Thermodynamics
Modern Methods in Heterogeneous Catalysis
F.C. Jentoft, November 1, 2002
Outline
Part I: Reaction + Catalyst
1. Thermodynamics of the target reaction
2. Thermodynamics of catalyst: bulk (see classes on
solids and defects) and surface
3. Thermodynamics of interaction between reactant and
catalyst (see class on adsorption)
Part II: Practical Matters
1. Vapor pressure
What Thermodynamics Will Deliver…
Gives “big picture”, essence, useful for estimates
Target Reaction - Motivation
 Why look at TD? …can’t change it anyway by catalysis
E
without catalyst
E
with catalyst
EA
EA
Reactants
Reactants
Products
Reaction coordinate
Products
Reaction coordinate
Target Reaction – Quantities to Look at
 Enthalpy of reaction ΔrH
exothermic / endothermic
ΔrH of side reactions
 Free Enthalpy (Gibbs Energy) ΔrG
exergonic / endergonic
 Equilibrium Constant K: Equilibrium Limitations
 Change of Temperature and Pressure (variables)
Enthalpy of Reaction
 Determines reactor setup (see classes on catalyst
testing and reaction engineering)
catalyst formulation / dilution
“hot spots” / heating power
isothermal operation in the lab
 Enthalpy of side reactions
parallel / secondary reactions
Enthalpy of Reaction, ΔrH
 Reaction enthalpy needs a reaction equation!!!
 A A   B B   CC   D D
 Calculate from enthalpies of formation of products and reactants
L
 r H    i  f H i 
i 1
ΔrH°:
ΔfH°:
vi:
standard enthalpy of reaction
standard enthalpies of formation
stoichiometric factors, positive for products, negative for reactants
Things to Watch in Calculations…..
 Stoichiometric factors
 Standard conditions
 State of the matter (solid, liquid, gaseous)
 Which data are available (sometimes only enthalpy of
combustion, ΔcH° )
Standard Conditions (IUPAC)
 International Union of Pure and Applied Chemistry
(IUPAC) www.iupac.org
Größen, Einheiten und Symbole in der Physikalischen
Chemie
VCH , Weinheim 1996
FHI library 50 E 49 (English version: 50 E 48)
 Standard state indicated by superscript ,°
Standard Conditions (IUPAC)
 „Standard state pressure“(IUPAC 1982)
p° = 105 Pa
„Standard atmosphere“ (before 1982)
p° = 101 325 Pa = 1 atm
 „Standard concentration“
c° = 1 mol dm-3
 „Standard molality“
m° = 1 mol kg-1
 „Standard temperature“
??
Standard Conditions (Textbooks)
 Atkins
STP „Standard temperature and pressure““
p = 101 325 Pa = 1 atm, T° = 273,15 K
SATP „Standard ambient temperature and pressure“
p° = 105 Pa = 1 bar, T° = 298,15 K
 Wedler
„Standarddruck“
p = 1.013 bar = 1 atm = 101.325 kPa
„Standardtemperatur“
T° = 298,15 K
Standard Conditions (Other)
 Catalysis Literature
NTP „Normal temperature and pressure““
20°C and 760 torr
70 degrees F and 14.7 psia (1 atmosphere)
Sources for Thermodynamic Data
 CRC Handbook of Thermophysical and Thermochemical
Data
Eds. David R. Lide, Henry V. Kehiaian
CRC Press Boca Raton New York 1994
FHI library 50 E 55
 D'Ans Lax
Taschenbuch für Chemiker und Physiker
Ed. C. Synowietz
Springer Verlag 1983
FHI library 50 E 54
Some Examples: Combustion
 Combustion of hydrogen (Knallgasreaktion)
1
O2 ( g )  H 2 ( g )  H 2O( g )
2
ΔcH° = -286 kJ mol-1
 Combustion of carbon
C(s)  O2 ( g )  CO2 ( g )
ΔcH° = -394 kJ mol-1
Reactions with CO2, H2O or other very stable molecules as products are
usually strongly exothermic, however….
