thermodynamic aspects of heterogeneous catalysis · pdf filethermodynamic aspects of...
TRANSCRIPT
![Page 1: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/1.jpg)
Thermodynamic Aspects of Heterogeneous Catalysis
Research
Raimund Horn
Fritz Haber Institute of the Max Planck Society Berlin
Emmy Noether Research Group „High Temperature Catalysis“
10/26/2012
Modern Methods in Heterogeneous Catalysis Research WS 2012/2013
1
![Page 2: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/2.jpg)
Introduction
2
One way of dealing
with thermodynamics!
or
![Page 3: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/3.jpg)
Content
3
1. Why does Thermodynamics matters in Catalysis?
2. Thermodynamic Quantities, Concepts and Tools
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
4. Chemical Equilibrium: Conversion and Selectivity Calculations for
Multiple Reactions
![Page 4: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/4.jpg)
1. Why does Thermodynamics matters in Catalysis?
4
The best-known „catalytic reactor“:
One reaction catalyzed bythe catalytic converter:
In the gas phase
MCOMOCOOCOOCO
2
22
CO
2OCO
CO + ½ O2 CO2 rHo (298K) = -283 kJmol-1
OCO C
OO
OOC OOC
2CO 2CO
On Pt
Pt
![Page 5: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/5.jpg)
1. Why does Thermodynamics matter in Catalysis?
5
TemperatureEnergetics of CO oxidation
RTEr exp
E
E
In the gas phase
On Pt
Taken from: G. Ertl, Catalysis: Science and Technology Vol. 4 1983 p. 245ff, all enthalpies in kJmol-1
![Page 6: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/6.jpg)
1. Why does Thermodynamics matter in Catalysis?
6
Kinetics
TEquilibrium Transport
TCTkr AA
RTGK R
0
ln TCTD
J
AAB
A
0
0
00 T
Tpp
FFvv
T
T AK
AKAads
ads
10
![Page 7: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/7.jpg)
1. Why does Thermodynamics matters in Catalysis?
7
Thermodynamics matters in Catalysis because
Thermodynamics determines the maximum extentof any given reaction
The reaction rate decreases withapproach to thermodynamic equilibrium
Heat release or uptake by chemical reactions leads tocomplex non-isothermal reactor behavior
Adsorption/Desorption thermodynamics determines theconcentration of adsorbed species and in turn the rate of surface reactions (e.g. Langmuir Hinshelwood rate expressions)
The kinetics of elementary steps are related to theirthermodynamics
macroscopic
microscopic
C
BAfA K
CCkrBA
![Page 8: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/8.jpg)
1. Why does Thermodynamics matter in Catalysis?
8Taken from: M. Salciccioli et al. Chem. Eng. Sci. 66 (2011) 4319
![Page 9: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/9.jpg)
9
Equilibrium Conversion and SelectivityCalculations for Multiple Reactions
(Examples)
Quantities, Concepts and Tools
First Law of TD, U, H, CV, Cp
Entropy S and Second Law of TD
Clausius Inequality and Gibbs Free Energy G
Chemical Potential µ
Chemical Equilibrium and Law of Mass Action
Chemical Conversion for a Single Reaction (Example)
Consequences for Reactor Design (Examples)
![Page 10: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/10.jpg)
2. Thermodynamic Quantities, Concepts and Tools?
10
2.1) Systems in Thermodynamics
System Surroundings Exchange of Matter
Exchange of Energy
e.g. a heatedflow reactor
e.g. an autoclave
e.g. a thermos bottleor the universe
open system closed system isolated system
![Page 11: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/11.jpg)
11
2.2) Processes
Irreversible Processes
2. Thermodynamic Quantities, Concepts and Tools?
![Page 12: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/12.jpg)
12
2.2) Processes
Reversible Processes
2. Thermodynamic Quantities, Concepts and Tools?
![Page 13: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/13.jpg)
13
Thermodynamic Quantity Symbol Intensive or Extensive? SI Unitmass m extensive kg
molar mass M intensive kgmol-1
temperature T intensive Kpressure P, p intensive Pafugacity f intensive Padensity intensive kgm-3
volume V extensive m3
molar volume Vm, v,… intensive m3mol-1
heat Q extensive Jwork W extensive J
inner energy U extensive Jenthalpy H extensive J
free energy, Helmholtz free energy F, A extensive Jfree enthalpy, Gibbs free energy G extensive J
