
E 1H
4EEA
r
a0
2
a0
(10.33)
Qualitative Features Of The Marcus Equation
16
-2.4 -4.8 -7.2 -9.6
-6
-4
-2
0
2L
og k
ac
, kcal/molerH
MarcusEquation
Figure 10.11 A Polanyi plot for the enolization of NO2(C6H4)O(CH2)2COCH3. Data of Hupke and Wu[1977].
Note Ln (kac) is proportional to Ea.
Marcus Is Great For Unimolecular Reactions
17
0 50 100 150 200 250
rate
, se
c-1
MarcusEquation
Data
105
106
107
108
109
1010
1011
H , kcal/moler
Figure 10.17 The activation energy for intramolecular electron transfer across a spacer molecule plotted as a function of the heat of reaction. Data of Miller et. al., J. Am. Chem. Soc., 106 (1984) 3047.
Marcus Not As Good For Bimolecular Reactions
18
-25 0 25 50 75 100 125
rate
, lit
mol s
ec
-1
MarcusEquation
Data
105
106
107
108
109
1010
1011
H , kcal/moler
-1
Figure 10.18 The activation energy for florescence quenching of a series of molecules in acetonitrite plotted as a function of the heat of reaction. Data of Rehm et. al., Israel J. Chem. 8 (1970) 259.
Comparison To Wider Bimolecular Data Set
19
-100 -50 0 50 1000-20
0
20
40
60
80
100
Heat Of Reaction, kcal/mole
Act
ivat
ion
Bar
rier,
kca
l/mol
e
Marcus
Blowers Masel
Figure 10.29 A comparison of the barriers computed from Blowers and Masel's model to barriers computed from the Marcus equation and to data for a series of reactions of the form R + HR1 RH + R1 with wO = 100 kcal/mole and = 10 kcal/mole.
EAO
Why Inverted Behavior?
20
rAB
rAB
rAB
E =0aEa
Medium distance Smaller Distance
InvertedRegion
Even Smaller Distance
At small distances bonds need to stretch to to TS.
Limitations Of The Marcus Equation
Assumes that the bond distances in the molecule at the transition state does not change as the heat of reaction changes Good assumption for
unimolecular reactions In bimolecular reactions
bonds can stretch to lower barriers
21
rAB
rAB
rAB
E =0aEa
Medium distance Smaller Distance
InvertedRegion
Even Smaller Distance
Explains Why Marcus Better For Unimolecular Than Bimolecular
22
-25 0 25 50 75 100 125
rate
, lit
mol s
ec
-1
MarcusEquation
Data
105
106
107
108
109
1010
1011
H , kcal/moler
-1
0 50 100 150 200 250
rate
, sec-1
MarcusEquation
Data
105
106
107
108
109
1010
1011
H , kcal/moler
Blowers-Masel Derivation
Fit potential energy surface to empirical equation.
Solve for saddle point energy. Only valid for bimolecular reaction.
23
Derive Analytical Expression
24
E
0 When H E
w + 0.5 H V - 2w H
V 4 w + HWhen -1 H E
H When H E
a
r Ao
O r P O r2
P O2
rr A
o
r r Ao
/
/
/
4 1
4 1
4 1
2 2
w w wO CC CH / 2
Bond energies(10.63)
(10.64)
V ww E
w EP O
O AO
O AO
2
(10.65)
Only parameter
Comparison To Experiments
25
-100 -50 0 50 1000-20
0
20
40
60
80
100
Heat Of Reaction, kcal/mole
Act
ivat
ion
Bar
rier,
kca
l/mol
e
Marcus
Blowers Masel
Figure 10.29 A comparison of the barriers computed from Blowers and Masel's model to barriers computed from the Marcus equation and to data for a series of reactions of the form R + HR1 RH + R1 with wO = 100 kcal/mole and Ea
o = 10 kcal/mole.
EAO
Comparison Of Methods
26
-100 -50 0 50 1000
0
50
100A
ctiv
atio
n E
nerg
y ,
kca
l/mole
Heat of Reaction, Kcal/mole
Blowers Masel
Marcus
Polanyi
Blowers Masel
MarcusPolanyi
Figure 10.32 A comparison of the Marcus Equation, The Polanyi relationship and the Blowers Masel approximation for =9 kcal/mole and wO = 120 kcal/mole.
Ea
o
Example: Activation Barriers Via The Blowers-Masel Approximation
27
Use a) the Blowers-Masel approximation b) the Marcus equation to estimate the activation barrier for the reaction H + CH3CH3 H2 + CH2CH3
Solution: Step 1 Calculate VP
VP is given by:
28
V ww E
w EP o
o A
o A
2
0
0
(11.F.2)
Where EA0 is the intrinsic barrier given in
Table 11.3. According to table 11.3 EA0=10
kcal/mole. One could calculate a value of wo from data in the CRC. However, I decided to assume a typical value for a C-H bond, i.e. 100 kcal/mole. I choose H r=-2 kcal/mole from example 11.C
Step 1 Continued
Substituting into equation (11.F.2) shows
29
V kcal molekcal mole kcal mole
kcal mole kcal molekcal moleP
2 100
100 10
100 10244 4/
/ /
/ /. /
(11.F.3)
Step 2: Plug Into Equation 11.F.1
30
E mole mole
mole mole mole
w Hmolea
p o r
100kcal 0.5 2kcal
244.4kcal 2 100kcal 2kcal
49.0Kcal
2
2 2 2/ * // / /
(V )/
(11.F.1)
E w HV w H
V w Ha o r
p o r
p o r
0 5
2
4
2
2 2 2. *
( )
By comparison the experimental value from Westley is 9.6 kcal/mole.
Solve Via The Marcus Equation:
31
E EH
Ea A
A
0
0
2
14
From the data above EA0 =10 kcal/mole,
H r =-2 kcal/mole. Plugging into equation (11.F.4)
E kcal mole
kcal mole
kcal molekcal molea
10 1
2
4 109 0
2
//
/. /
which is the same as the Blowers-Masel approximation.
(11.F.4)
Summary
Polayni: fair approximation – good over a limited range of H
Marcus: Great for unimolecular Blowers-Masel Great for bimolecular
Only small differences between methods unless magnitude of heat of reaction is larger than 3-4 times Ea
0
32
Query
What did you learn new in this lecture?
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