Steam Reforming of Methanol
CH3OH ( g )  H 2O( g )  CO2 ( g )  3H 2 ( g )
ΔcH° = 93 kJ mol-1
State of the Matter
 Formation of benzene at 298.15 K
6 C ( s)  3 H 2 ( g )  C6 H 6 ( g )
ΔfH° = 82.93 kJ mol-1
6 C ( s)  3 H 2 ( g )  C6 H 6 (l )
ΔfH° = 49.0 kJ mol-1
 Enthalpy of evaporation of benzene?
ΔvapH° = 30.8 kJ mol-1 at 80°C
Partial Oxidation of Propene
 Oxidation of propene to acrolein
1
C3 H 6  O2  C3 H 4O  H 2O
2
ΔrH° = ??? kJ mol-1
Examples for Sources
Examples for Sources
Partial Oxidation
 Only enthalpy of combustion, ΔcH°, of acrolein is given
C3 H 4O( g )  3.5O2 ( g )  3CO2 ( g )  2H 2O( g )
ΔcH° = -1633 kJ mol-1
Enthalpies of combustion are easily determined quantities
(e.g. from quantitative combustion in a bomb calorimeter)
Use Hess’s Law
3C( s)  2H2 ( g )  4 O2 ( g )  3CO2 ( g )  2H2O( g ) ΔcH° = -1754 kJ mol-1
C3H 4O(l )  3.5O2 ( g )  3CO2 ( g )  2 H 2O( g ) ΔcH° = -1633 kJ mol-1
3C ( s)  2 H 2 ( g )  0.5O2 ( g )  C3H 4O(l )
Enthalpy is a State Function
ΔfH° = -121 kJ mol-1
Partial vs. Total Oxidation
 Oxidation of propene to acrolein
1
C3 H 6  O2  C3 H 4O  H 2O
2
ΔrH° = -427 kJ mol-1
E
EA
Reactants
 Oxidation of acrolein to CO2
EA
Partial
Oxidation
Product
Total
Oxidation
Products
Reaction coordinate
C3 H 4O( g )  3.5O2 ( g )  3CO2 ( g )  2H 2O( g )
ΔcH° = -1633 kJ mol-1
Dehydrogenation vs. Oxidative
Dehydrogenation
 Dehydrogenation of isobutane to isobutene
i  C4 H10 ( g )  i  C4 H 8 ( g )  H 2 ( g )
ΔrH° = 117 kJ mol-1
 Oxidative dehydrogenation of isobutane to isobutene
i  C4 H10 ( g )  0.5O2 ( g )  i  C4 H 8 ( g )  H 2O( g )
ΔrH° = -124 kJ mol-1
Oxidative Dehydrogenation:
Thermodynamic Traps
 Combustion of isobutene
i  C4 H8 ( g )  6 O2 ( g )  4 CO2 ( g )  4 H 2O( g )
ΔcH° = - 2525 kJ mol-1
Nevertheless, the oxidative dehydrogenation of isobutene is in
commercial operation (CrO3/Al2O3 or supported Pt catalyst)
Dehydrogenation
 Dehydrogenation of ethylbenzene to styrene
C8 H10 (l )  C8 H 8 (l )  H 2 ( g )
ΔrH° = 117 kJ mol-1
Change of ΔrH with Temperature
 Most of the time, we are not interested in room temperature
Enthalpy
Products, T2
Reactants, T2 ΔrH1
Δ rH 2
Products, T1
Reactants, T1
Reaction coordinate
How to Calculate ΔrH as Function of T
 Each enthalpy in the reaction equation changes according to
Kirchhoff’s law
TE
H 2  H1  dH  H1   C p dT
TA
 And, if Cp = constant over the temperature range of interest
TE
dH   C p dT  C p T
TA
T2
 r H T2   r H T1   C p dT
T1
Heat Capacity as a Function of T,
Condensed Phases
Heat Capacity as a Function of T, Gases
How to Calculate ΔrH as Function of T
 Cp as a function of temperature is usually a polynomial
expression such as
T1
T2
C p  C  a  b 2  ...
K
K
 If there is a phase transition within the temperature range, it
must be accounted for
TU
TE
TA
TU
dH   C p1dT  U H   C p 2 dT
Isomerization
 Isomerization of butane
n  C4 H10 ( g )  i  C4 H10 ( g )
ΔrH° = - 7 kJ mol-1
ΔrS° = -15 J mol-1
ΔrG°= - 2.3 kJ mol-1
 Consistency check....
G  H  TS
Free Enthalpy ΔrG, and
Equilibrium Constant K
 Composition dependence of ΔrG
L
 r G   r G  RT ln  ai
i
i 1
 Thermodynamic equilibrium constant
K th  ai
i
(dimensionless)
i
 Relation between ΔrG° and K in equilibrium, ΔrG=0
 r G   RT ln Kth
Different Equilibrium Constants K
 Kp
K p  pi
i
[Pai]
i
 correlation between Kth and Kp
K th  po
  i
L
 pi
i
i
L