2.3) Important Quantities
2. Thermodynamic Quantities, Concepts and Tools?
![Page 14: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/14.jpg)
14
Thermodynamic Quantity Symbol Intensive orExtensive SI Unit
entropy S extensive JK-1
molare inner energy Um,u intensive Jmol-1
molar enthalpy Hm,h intensive Jmol-1
molar free energy Am, a, Fm, f intensive Jmol-1
molar free enthalpy Gm, g intensive Jmol-1
chemical potential µ intensive Jmol-1
molar entropy Sm,s intensive JK-1mol-1
heat capacity at constant volume CV extensive JK-1
heat capacity at constant pressure CP extensive JK-1
specific heat capacity c(V,p) intensive Jkg-1K-1
molar heat capacity Cm(V,p), cm(V,p) intensive Jmol-1K-1
2.4) Important Quantities
2. Thermodynamic Quantities, Concepts and Tools?
![Page 15: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/15.jpg)
15
2.4.1) Internal Energy U in J
..... magnelnucchemrotvibtrans UUUUUUUU
VC (internal pressure )
0 for ideal gases
WQU First Law of Thermodynamics:
2. Thermodynamic Quantities, Concepts and Tools?
![Page 16: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/16.jpg)
16
2.4.2) Internal Energy U in J
WQU
The First Law of Thermodynamics is important for describing non-isothermalreactors (energy balance) but says nothing about the direction of a physical orchemical process!
2. Thermodynamic Quantities, Concepts and Tools?
![Page 17: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/17.jpg)
17
2.4.3) Enthalpy H in J
weight
area
....
),....,,,,(
1,,1,,
21
1
dnnHdp
pHdT
THdH
nnnpTHH
jjj nTpnTnp
k
pC (isothermer drosseleffekt in m3) 0 for ideal gases
2. Thermodynamic Quantities, Concepts and Tools?
![Page 18: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/18.jpg)
18
2.4.3) Enthalpy H in J
2. Thermodynamic Quantities, Concepts and Tools?
iiiii
DCBA nndndDCBA 0, 1 extent of reaction
H
Tp,
H
enthalpy of reaction i
ii HH
322 23
21 NHHN example:
3221
23
21
NHHN HHHH
The standard enthalpy of formation Hf° or standard heat of formation of acompound is the change of enthalpy that accompanies the formation of 1mole of the compound from its elements, with all substances in their standardstates. The standard state of a gas is the (hypothetical) ideal gas at 1bar and298.15K. For liquids and solids it is the pure substance at 1bar and 298.15K.
32231
23
21)( 3 NHHNfNH HHHNHHH
Hess Law
![Page 19: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/19.jpg)
19
2.4.4) Heat capacities CV, Cp in J/K RCC mVmp ,,for ideal gases
2. Thermodynamic Quantities, Concepts and Tools?
![Page 20: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/20.jpg)
20
2.4.4) Heat capacities CV, Cp in J/K
2. Thermodynamic Quantities, Concepts and Tools?
KmolJCC
molkJNHHN
ipiipr
186.22 9.45H 23
21
r322
22 23
21 HN
barpKT
115.298
31NHbarp
KT1
15.298
molkJ9.45
22 23
21 HN
barpKT
1400
31NHbarp
KT1400
molkJ2.48
2
1
r12 )(H)(HT
Tprr dTCTT
Kirchhoff‘s law
pC
TH
rp
r
![Page 21: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/21.jpg)
21
2.4.5) EntropyExample: 3 Molecules (A,B,C) distributed among 4 energy states(0=0, 1= 1, 2=21, 3=31) with a total energy of total=31 (isolated system)
Energy State Energy Macrostate
I II III
3 31 A B C
2 21 C B C A B A
1 11 B C A C A B ABC
0 01 BC AC AB A A B B C C
# of Microstates(statistical weight W) 3 6 1
WkS ln
2. Thermodynamic Quantities, Concepts and Tools?
![Page 22: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/22.jpg)
22
2.4.5) Entropy
Second Law of Thermodynamics
2. Thermodynamic Quantities, Concepts and Tools?
![Page 23: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/23.jpg)
23
2.4.5) Entropy
irreversibleprocess
high
low
TT
1
reversibleprocess
2. Thermodynamic Quantities, Concepts and Tools?
Sadi Carnot
![Page 24: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/24.jpg)
