1
Chapter 5Lecture 13-14
- Thermodynamic Web- Departure Functions- Review Equations of state (chapter 4, briefly)
Chapter 6Chapter 6- Equilibrium (chemical potential)
* Pure Component* Mixtures
Ch t 7Chapter 7- Fugacity (chemical potential fugacity equilibrium calculations)
* Vapor (overview), liquid, solids- Activity Coefficients [Fugacity Coefficients (overview)]y [ g y ( )]
Chapter 8- Phase Equilibrium
* Diagrams* Vapor Liquid (VLE)* Vapor – Liquid (VLE)* Liquid – Liquid (LLE)* Solid – Liquid (SLE)
Chapter 9- Reaction Equilibria
Chemical Reaction Equilibrium 2
3 COHOHCHOH )(2)(2)(3)(2 3 gggg COHOHCHOH
Example: methanol reforming in a fuel cell
???• Will reaction occur?• Is it reversible or irreversible?• Is it endothermic or exothermic?• How fast will the reaction occur?
MotivationMotivation Starting point for process reactor design Limits , if any (equilibrium), on the reaction Heat transfer needs Heat transfer needs
Chemical Reaction Equilibrium 3
3 COHOHCHOH )(2)(2)(3)(2 3 gggg COHOHCHOH
CHMW 3
Desired Trxn = 100 oCDesired P is < 10 bar
Initially: 1 mole MeOHAnd 2 moles H2O
Let react and come to the end Equilibrium reached? Irreversible? What are final concentrations (or
moles of each species) in the reactor?
Chemical Reaction Equilibrium 4
CHMW 3
Let number of moles of CO2 formed [at any time] by reaction
Inventory: (note: number of moles of CO at any time)
nnInventory: (note: number of moles of CO2 at any time) CCO nn
2
[# mol CO2 at any t = initial # mols + amt formed via reaction] oCC nn
MeOH
H2O
oMM nn
oWW nn
1
2
ioii nn
)( reactants2
CO2
WW
3o
oCC nn
30
0 )()(
i
i
reactants
products
H2
TOTAL
3 oHH nn 30
2 oTT nn 23Tn
Chemical Reaction Equilibrium 5
CHMW 3
So to find number of moles of each species at equilibrium, must find eqo
components
RTgK
orxn
ln with
p
ii
ofi
orxn gg
1
K = equilibrium “constant” = f(T, components)gibbs energy of formation of i o
fg
Relate K to and ultimately the number of moles of each component in the reactor at equilibrium.
i ˆ i
io
i
i
ffK
ˆ
Chemical Reaction Equilibrium 6
Chemical Reaction Equilibrium 7
CHMW 3
Gas phase reaction….CHMWi
fffff
ˆˆˆˆˆ
oC
Co
H
Ho
M
Mo
W
W
io
i
i
ff
ff
ff
ff
ffK
1311
1311 ˆˆˆˆ
oC
Co
H
Ho
M
Mo
W
W
ff
ff
ff
ffK
oooC
oH
ffffff
ff
3
13
ˆˆˆˆ
o
Co
H
oM
oW
MW
CH
oM
oW
CH
ffff
ffff
ff
ff
ffK 311 ˆˆˆˆ
oM
oW ff
Chemical Reaction Equilibrium 8
Gas phase reaction CHMW 3Gas phase reaction….
oM
oWCH ffffK 3
3
ˆˆˆˆ
if Py ii o
Co
HMW ffff 3 oif bar1
barbarPPyy 11ˆˆ 333
barbarbarbar
PPPP
yyyyK
MW
CH
MW
CH
1111
ˆˆ 3
Simplification: if have ideal vapor phase, then:3
CH nn
223
1barP
yyyyK
MW
CH2
23
2
2
TMW
CH
MW
TT
nP
nnnn
barP
nnnn
TT nn
Chemical Reaction Equilibrium 9
Gas phase reaction CHMW 3Gas phase reaction….
2
23CH
nP
nnnnK
.....etcnn oMM
2oTMW nnn 2 o
TT nn
233 P g o 22312
3
PK
RTgK rxn
ln
KJFrom tables calculate molKJKg o
rxn 83.3298
692.4298 KK
11
KK no reaction
irreversible reaction99979.025 Catso o
mol CO2 at EQ2 Q
Chemical Reaction Equilibrium 10
T = 100oC ???? CHMW 3Trxn= 100oC ????
2
ln hd
Kd orxn
van’t Hoff eqn:2RTdT
11298ho)(Tfho
29811298exp298
TRhKTK rxn )(Tfho
rxn
T orxn dT
RTThKTK 2exp298 )(Tfho
rxn RT298
T
oo dTCphTh )298()( iirxn CpCp rxnrxnrxn dTCphTh298
)298()( i
iirxn pp
Chemical Reaction Equilibrium 11
Chemical Reaction Equilibrium 12
T = 100oC CHMW 3Trxn= 100oC
molKJho
rxn 97.48)298(
molKJho
rxn 21.52)15.373(
Temperature
25oC (298K) 100oC 100oC .consthorxn )(Tfho
rxn
K 4.692 251.26 284.08
0 99979 1
rxn )(frxn
bar030 0.99979 1
0.99578 0.996
bar03.0
bar1
Chemical Reaction Equilibrium 13
Liquid phase reactionsqu d p ase eac o s
i
ifK
ˆ
fxf ˆi
oif
K
iiii fxf
i
i
i
io
i
iii
io
i
iii
ffx
ffxK
Frequently simplified to: iiixK
i
Chemical Reaction Equilibrium (example)14
Haber Process: Trxn= ~500oC & ~300 bar322 23 NHHN abe ocess: rxn 500 C & 300 ba322 23 NHHN
23
23 P
yK NH
322
Pyy
KHN
51081.525 xCK o
2292)25( KJCh oo
222.92)25( Nmol
KJChrxn
3724)500( KJCh oo 510511500 CK o
237.24)500( Nmol
KJCh oorxn 51051.1500 xCK o
00301bar 370300bar 003.01 bar 37.0300 bar
Chemical Reaction Equilibrium (example)15
Haber Process: Trxn= ~500oC & ~300 bar322 23 NHHN abe ocess: rxn 500 C & 300 ba322 23 NHHN
Chemical Reaction Equilibrium (example)
16
q
