msc course adsorption, kinetics & catalysis · 2012. 2. 19. · adsorption, kinetics &...
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1
MSc course
Adsorption, Kinetics & Catalysis
Kinetics
Chapter 2.1-2.6
Prof. Frank de Groot
MSc “Nanomaterials Chemistry and Physics”
Utrecht University
• master / University of Nijmegen / 1987 / Theoretical Chemistry
• PhD / University of Nijmegen / 1991 / Solid State Chemistry
• post-doc / LURE, CNRS Orsay, France / 1993
• post-doc / Groningen (KNAW academy researcher) / 1995
• assistant professor (UD) / Utrecht / 1999 (2001 vidi)
• associate professor (UHD) / Utrecht / 2003 (2006 vici)
• professor / Utrecht / 2009
•
Research
4
Introduction to the course
• Course objectives
– General knowledge on main catalytic processes
– Key concepts in catalysis
• Adsorption
• Kinetics
• Catalysis - mechanisms
• Porosity and surface area – physisorption
• Diffusion
5
Introduction to the course (2)
Steps in diffusion, adsorption and catalysis
Solid catalyst
Pore
6
Introduction to the course (3)
• Course material
– I. Chorkendorff and J.W. Niemantsverdriet.
“Concepts of Modern Catalysis and Kinetics”, 2nd
Edition, Wiley-VCH (2007)
– Handouts, slides
7
Introduction to the course (4)
• Course lay-out – see also lecture schedule
– Oil refining, petrochemistry (Ch 9) KdJ
– Synthesis gas (Ch 8) KdJ
– Kinetics (Ch 2) FdG
– Reaction rate theory (Ch 3) FdG
– Diffusion (Ch 5) KdJ
– Surface reactivity (Ch 6) FdG
– Physisorption PdJ
– Examination
• NIOK course “Catalytic Surface Science”, optional
• Rate Equation
• Arrhenius Equation
• Order of a reaction
• Steady State Approximation
• Chain reactions
• Concentration in coupled reactions
Chapter 2 Kinetics (lecture 1)
‘classical kinetics’
Chemical reaction:
Methanol synthesis
• (a, b, p, q) >> stoichiometric coefficients
• (A, B) >> Reactants
• (P, Q) >> Products
Chemical reaction:
Methanol synthesis
• (a, b, p, q) >> stoichiometric coefficients
• (A, B) >> Reactants
• (P, Q) >> Products
Chemical reaction:
Methanol synthesis
• (a, b, p, q) >> stoichiometric coefficients
• (A, B) >> Reactants
• (P, Q) >> Products
Chemical reaction:
Methanol synthesis
• (a, b, p, q) >> stoichiometric coefficients
• (A, B) >> Reactants
• (P, Q) >> Products
• Rate Equation
• Arrhenius Equation
• Order of a reaction
• Steady State Approximation
• Chain reactions
• Concentration in coupled reactions
Chapter 2 Kinetics (lecture 1)
‘classical kinetics’
Rate Equation
= change in concentration/
change in time
= d[A]/dt
Chemical reaction
• (a, b, p, q) >> stoichiometric coefficients
• (A, B) >> Reactants
• (P, Q) >> Products
qQpPbBaA
k
k
Chemical reaction
• (a, b, p, q) >> stoichiometric coefficients
• (A, B) >> Reactants
• (P, Q) >> Products
qQpPbBaA
k
k
dt
Bd
bdt
Ad
ar 11
dt
Qd
qdt
Pd
pr 11
Rate equation
rrr
qpbaQPkBAkr
qQpPbBaA
k
k
Equilibrium constant
beq
a
eq
q
eq
p
eq
BA
QP
k
kK
qQpPbBaA
k
k
• Rate Equation
• Arrhenius Equation
• Order of a reaction
• Steady State Approximation
• Chain reactions
• Concentration in coupled reactions
Chapter 2 Kinetics
History
• In 1812, the Russian chemist Kirchhof found that when a
water suspension of starch is boiled, no change occurs in the starch. • When a few drops of concentrated sulfuric acid are added to the
same suspension before boiling, the starch breaks down into glucose.
• The acid can be recovered unchanged from the reaction. • Kirchhof concluded that it had played a helping role in the
breakdown of the starch, without itself having undergone any change.
Starch → [H2SO4] → glucose
Arrhenius equation
Arrhenius equation
RTEAAeTk/
)(
Arrhenius equation
RTEAAeTk/
)(
Discovered by:
Jacobus van ‘t Hoff (1884)
Arrhenius equation
Arrhenius equation
RTEAAeTk/
)(
= The fraction of the molecules
present in a gas which have
energies equal to or in excess of
activation energy at a particular
temperature. (Boltzman
distribution; More in chapter 3)
Arrhenius equation
RTEAAeTk/
)(
= A term which includes factors
like the frequency of collisions and
their orientation. It varies slightly
with temperature, although not
much. It is often taken as constant
across small temperature.
