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

Reactants

Products

E

EA

without catalyst

Reaction coordinate

Reactants

Products

E

EA

with catalyst

Reaction coordinateMust look at T

D because we can’t change it!

Target Reaction – Quantities to Look at

Enthalpy of reaction ΔrH

exothermic / endothermicΔrH 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!!!

Calculate from enthalpies of formation of products and reactants

L

iifir HH

1

ΔrH°: standard enthalpy of reactionΔfH°: standard enthalpies of formationvi: stoichiometric factors, positive for products, negative for reactants

DCBA DCBA

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)

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 ,°

www.iupac.org

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)

AtkinsSTP „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)

ALWAYS CHECK / SPECIFY THE CONDITIONS !!

ALWAYS CHECK / SPECIFY THE CONDITIONS !!

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)

ΔcH° = -286 kJ mol-1

)()()(2

1222 gOHgHgO

Combustion of carbon

ΔcH° = -394 kJ mol-1

)()()( 22 gCOgOsC

Reactions with CO2, H2O or other very stable molecules as products are usually strongly exothermic, however….

Steam Reforming of Methanol

)(3)()()( 2223 gHgCOgOHgOHCH

ΔcH° = 93 kJ mol-1

State of the Matter

Formation of benzene at 298.15 K

)()(3)(6 662 gHCgHsC

ΔfH° = 49.0 kJ mol-1

)()(3)(6 662 lHCgHsC

Enthalpy of evaporation of benzene?

ΔvapH° = 30.8 kJ mol-1 at 80°C

ΔfH° = 82.93 kJ mol-1

Partial Oxidation of Propene

Oxidation of propene to acrolein

ΔrH° = ??? kJ mol-1

OHOHCOHC 243263 2

1

Examples for Sources

Examples for Sources

Partial Oxidation

Only enthalpy of combustion, ΔcH°, of acrolein is given

ΔcH° = -1633 kJ mol-1

)(2)(3)(5.3)( 22243 gOHgCOgOgOHC

Enthalpies of combustion are easily determined quantities (e.g. from quantitative combustion in a bomb calorimeter)

Use Hess’s Law

)(2)(3)(4)(2)(3 2222 gOHgCOgOgHsC ΔcH° = -1754 kJ mol-1

ΔcH° = -1633 kJ mol-1)(2)(3)(5.3)( 22243 gOHgCOgOlOHC

)()(5.0)(2)(3 4322 lOHCgOgHsC ΔfH° = -121 kJ mol-1

Enthalpy is a State Function

Partial vs. Total Oxidation

Oxidation of propene to acrolein

ΔrH° = -427 kJ mol-1

OHOHCOHC 243263 2

1

Oxidation of acrolein to CO2

ΔcH° = -1633 kJ mol-1

)(2)(3)(5.3)( 22243 gOHgCOgOgOHC

Reactants

Partial Oxidation Product

EEA

Reaction coordinate

Total Oxidation Products

EA

Dehydrogenation vs. Oxidative Dehydrogenation

)()()( 284104 gHgHCigHCi

Oxidative dehydrogenation of isobutane to isobutene

ΔrH° = -124 kJ mol-1

)()()(5.0)( 2842104 gOHgHCigOgHCi

Dehydrogenation of isobutane to isobutene

ΔrH° = 117 kJ mol-1

Combustion of isobutene

ΔcH° = - 2525 kJ mol-1

Oxidative Dehydrogenation:Thermodynamic Traps

)(4)(4)(6)( 22284 gOHgCOgOgHCi

Nevertheless, the oxidative dehydrogenation of isobutene is in commercial operation (CrO3/Al2O3 or supported Pt catalyst)

Dehydrogenation of ethylbenzene to styrene

ΔrH° = 117 kJ mol-1

Dehydrogenation

)()()( 288108 gHlHClHC

Change of ΔrH with Temperature

Most of the time, we are not interested in room temperature

Reactants, T1

Products, T1

Enthalpy

Reaction coordinate

Products, T2

Reactants, T2 ΔrH1

ΔrH2

How to Calculate ΔrH as Function of T

Each enthalpy in the reaction equation changes according to

Kirchhoff’s law

TCdTCHd p

T

T

p

E

A

E

A

T

T

pdTCHHdHH 112

And, if Cp = constant over the temperature range of interest

2

1

12

T

T

pTrTr dTCHH

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

If there is a phase transition within the temperature range, it must be

accounted for

E

U

U

A

T

T

pU

T

T

p dTCHdTCHd 21

...2

21

K

Tb

K

TaCC p

Cp as a function of temperature is usually a polynomial expression such as

Consistency check....

Isomerization of butane

ΔrH° = - 7 kJ mol-1

ΔrS° = -15 J mol-1

ΔrG°= - 2.3 kJ mol-1

Isomerization

)()( 104104 gHCigHCn

STHG

Free Enthalpy ΔrG, and Equilibrium Constant K

Relation between ΔrG° and K in equilibrium, ΔrG=0

thr KRTG ln

i

ithiaK

(dimensionless)

L

iirr

iaRTGG1

ln

Thermodynamic equilibrium constant

Composition dependence of ΔrG

correlation between Kth and Kp

Different Equilibrium Constants K

i

ipipK

For low pressures (a few bars and less), the fugacity coefficients are about 1All pressures, including po should be in the same units.

[Pai]

L

ii

L

iioth

iii fppK

poth KpK i

Kp

With and

Isomerization of butane

ΔrG°= - 2.3 kJ mol-1

Isomerization Equilibrium

53.2RT

G

th eK

xv

p KpK i

at 298 K

)()( 104104 gHCigHCn

28 % 72 %

poth KpK i

Equilibrium Constant Temperature Dependence

2

ln

RT

H

T

K

p

van’t Hoff’s Equation

.ln constRT

HK p

Indefinite integration

211,

2, 11

TTR

H

K

K

pTp

Tp Definite integration

Equilibrium Temperature Dependence

Start your research by calculating the thermodynamics of your reaction!

H = const.

0102030405060708090

100

200 250 300 350 400 450 500 550 600 650 700

Temperature / K

Frac

tion

%

Isobutane

n -Butane

H= f(T); Cp = const.

0102030405060708090

100

200 250 300 350 400 450 500 550 600 650 700

Temperature / K

Frac

tion

%

Isobutane

n -Butane

Part II: Practical Matters

Vapor pressure and saturators

Saturator, 100 ml Methanol79.17 g, is 2.47 mol

Gas outGas in

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

VT

H

V

S

T

p

coex

.

General differential form of the Clausius-Clapeyron Equation

2. RT

Hp

T

p

coex

For sublimation and evaporation

assumes ideal behavior of the gas phase

21

11ln

1

2

TTR

H

p

p

T

T August’s vapor pressure formulaassumes 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

21

12

11

TTR

H

TT epp

The carrier gas will dissolve in the liquid and the vapor pressure will be lowered

Methanol Vapor Pressure

H assumed constant

0

50

100

150

200

250

300

350

280

290

300

310

320

330

340

350

360

Temperature / K

Va

po

r P

res

su

re /

kP

a

H assumed constant

0

5

10

15

20

25

30

285

287

289

291

293

295

297

299

301

303

Temperature / K

Va

po

r P

res

su

re /

kP

a

Small temperature changes can cause significant changes in vapor pressure