kinetics
Physical Chemical Chemistry
Lecture 5
Theoretical chemical kinetics
Temperature dependence of
rate constants
k (T )
A exp( Ea / RT )
Empirical theory of
Arrhenius gives a useful
way to parameterize
rate constants
A pre-exponential
factor
Ea activation energy
Often seen in analysis
of kinetic data
Elementary reactions
Chemical reactions are often more complex than
presented and do not occur as a single step
Some reactions do occur in a single step -elementary reactions
Generally involve simple mono- or bimolecular interactions
Order in elementary reactions is the stoichiometry number,
called molecularity
H2
H
2 O H 2O2
Br HBr
v k[ H 2 ]1[O]2
v k[ H ]1[ Br ]1
Understand the nature of reactions
Predict reaction outcomes based on
Reactants
Conditions
Requires integration of theory and
experimental results
Non-Arrhenius behavior
Arrhenius behavior is
empirical
For some reactions the
temperature
dependence of the rate
constant is not
exponential
Theory does not easily
predict Arrhenius form
Amazing that Arrhenius
behavior is so often
seen
Simple collision theory of gasphase kinetics
To participate in a
v
bimolecular reaction,
molecules must
vmax
approach each other
SCT: gas-phase reaction
rate proportional to
collision frequency
SCT does not generally
AB
agree with experimental
rates
k max
Points out how to think
about theory of
chemical reactions
Z AB
Z AB
AB v AB n* n*
AB
8kT
AB L
C AC B
2
d AB
collision cross section
AB L
8kT
1
Correcting simple collision
theory
Relation of SCT parameters to
Arrhenius parameters
SCT neglects two features
Collision must be sufficiently
energetic to cause reaction
Molecules must have proper
orientation to allow reaction
Empirically add two
factors to account for
these features
v Z AB p exp( Emin / RT )
8kT
p AB L
exp( Emin / RT ) C AC B
p steric factor
Emin minimum energy for
reaction
k
p AB L
8kT
exp( Emin / RT )
Like van der Waalss
improvement of the idealgas law
Experimental SCT and
Arrhenius parameters
Many experimental data
reported as Arrhenius
behavior
Comparison with SCT
necessary to connect
theory and experiment
Predicts a temperaturedependent activation
energy and preexponential factor
(which may not be the
observation)
Arrhenius behavior
ln k
Ea
T
RT 2
By comparison of differentials
RT
Ea Emin
2
A p e1/ 2 k max
Computer modeling of
potential-energy surfaces
Reaction
Range
ln A
Ea
p
H + D2 HD + D
300 750
24.61
39.3
0.088
H + HCl H2 + Cl
200 500
23.85
14.6
0.039
H + HBr H2 + Br
1000 - 1700
25.42
15.5
0.076
O + O3 2 O2
273 900
23.21
20.0
0.037
N + NO N2 + O
300 6000
23.28
~0
0.040
CH3 + C6H6 CH4 + C6H5
456 600
17.04
38.5
2.7 10-5
BH3 + BH3CO CO + B2H6
273 333
19.34
29.3
PH3 + B2H6 PH3BH3 +BH3
249 10-6
CO 273
14.97
47.7
7.4 + O2 O + CO2
2400 3000
21.97
213.4
4.3 10-3
F2 + ClO2 F + FClO2
227 247
16.37
33.5
5.2 10-5
2.9 10-4
Potential energy of
configuration of
molecules controls
interaction
Model time-dependent
approach of molecules
with (classical or
quantum) simulation
Example:
(a) The range of validity is expressed in kelvins.
(b) A is in dm3 mol-1 s-1.
(c) Ea is in kJ mol-1.
Computer simulation of
reaction
Reactive encounters
go through the
reactive region
Unreactive
encounters go to the
reactive region and
return in the same
channel
M. Karplus, R. N. Porter, and R. D. Shamra, J. Chem.
Phys., 43,3258 (1965).
D + H2 HD + H
Several parameters
Distances
Angles
Simulation of a reactive event
Follow the time
course of the
approach
Atoms exchange
partners
Time scale is very
short
Repeat many times
and measure
fraction of times
that reactive events
happen
2
Activated-complex
mathematics
Activated-complex theory
Theory developed by H.
Eyring, M. Evans, and
M. Polanyi
Proposed the existence
of an activated
complex, a precursor to
products
The activated complex
forms product(s) by a
first-order process
Reaction velocity
v
proportional to
activated-complex
K
concentration
Quasi-equilibrium
between reactants and v
activated complex
Statistical mechanics
defines disappearance
rate constant of
activated complex, f
Activated-complex theory gives a form for
the biomolecular rate constant, k2, in terms
of the parameters of the activated complex
S H
RT
exp
exp
hLC
R RT
This is not Arrhenius-like behavior
Difficult to distinguish from Arrhenius
behavior under many circumstances
Different way to parameterize the SCT rate
constant
Phase/Molecularity
Solution
Gas, unimolecular
Gas, bimolecular
Gas, termolecular
Activation Energy, Ea Pre-exponential factor, A
H RT
eRT
S
exp(
)
hLC
R
H RT
eRT
S
exp(
)
hL
R
H 2RT
e2 RT
S
exp(
)
hLC
R
H 3RT
e3RT
S
exp(
)
hLC 2
R
C
C
C A CB
fK
CC
C A B
S
H
RT
exp
exp
C C
hLC
R
RT A B
Evaluate by plotting
ln(k/T) versus 1/T
Example
OH
CH4
CH3
H2 O
From slope and
intercept
H = 12.0 kJ/mol
S = -33.2 J/K-mol
T. Gierczak, R. Talukdar, S. Herndon, G. Vaghjiani, A. Ravishankara,
J. Phys. Chem, 101A, 3125 (1997).
Alternative to
Arrhenius parameters
Relation of Eyring and
Arrhenius parameters
Need to be able to convert between the two
parameterizations of kinetic data
Use differential of Eyring form to show relationships
a
a Aa B
Evaluation of Eyring
parameters
Eyrings equation
k2
f C
Summary
Theories of simple reactions
Simple collision theory
Modified collision theory
Computer simulation
Activated-complex theory
Parameterization of reaction dynamics
Activation energy and pre-exponential
factor
Equilibrium thermodynamic properties of
activated complex
3