(more in chapter 3: reaction rate
theory)
Gas constant R
R= 8.3144 J K-1 mol-1
R = Na * kb
= Avogadro * Boltzmann
= 6·1023 * 1.38 ·10-23
RTEAAeTk/
)(
ºC Rate
0 7.78E-7
25 3.46E-5
45 4.98E-4
55 0.0015
65 0.00487
Arrhenius equation
RTEAAeTk/
)(
Arrhenius equation
RTEAAeTk/
)(
RTEAeATk/
lnln)(ln
RTEATk A /ln)(ln
Arrhenius equation
RTEATk A /ln)(ln
Arrhenius equation
ºC Rate
0 7.78E-7
25 3.46E-5
45 4.98E-4
55 0.0015
65 0.00487
Arrhenius equation
ln k
1/T (K-1)
RTEATk A /ln)(ln
EA= 103 KJ/mol
• Rate Equation
• Arrhenius Equation
• Order of a reaction
• Steady State Approximation
• Chain reactions
• Concentration in coupled reactions
Chapter 2 Kinetics
First order reaction
Equation
Time evolution (integrated equation)
Half time
Linearized equation
First order reaction Equation
PRk
Rkrdt
Rd
First order reaction (time evolution)
Rkrdt
Rd
kdtR
Rd
tR
RR
Rddtk
00
First order reaction (time evolution)
tR
RR
Rddtk
00
kteRR 0
kteR
R lnln0
First order reaction (time evolution)
kteRR 0PRk
RRP 0
)1(0
00
kt
kt
eR
eRRP
First order reaction (half time)
kteRR 0
021 RR
021
0 ReR kt
21kte
First order reaction (half time)
21kte
21lnln kte
2ln kt
ktt 2ln
21
First order reaction (half time)
kteRR 0
S-1
First order reaction (linearize)
kteRR 0
kteR
R 0
kteR
R lnln0
First order reaction (linearize)
kteR
R lnln0
ktR
R
0
ln
kt
R
R0ln
First order reaction (linearize)
kt
R
R0ln
First order reaction
Equation
Time evolution (integrated equation)
Half time
Linearized equation
First order reaction
(exercise)
The decomposition reaction SO2Cl2(g) --->
SO2(g) + Cl2(g) is a first order reaction with
rate constant k=2.2 x 10-5 sec-1 at 320C. What
percent of SO2Cl2 is decomposed at 320C after
90 minutes?
Zeroth order reaction
PRk
Excess R
kr
dt
Rd
Zeroth order reaction (time evolution)
tR
R
dtkRd00
ktRR 0
Zeroth order reaction (half time)
021 RR
ktRR 0
021
0 RktR
021 Rkt
k
Rt
20
21
Zeroth order reaction (half time)
ktRR 0
Reaction order (units)
Order one, the rate coefficient has units of s-1
Order zero, the rate coefficient has units of mol·L-1·s-1
Reaction order (units)
Order one, the rate coefficient has units of s-1
Order zero, the rate coefficient has units of mol·L-1·s-1
Order two, the rate coefficient has units of L·mol-1·s-1
Order n, the rate coefficient has units of mol1-n·Ln-1·s-1
Second order reaction
PRk2
2Rkrdt
Rd
kdt
R
Rd2
Second order reaction (time evolution)
tR
R R
Rddtk
00
2
kt
RR
0
11
Second order reaction (time evolution)
kt
RR
0
11
kt
RR
0
11
kt
R
R
0
1
1
Second order reaction (half time)
021 RR
kt
RR
00
12
kt
R
0
1
kRt
021
1
Zeroth order reaction (half time)
ktRR 0
kt
R
R
0
1
1
Second order reaction (half time)
Second order reaction (linearize)
kt
RR
0
11
The following data were obtained on the rate of hydrolysis of 17 %
sucrose in 0.99 mol L-1 HCl aqueous solution at 35 C.
t / min 9.82 59.60 93.18 142.9 294.8 589.4
Sucrose remaining, % 96.5 80.3 71.0 59.1 32.8 11.1
What is the order of the reaction with respect to sucrose, and what is the
value of the rate constant k?
