Chemical Engineering Thermodynamics - Brief Overview Notes | EduRev

: Chemical Engineering Thermodynamics - Brief Overview Notes | EduRev

 Page 1


Chemical Engineering 
Thermodynamics
A Brief Review
SHR Chapter 2
1 Thermo.key - February 7, 2014
Page 2


Chemical Engineering 
Thermodynamics
A Brief Review
SHR Chapter 2
1 Thermo.key - February 7, 2014
“Rate” vs. “State”
Thermodynamics tells us how things “end up” (state) but not how (or how 
fast) they “get there” (rate)	

Limitations on getting to equilibrium:	

• Transport (mixing): diffusion, convection	

? example: why doesn’t more of the ocean evaporate to make higher humidity in the deserts? (heat transfer 
alters dew point locally, atmospheric mixing limitations, etc.)	

• Kinetics (reaction): the rate at which reactions occur are too slow to get to equilibrium	

? example: chemical equilibrium says trees (and our bodies) should become CO
2
 and H
2
O (react with air)	

? example: chemical equilibrium says diamonds should be graphite (or CO
2
 if in air)	

Sometimes, mixing & reaction are suf?ciently fast that equilibrium 
assumptions are “good enough.”	

• if we assume that we can use thermodynamics to obtain the state of the system, we avoid a lot 
of complexity.	

? do it if it is “good enough!”	

• Most unit operations (e.g. distillation) assume phase equilibrium, ignoring transport limitations.	

? good enough if things are mixed well and have reasonable residence/contact times.
2 Thermo.key - February 7, 2014
Page 3


Chemical Engineering 
Thermodynamics
A Brief Review
SHR Chapter 2
1 Thermo.key - February 7, 2014
“Rate” vs. “State”
Thermodynamics tells us how things “end up” (state) but not how (or how 
fast) they “get there” (rate)	

Limitations on getting to equilibrium:	

• Transport (mixing): diffusion, convection	

? example: why doesn’t more of the ocean evaporate to make higher humidity in the deserts? (heat transfer 
alters dew point locally, atmospheric mixing limitations, etc.)	

• Kinetics (reaction): the rate at which reactions occur are too slow to get to equilibrium	

? example: chemical equilibrium says trees (and our bodies) should become CO
2
 and H
2
O (react with air)	

? example: chemical equilibrium says diamonds should be graphite (or CO
2
 if in air)	

Sometimes, mixing & reaction are suf?ciently fast that equilibrium 
assumptions are “good enough.”	

• if we assume that we can use thermodynamics to obtain the state of the system, we avoid a lot 
of complexity.	

? do it if it is “good enough!”	

• Most unit operations (e.g. distillation) assume phase equilibrium, ignoring transport limitations.	

? good enough if things are mixed well and have reasonable residence/contact times.
2 Thermo.key - February 7, 2014
Some T erminology...
M=
C
X
i=1
y
i
¯
M
i
Gibbs-Duhem 
Equation:
?
@M
@ P
?
T,y
dP +
?
@M
@ T
?
P,y
 C
X
i=1
y
i
d
¯
M
i
=0
“Partial Molar” property
M   -	

arbitrary thermodynamic      property (per mole)	

N
i	

-	

moles of species i 	

     
y
i	

-	

mole fraction of species i 
      
(liquid or gas)
Note at constant T and P, 
C
X
i=1
y
i
d
¯
M
i
=0
“Excess” propertyM
E
? M M
ideal
how much M deviates from 
the ideal solution behavior.
“Residual” property
M
ideal
=
C
X
i=1
y
i
M
i
how much M deviates from 
the ideal gas ( M
ig
 ) behavior.
M
ig
=
C
X
i=1
y
i
M
ig
i
M
R
? M M
ig
change in M due to adding a differential amount 
of species i.  For ideal mixtures, 
¯
M
i
=M
i
¯
M
i
? ?
@ NM
@ N
i
?
T,P,N
j
3 Thermo.key - February 7, 2014
Page 4


Chemical Engineering 
Thermodynamics
A Brief Review
SHR Chapter 2
1 Thermo.key - February 7, 2014
“Rate” vs. “State”
Thermodynamics tells us how things “end up” (state) but not how (or how 
fast) they “get there” (rate)	

Limitations on getting to equilibrium:	

• Transport (mixing): diffusion, convection	

? example: why doesn’t more of the ocean evaporate to make higher humidity in the deserts? (heat transfer 
alters dew point locally, atmospheric mixing limitations, etc.)	

• Kinetics (reaction): the rate at which reactions occur are too slow to get to equilibrium	

? example: chemical equilibrium says trees (and our bodies) should become CO
2
 and H
2
O (react with air)	

? example: chemical equilibrium says diamonds should be graphite (or CO
2
 if in air)	

Sometimes, mixing & reaction are suf?ciently fast that equilibrium 
assumptions are “good enough.”	