24
2.4.5) Entropy Rudolph Clausius
Clausius Inequality
2. Thermodynamic Quantities, Concepts and Tools?
TdQdS
![Page 25: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/25.jpg)
25
2.4.6) Helmholtz Free Energy (Free Energy) andGibbs Free Energy (Free Enthalpy)
Clausius Inequality dHQ
dUQ
p
V
spontaneous process at constant volume
spontaneous process at constant pressure 00
TdSdHTdSdU
Helmholtz Free Energy (Free Energy):
Gibbs Free Energy (Free Enthalpy):
2. Thermodynamic Quantities, Concepts and Tools?
TdSdQTdQdS 0
![Page 26: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/26.jpg)
26
2.4.7) Dependencies of G by Combining the First and Second Law of Thermodynamics
pdVTdSWQWQdU revrev
VdppdVdUdHpVUH
VdpTdSVdppdVpdVTdSdH
SdTVdPSdTTdSVdpTdSSdTTdSdHdG
STGV
pG
pT
2. Thermodynamic Quantities, Concepts and Tools?
![Page 27: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/27.jpg)
27
2.4.8) Gibbs Free Energy in Mixtures and the Chemical Potential
inTpinTpnTp
dnnGdn
nGdn
nGSdTVdPdG
ijjj
,,
2,,2
1,,1
....21
ijnTpii n
G
,,
chemical potential of i
0 ,,,
,,,,
BiAiBi
BiBiAiAi
dndndndG
T,p=const.
2. Thermodynamic Quantities, Concepts and Tools?
![Page 28: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/28.jpg)
28
2.4.8) Gibbs Free Energy in Mixtures and the Chemical Potential
im
nTpip
i Sn
ST
ij
,,,
imnTpiT
i VnV
pij
,,,
Example: pure ideal gas
2. Thermodynamic Quantities, Concepts and Tools?
pRT
nVVnRTpV m
![Page 29: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/29.jpg)
29
2.4.8) Gibbs Free Energy in Mixtures and the Chemical Potential
Membrane permeable for i (e.g. Pd and i=H2)
for ideal gaseous andliquid mixtures
for real systems
in any case
2. Thermodynamic Quantities, Concepts and Tools?
![Page 30: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/30.jpg)
30
2.5) Chemical Equilibrium
iiiDCBA nnDCBA 0, extent of reaction
2. Thermodynamic Quantities, Concepts and Tools?
in equilibrium
![Page 31: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/31.jpg)
31
G
R e a k tio n s k o o rd in a te
T = k o n s t.p = ko n s t.
d G = 0
G T=const.
p=const.
G=0
2.5) Chemical Equilibrium
2. Thermodynamic Quantities, Concepts and Tools?
![Page 32: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/32.jpg)
32
standard state for all gases is the pure ideal gas at 1bar
activity of an ideal gas
pK
2.5) Chemical Equilibrium
2. Thermodynamic Quantities, Concepts and Tools?
law of mass action
![Page 33: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/33.jpg)
33
pK
2.5) Chemical Equilibrium
)( pfK p
)( pfK
ii
iii
ppK
ppxppxK x
ii
ii
RTcpRTnVp iiii
ii
iii
ppK
pRTcpRTcK c
ii
ii
)( pfK x
)( pfK c
2. Thermodynamic Quantities, Concepts and Tools?
![Page 34: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/34.jpg)
34
2.5) Chemical Equilibrium
2. Thermodynamic Quantities, Concepts and Tools?
Temperature Dependance of K:
Gibbs Helmholtz Equation
van‘t Hoff Equation
![Page 35: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/35.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
35
Example: Calculate the maximum NH3 yield of the Haber-Bosch-Process for25°C 600 °C and 1bar p 500 bar! Assume a stoichiometric feed andideal gases for simplicity!