Exercise
Zero-Order First-Order Second-Order
Rate Law
Integrated
Rate Law
Linear Plot
to determine k
Half-life
Rkrdt
Rd 2Rkr
dt
Rd
kr
dt
Rd
kt
RR
0
11 ktRR 0 kteRR 0
kt
R
R0ln
kRt
021
1
k
Rt
20
21 k
tt 2ln
21
• Rate Equation
• Arrhenius Equation
• Order of a reaction
• Steady State Approximation
• Chain reactions
• Concentration in coupled reactions
Chapter 2 Kinetics
Steady State Approximation
PIRkk 21
PIRk
k
k
2
1
1
PIRkk21
Steady State Approximation
PIRkk21
IkRkdt
Rd 11
IkIkRkdt
Id 211
Ikdt
Pd 2
Steady State Approximation
PIRkk21
0
dt
Id
Steady State Approximation
PIRkk21
0
dt
Id
Steady State Approximation
0211 IkIkRk
RkIkk 121 )(
)( 21
1
kk
RkI
0
dt
Id
Steady State Approximation
0
dt
Id
)( 21
122
kk
RkkIk
dt
Pd
)( 21
1
kk
RkI
Steady State Approximation
RKk
k
Rkkkkdt
Pd12
1
12
)(12
Rk
k
Rkkkkdt
Pd
1
2
12
)(12
PIRkk21
)( 21
122
kk
RkkIk
dt
Pd
Example:
Example:
= 0
Example:
Alternatives to the Steady State Approximation
• Coupled reactions: k-1=0
• Pre-equilibrium solution: [I]=k+1[R]
• Exact solution
PIRkk21
Coupled reactions (concentrations)
PIRkk 21
Rkdt
Rd1
tkeRR 1
0
Coupled reactions (concentrations)
PIRkk 21
IkRkdt
Id21
)( 21
12
10
tktkee
kk
kRI
Coupled reactions (concentrations)
PIRkk 21
IRRP 0
)()(1 21
12
1
12
20
tktke
kk
ke
kk
kRP
Figure 2.5
0,0
0,2
0,4
0,6
0,8
1,0
0,0
0,2
0,4
0,6
0,8
1,0
0,0
0,2
0,4
0,6
0,8
1,0
0 1 2 3 4 5 6 7 8 9 10
k1t
k2 = 0.2 k1
k2 = k1
k2 = 10 k1
[R]
[R]
[R]
[P]
[P]
[P]
[I]
[I]
[I]
concentr
ation
Coupled reactions (concentrations)
I
P R
I
P
R
I
P
R
Alternatives to the Steady State Approximation
• Coupled reactions: k-1=0
• Pre-equilibrium solution: [I]=k+1[R]
• Exact solution
PIRkk21
http://www-jmg.ch.cam.ac.uk/tools/magnus/kinetic.html
• Rate Equation
• Arrhenius Equation
• Order of a reaction
• Steady State Approximation
• Concentration in coupled reactions
• Chain reactions
Chapter 2 Kinetics
Chain reaction
OOk
212
NNONOk
22
ONOONk
3
2
242 OO
k
}2{ 25 NN
k
NOON effk222
Chain reaction
2322 ONkNOkdt
NOd
2322 ONkNOkdt
Nd
2421
2322
22 OkOk
ONkNOkdt
Od
Chain reaction: steady state
0
dt
Nd
0
dt
Od
Chain reaction: steady state
0
dt
Od
0222
421
2322
OkOk
ONkNOk
0222
421 OkOk
Chain reaction: steady state
0
dt
Od
21
2
4 OkOk
24
1 OOk
k
Chain reaction: steady state
02322 ONkNOkdt
Nd
0232224
1 ONkNOkk
k
232224
1 ONkNOkk
k
Chain reaction: steady state
2
2
2
4
1
3
2 NO
ON
k
k
k
k
2
2
4
1
3
2
O
NN
k
k
k
k
Chain reaction: steady state
2
2
4
1
3
2
O
NN
k
k
k
k
2322 ONkNOkdt
NOd
24
1 OOk
k
Chain reaction: steady state
2322 ONkNOkdt
NOd
2
2
23
222
4
1
3
2
4
1
OO
Nk
NOk
k
k
k
k
k
k
dt
NOd
Chain reaction: steady state
2224
12 NOkk
k
dt
NOd
The decomposition of N2O5 → NO2 + NO3 is postulated to take place via two elementary steps:
a. N2O5 + N2O5 N2O5* + N2O5
b. N2O5* → NO2 + NO3
1. Calculate the rate equation, using the steady-state
approximation
2. Assume that reaction b is much faster than the back-
reaction of reaction a. What is the reaction order?
3. Assume that reaction b is much slower than the
back-reaction of reaction a. Reaction order?
Exercise
a. N2O5 + N2O5 N2O5* + N2O5
b. N2O5* → NO2 + NO3
Exercise
*
522
*52521
2521
*52
ONk
ONONk
ONkdt
ONd
Exercise
*522
*52521
2521 ONkONONkONk
)( 2521
2521*
52
kONk
ONkON
Exercise
*522
3 ONkrdt
NOd
)( 2521
25212
kONk
ONkkr
Exercise
)( 2521
25212
kONk
ONkkr
5212
521
25212
)(12
ONKkONk
ONkkr
kk
2521
2
25212
)(12
ONkk
ONkkr
kk
Lindemann-Hinshelwood mechanism
Exercises
Exercises (page 417 and further)
2.5 and 2.6
Questions via email to [email protected]
or room N207 (went)
Next time the exercises will be discussed
Exercises