break link between thermodynamics and kinetics
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Motivation and Strategy
Some Important Concepts
Rate Equations
Mechanisms and Kinetics
Temperature Dependence of Rate Constant
Compensation Effect
What Kinetics Will (Not) Deliver…
Reaction rates
Rate equation / reaction order
Rate constant
Apparent activation energies
Will not deliver a mechanism…..
But any mechanism we think of should be consistent
with the kinetic data….
Motivation
Reactants
Products
E
EA
Catalyst A
Reaction coordinate
Reactants
Products
E
EA
Catalyst B
Reaction coordinate
Design Parameters for Setup
Compare catalysts: Activation energy EA
Equilibrium conditions
Microscopic Reversibility
1
1
]][[
][
k
kK
BA
AB
A* + B
ABA + B k1
k-1
k2
k-2
k3
k-3
32
32
]][[
][
kk
kkK
BA
AB
Unidirectional reaction with identical rates is not an option
Steady State Approximation
Bodenstein’s approximation for consecutive reactions
If k1*>>k1, then
A B Ck1 k1
*
0][
dt
Bd
Simplifies Rate Equations
Rate Equations I
With a,b,c, the individual reaction order with respect to a
particular reactant and the total reaction order n the sum of the
exponents
With r the reaction rate in units of mol/l per time
...][][][ cba CBAkr
Typical rate equation:
Rate Equations II
Typical rate equation:
With k the rate constant in units of min-1 for a first order
reaction, for higher orders in inverse units of concentration in
different powers
...][][][ cba CBAkr
11min
n
mol
l
Catalysis in Solution:Specific Acid / Base Catalysis
Rate constant a linear function of pH
.loglog3
constckOH
rckr pseudo 1st order
Proton donor: H3O+ (solvated protons)
Proton acceptor: OH-
Rate equation (analogous for base catalysis)
Specific Acid Catalysis
Dependence of the observed rate constant for oximation of
acetone on pH at 25°C. The rate equation is r = kobs * Cacetone
Catalysis in Solution:General Acid Base Catalysis
Proton donor HA, H2O...
Proton acceptor B, H2O
Rate equation
.loglog constKk A
HAr cckr 2nd order
HA
AHA c
ccK
H+ + A-HA
Rates in Heterogeneous Catalysis
Rate with respect to mass or surface area
catalystg
mol
min
surfacecatalystm
mol2min
Turn Over Frequency
Rate with respect to number
of active sites
low site density high site density
Turnover frequency is the number of molecules formed per active
site per second (in a stage of saturation with reactant, i.e. a zero
order reaction with respect to the reactant)
1
s
ssite
molecules
TOF, TON, Catalysis
TON
Total number of product formed molecules per active site
TON= TOF*catalyst life time
TON = 1 stoichiometric reaction
TON 102 catalytic reaction
TON = 106-107 industrial application
TON origins from enzyme kinetics, definitions vary
Reaction Steps in Heterogeneous Catalysis
Diffusion of reactant to catalyst
Adsorption of reactant on catalyst surface
Reaction
Desorption of products from catalyst surface
Diffusion of products away from catalyst
We want to know the reaction kinetics. Diffusion should thus not be a rate limiting step.
Interfacial Gradient Effects
Mass transfer bulk of fluid to surface
Case 1: reaction at surface instantaneous
global rate controlled through mass transfer
“diffusion control”, favored at high T
Case 2: reactant concentration at surface same as in bulk
fluid
global rate controlled through reaction rate
“reaction controlling”, favored at low T and high turbulence
Langmuir Hinshelwood Mechanism
Both species are adsorbed, adsorption follows Langmuir
isotherm (see class next week)
A B
AA
AAA pK
pK
1
21 BBAA
BBAABA
pKpK
pKpKkkr
Eley Rideal Mechanism
Only one species is adsorbed, adsorption follows
Langmuir isotherm
A
B
AA
BAABA pK
ppKkpkr
1
Structure Insensitivity
rate per exposed metal surface area is NOT a function of
the metal particle size
active site 1-2 atoms
Example: the hydrogenation of cyclohexene
+ H2
Structure Sensitivity
also: ammonia synthesis (reactions involving C-C, N-N
bond breaking)
C2H6 + H2 2 CH4
rate per exposed metal surface area is a function of the
metal particle size / the exposed facet plane
active site an ensemble of atoms
Example: the hydrogenolysis of ethane
Temperature Dependence of Rate Constant
Once a rate equation has been established, a rate
constant can be calculated
The rate constant is temperature dependent
There are three different ways to derive this relation:
Arrhenius Theory
Collision Theory
Transition State Theory (Eyring)
Arrhenius Theory
BAk1
k-1 1
1
k
kK
2
ln
RT
H
T
K
p
van’t Hoff’s Equation
211 lnln
RT
H
T
k
T
k
211ln
RT
E
T
k
211ln
RT
E
T
k
HEE 11
Arrhenius Theory
With E the apparent activation energy in kJ mol-1
A the frequency factor
Plot of ln k vs. 1/T gives a slope of -EA/R
which allows the calculation of the activation energy
A rule of thumb: the rate doubles for 10 K rise in
temperature
RT
EAk Alnln
Collision Theory
According to the simple collision theory, the
preexponential factor is dependent on T1/2
with NA Avogadro’s number, σ cross section, μ reduced
mass, k Boltzmann’s constant
Tk
NA A 8
A + BC A B C AB + C
Activated Complex Theory
Evans/Polanyi, Eyring
based on statistical thermodynamics
Results of Activated Complex Theory
Rate constant (based on number of moles)
Kh
kTkn
Function of T
From the equilibrium constant for the activated complex,
a standard free enthalpy of activation can be calculated
KRTG ln
Example for Arrhenius Plot
2 different slopes may indicate change in mechanismor change from reaction to diffusion control
Compensation Effect
A “sympathetic variation of the activation energy with the
ln of the pre-exponential factor”
RT
EAk Alnln
.ln constmEA A
ln A and EA/RT have the same order of magnitude but
different signs
Change in EA may b compensated by change in A
Compensation Effect: Explanations
“Apparent” activation energy EA,app derived from
measured rate and rate equation
With increasing temperature, the “true” reaction rate will
increase
With increasing temperature the coverage decreases
(exothermic adsorption), leading to a smaller measured
rate
EA,app is a weighted sum of the EA,true and the enthalpy of
adsorption
Literature
Gabor A. Somorjai, Introduction to Surface Chemistry and
Catalysis, John Wiley, New York, 1994
Bruce C. Gates, Catalytic Chemistry, John Wiley, New York, 1992
G Ertl, H. Knözinger, J. Weitkamp, Handbook of Heterogeneous
Catalysis, Wiley-VCH, Weinheim 1997
G. Wedler, Physikalische Chemie, Verlag Chemie Weinheim
G.F. Froment, K.B. Bischoff, Chemical Reactor Analysis and
Design, Wiley 1990
Compensation effect: G.C. Bond, Catal. Today 1993, J. Catal. 1996
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