)()(23
21
322 gNHgHgN Equation:
Thermodynamic Data (NIST Chemistry Webbook, CRC Handbook, PC books...):
Species Hf° / kJmol-1 S° / Jmol-1K-1 Cp°/ Jmol-1K-1
A B / 10-3 K-1 C / 10-6 K-2
N2 0 191.6 24.98 5.912 -0.3376H2 0 130.7 29.07 -0.8368 2.012NH3 -45.9 192.8 25.93 32.58 -3.046
211/ TCTBAmolKJC p
![Page 36: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/36.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
36
Calculate K for 25°C: STHG
73815.298314.8
1037.16expexp
37.161005.9915.2989.45
05.998.19217.130)2/3(6.1912/1
9.45)9.45(10)2/3(02/1
3
3
KJmolKmolJ
RTGK
molkJ
KmolkJK
molkJG
KmolJ
KmolJS
molkJ
molkJH
Species i Hf° / kJmol-1 S° / Jmol-1K-1 Cp°/ Jmol-1K-1
A B / 10-3 K-1 C / 10-6 K-2
N2 -1/2 0 191.6 24.98 5.912 -0.3376H2 -3/2 0 130.7 29.07 -0.8368 2.012NH3 1 -45.9 192.8 25.93 32.58 -3.046
![Page 37: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/37.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
37
Calculate X from K:
Species i ni0/mol ni/mol xi
N2 -1/2 1/2 1/2-1/2 (1/2-1/2)/(2-)H2 -3/2 3/2 3/2-3/2 (3/2-3/2)/(2-)NH3 1 0 /(2-) 2 2- 1
iiii
n
nii
i
nnddndndi
i
000
1
2/1)2/1(
0,2
2
0,2
20,2
N
N
N
NN
n
nnn
X
2/32/1
1
2/3
2
2/1
2
13
22/32/3
22/12/1
2
pp
pp
pp
pp
pp
pp
aKHN
NH
ii
i
![Page 38: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/38.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
38
Solution: Graphical Solution (e.g. with Excel, Origin....)
T=298.15 K and p=1 bar
2/32/1
1
22/32/3
22/12/1
2738
pp
pp
pp
![Page 39: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/39.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
39
T dependance of K:
T
Tp
TdTR
THTKTKRT
HT
K
1
212 lnlnln
T
Tp TdTCTHTH
1
1
Speciesi
Hf° / kJmol-1
S° / Jmol-1K-1
Cp°/ Jmol-1K-1
A B CN2 -1/2 0 191.6 24.98 5.912 -0.3376H2 -3/2 0 130.7 29.07 -0.8368 2.012NH3 1 -45.9 192.8 25.93 32.58 -3.046
2630
20
1090.5109.3017.30
....
TTTC
AATCTBATC
p
iiip
![Page 40: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/40.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
40
T dependance of K: T
Tp TdTCTHTH
1
1
323
12
111
31
321
211
21
3232
32
1
TCTBTATCTBTATH
TTCTTBTTATH
TdTCTBATHTHT
T
20 TCTBATC p
T
Tp
TdTR
THTKTKRT
HT
K
1
212 lnlnln
![Page 41: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/41.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
41
T dependance of K:
31
2111
22
3231
2111
32.
32.
3232
TCTBTATHconst
TRC
RB
RTA
RTconst
RTTH
TCTBTATCTBTATHTH
21
21
111
21
62ln11.lnln
32.lnln
1
TTRCTT
RB
TT
RA
TTRconstTKTK
TdTRC
RB
RTA
TRconstTKTK
T
T
![Page 42: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/42.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
42
T dependance of K:
2/32/1
1
22/32/3
22/12/1
2)(lnexp
pp
pp
pp
TK
21
21
111 62
ln11.lnln TTRCTT
RB
TT
RA
TTRconstTKTK
Solve
numerically or graphically with p and T as parameters gives = (p,T)!
![Page 43: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/43.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
43
Solution: Numerical Solution (e.g. with Matlab, Mathematica....)
KT /barp /
typical process conditions forindustrial ammonia synthesis
![Page 44: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/44.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
44
Thermodynamics says nothing about the rate at which a process proceeds!
![Page 45: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/45.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
45
molkJH
SOOSO
r
CSOKOV
/99
2/1 3600400,22 4252
Te
Ta
![Page 46: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/46.jpg)
3. Chemical Equilibrium: Reactor Conversion for a Single Reaction
46
molkJKHOHCHHCO r / 8.90300 2 32
Linde Isothermal Reactor, e.g. for
methanol synthesis
![Page 47: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/47.jpg)
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
47
4.1 Theory min,.....,, 21, NpT nnnGG
but the ni cannot vary independently because they have to fulfill thematerials balances
N
ikiki bna
1
number of atoms of element k in species i
moles of species i in the reaction mixture
total moles of atoms of elementk in the reaction mixtures
N
i
M
k
N
ikiki
N
ikikikiki bnabnabna
1 1 1k
1k 0 0 0
Lagrange Multipliers
![Page 48: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/48.jpg)
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
48
M
k
N
ikikipT bnaGF
1 1k,
Lagrange Function
01
k1
k,,,,
M
kkii
M
kki
npTinpTi
aanG
nF
ijij
0ln1
0
M
kkikii aaRTG
01
k
N
ikiki bna
set of N equations(1 for each of the N species)
set of M equations(1 for each of the M elements)
N + M unknowns (n - mole numbers + m - lambdas)
4.1 Theory
![Page 49: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/49.jpg)
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
49
4.2 Example: Calculate the equilibrium composition of a steam reformingmixture consisting of CH4, H2O, CO, CO2 and H2 at T=1000K and p=1bar. n0,CH4=2mol, n0,H2O=3mol. Ideal gases can be assumed.