i
fi
i
For low pressures (a few bars and less), the fugacity coefficients are about 1
All pressures, including po should be in the same units.
Kth  po
  i
Kp
Isomerization Equilibrium
 Isomerization of butane
ΔrG°= - 2.3 kJ mol-1
Kth  e

G
RT
 2.53
 With Kth  po   i K p and K p  p  vi K x
n  C4 H10 ( g )  i  C4 H10 ( g )
28 %
72 %
at 298 K
Equilibrium Constant
Temperature Dependence
H 
  ln K 



2

T
RT

p
ln K p
H 

 const .
RT
 K p ,T 2 



  H   1  1 
T T 
K

R
p
,
T
1
2 
 1

p
van’t Hoff’s Equation
Indefinite integration
Definite integration
Equilibrium Temperature Dependence
100
90
80
n -Butane
70
60
50
40
30
Isobutane
20
10
0
200 250 300 350 400 450 500 550 600 650 700
Temperature / K
H= f(T); Cp = const.
Fraction %
Fraction %
H = const.
100
90
80
n -Butane
70
60
50
40
30
Isobutane
20
10
0
200 250 300 350 400 450 500 550 600 650 700
Temperature / K
Start your research by calculating the thermodynamics of your reaction!
Part II: Practical Matters
 Vapor pressure and saturators
Gas in
Gas out
Saturator, 100 ml Methanol
79.17 g, is 2.47 mol
Methanol Thermodynamic Data
Heat Consumed by Evaporation
 Assumption: saturator is adiabatic, evaporate 20 ml of
methanol, all energy for evaporation taken from remaining
80 ml methanol
 20 ml is about 0.5 mol, need about 17.7 kJ for evaporation
 80 ml is about 2 mol, Cp of liquid MeOH is 81.6 J mol-1 K-1
 The temperature of the methanol would theoretically drop
by 108 K
The Clausius-Clapeyron Equation
S
H
 p 


 
 T coex. V TV
General differential form of the
Clausius-Clapeyron Equation
H
 p 

p


2

T
RT

coex.
For sublimation and evaporation
assumes ideal behavior of the gas phase
H
ln

pT1
R
pT2
1 1
  
 T1 T2 
August’s vapor pressure formula
assumes enthalpy is constant
within given temperature range
Vapor Pressure and Temperature
 At 64.4°C, the vapor pressure of methanol is 755 torr
and the enthalpy of evaporation is 35.4 kJ mol-1
 T1 = 337.6 K, p = 100.66 kPa
pT2  pT1 e
H  1 1
 
R  T1 T2



 The carrier gas will dissolve in the liquid and the vapor
pressure will be lowered
Methanol Vapor Pressure
H assumed constant
30
300
25
Vapor Pressure / kPa
350
250
200
150
100
15
10
Temperature / K
Small temperature changes can cause significant
changes in vapor pressure
3
30
1
30
9
29
7
29
5
29
3
29
1
29
9
28
7
28
28
0
36
0
35
0
34
0
33
0
32
0
31
0
0
29
30
Temperature / K
5
0
0
0
20
5
50
28
Vapor Pressure / kPa
H assumed constant