Thermodynamics
Download
Report
Transcript Thermodynamics
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 H6 ( g )
ΔfH° = 82.93 kJ mol-1
6 C(s) 3 H 2 ( g ) C6 H6 (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
C3H4O(l ) 3.5O2 ( g ) 3CO2 ( g ) 2H2O( g ) ΔcH° = -1633 kJ mol-1
3C( s) 2H2 ( g ) 0.5O2 ( g ) C3H4O(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 H8 ( g ) H 2 ( g )
ΔrH° = 117 kJ mol-1
Oxidative dehydrogenation of isobutane to isobutene
i C4 H10 ( g ) 0.5O2 ( g ) i C4 H8 ( 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 ) 4H2O( 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 H8 (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 dH H1 C p dT
TA
And, if Cp = constant over the temperature range of interest
TE
dH 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
dH 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 TS
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
Kth 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
[Pai]
i
correlation between Kth and Kp
Kth 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 p RT
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 TV
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