From thermodynamic tables (e.g. CRC Handbook) we extract:
Species CH4 H2O CO CO2 H2
Gf° (1000K) / Jmol-1 19475 -192603 -200281 -395865 0
Species CH4 H2O CO CO2 H2
# of C atoms aC,CH4=1 aC,H2O=0 aC,CO=1 aC,CO2=1 aC,H2=0# of O atoms aO,CH4=0 aO,H2O=1 aO,CO=1 aO,CO2=2 aO,H2=0# of H atoms aH,CH4=4 aH,H2O=2 aH,CO=0 aH,CO2=0 aH,H2=2
From the species formulas we obtain:
![Page 50: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/50.jpg)
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
50
4.2 Example: Formulating the equations
0ln1
0,
M
kki
ki
if aRT
aRTG
ii
i
ii
ii
ii n
nbarbar
nn
ppx
ppa
11
01000314.8
41000314.8
ln1000314.8
19475 4
HC
ii
CH
nn
01000314.81000314.8
2ln1000314.8
192603 2
OH
ii
OH
nn
01000314.81000314.8
ln1000314.8
200281
OC
ii
CO
nn
01000314.8
21000314.8
ln1000314.8
395865 2
OC
ii
CO
nn
0224 COCOCH nnn
032 22 COCOOH nnn
014224 224 HOHCH nnn
CH4:
H2O:
CO:
CO2:
H2: 01000314.8
2ln 2
H
ii
H
nn
atom balance on C
atom balance on O
atom balance on H
starting valuesn0,CH4 = 2 moln0,H2O = 3 mol.
![Page 51: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/51.jpg)
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
51
4.2 Example: Solving the system of nonlinear equations e.g in Matlab (fsolve)
ii
H
CO
CO
OH
CH
nnnnnn
651.8795.5319.0
507.1856.0175.0
2
2
2
4
ii
H
CO
CO
OH
CH
xxxxxx
16698.00368.0
1742.00990.00202.0
2
2
2
4
The most difficult thing is to find starting values that work. Make educatedguesses based on physical or chemical knowledge (0 xi 1), e.g.
28812
5.0ln1000314.801000314.8
2ln 0,2
HH
ii
H
nn
![Page 52: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/52.jpg)
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
52
4.3 Another Example: Equilibrium Calculations with CHEMKIN
Methan Oxidation on Rh and Pt Coated Foam Catalysts (T 1000°C)
CH4 + O2
H2, CO, H2O, CO2
~ 10-3 s
p, H const.
![Page 53: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/53.jpg)
5 wt% Rh on 80ppi -Al2O3 foam, feed 5 ln/min, C/O = 1.0, Ar/O2 = 79/21, 1 bar
R. Horn*, K. A. Williams, N. J. Degenstein, A. Bitsch-Larsen, D. Dalle Nogare, S. A. Tupy, L. D. Schmidt J. Catal. 249 (2007) 380-393
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
4.3 Another Example: Equilibrium Calculations with CHEMKIN
![Page 54: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/54.jpg)
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
4.4 Take home message: Some months in the Lab can save you one day in the Library!!!
typical transient experiment
![Page 55: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/55.jpg)
4. Chemical Equilibrium: Conversion and Selectivity Calculations for Multiple Reactions?
4.4 Take home message: Some months in the Lab can save you one day in the Library!!!
tr/ss = 98%
tr/ss = 99%
![Page 56: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/56.jpg)
Thermodynamics matters in Catalysis!!!
56
Kinetics
TEquilibrium Transport
TCTkr AA
RTGK R
0
ln TCTD
J
AAB
A
0
0
00 T
Tpp
FFvv
T
T AK
AKAads
ads
10
![Page 57: Thermodynamic Aspects of Heterogeneous Catalysis · PDF fileThermodynamic Aspects of Heterogeneous Catalysis Research ... Adsorption/Desorption thermodynamics ... M. Salciccioli et](https://reader034.vdocuments.us/reader034/viewer/2022042611/5a78547f7f8b9a77438b4ebe/html5/thumbnails/57.jpg)
Maybe the better way to deal with Thermodynamics?
57
Thank you very much for your attention!!!