• if we assume that we can use thermodynamics to obtain the state of the system, we avoid a lot 
of complexity.	

? do it if it is “good enough!”	

• Most unit operations (e.g. distillation) assume phase equilibrium, ignoring transport limitations.	

? good enough if things are mixed well and have reasonable residence/contact times.
2 Thermo.key - February 7, 2014
Some T erminology...
M=
C
X
i=1
y
i
¯
M
i
Gibbs-Duhem 
Equation:
?
@M
@ P
?
T,y
dP +
?
@M
@ T
?
P,y
 C
X
i=1
y
i
d
¯
M
i
=0
“Partial Molar” property
M   -	

arbitrary thermodynamic      property (per mole)	

N
i	

-	

moles of species i 	

     
y
i	

-	

mole fraction of species i 
      
(liquid or gas)
Note at constant T and P, 
C
X
i=1
y
i
d
¯
M
i
=0
“Excess” propertyM
E
? M M
ideal
how much M deviates from 
the ideal solution behavior.
“Residual” property
M
ideal
=
C
X
i=1
y
i
M
i
how much M deviates from 
the ideal gas ( M
ig
 ) behavior.
M
ig
=
C
X
i=1
y
i
M
ig
i
M
R
? M M
ig
change in M due to adding a differential amount 
of species i.  For ideal mixtures, 
¯
M
i
=M
i
¯
M
i
? ?
@ NM
@ N
i
?
T,P,N
j
3 Thermo.key - February 7, 2014
Phase Equilibrium
G =G(T,P,N
1
,N
2
,...,N
C
)
Gibbs Energy 
(thermodynamic property)
Phase Equilibrium 
is achieved when 
G is minimized.
dG= SdT+VdP+
C
X
i=1
?
@ G
@ N
i
?
P,T,N
j
dN
i
µ
i
? ?
@ G
@ N
i
?
P,T,N
j
Chemical Potential	

(thermodynamic property, 
partial molar Gibbs energy)
In phase equilibrium,	

   T
(1)
 = T
(2)
 = ? = T
(N)
 	

   P
(1)
 = P
(2)
 = ? = P
(N)
For multiple 
phases in a 
closed system, 
G
system
=
N
X
p=1
G
(p)
dG
system
=
N
X
p=1
dG
(p)
For a nonreacting 
system, moles 
are conserved.
dG
system
=
N
X
p=2
"
C
X
i=1
?
µ
(p)
i
 µ
(1)
i
?
dN
(p)
i
#
T,P
dG
system
=
N
X
p=1
"
C
X
i=1
µ
(p)
i
dN
(p)
i
#
T,P
T o minimize G, dG=0.  But each 
term in the summation for dG is 
independent, so each must be zero.
µ
(p)
i
=µ
(1)
i
=µ
(2)
i
= ···=µ
(N)
i
For phase equilibrium, the 
chemical potential of any 
species is equal in all phases.
SHR §2.2
¯
f
i
=Cexp
?
µ
i
RT
?
Solution:  Partial Fugacity
C is a temperature-
dependent constant.
¯
f
(p)
i
=
¯
f
(1)
i
=
¯
f
(2)
i
= ···=
¯
f
(N)
i
For phase equilibrium, the fugacity 
of any species is equal in all phases.
Problem:
µ
i
!1 P! 0 as
N
X
p=1
dN
(p)
i
=0 dN
(1)
i
= N
X
p=2
dN
(p)
i
4 Thermo.key - February 7, 2014
Page 5


Chemical Engineering 
Thermodynamics
A Brief Review
SHR Chapter 2
1 Thermo.key - February 7, 2014
“Rate” vs. “State”
Thermodynamics tells us how things “end up” (state) but not how (or how 
fast) they “get there” (rate)	

Limitations on getting to equilibrium:	

• Transport (mixing): diffusion, convection	

? example: why doesn’t more of the ocean evaporate to make higher humidity in the deserts? (heat transfer 
alters dew point locally, atmospheric mixing limitations, etc.)	

• Kinetics (reaction): the rate at which reactions occur are too slow to get to equilibrium	

? example: chemical equilibrium says trees (and our bodies) should become CO
2
 and H
2
O (react with air)	

? example: chemical equilibrium says diamonds should be graphite (or CO
2
 if in air)	

Sometimes, mixing & reaction are suf?ciently fast that equilibrium 
assumptions are “good enough.”	

• if we assume that we can use thermodynamics to obtain the state of the system, we avoid a lot 
of complexity.	

? do it if it is “good enough!”	

• Most unit operations (e.g. distillation) assume phase equilibrium, ignoring transport limitations.	

? good enough if things are mixed well and have reasonable residence/contact times.
2 Thermo.key - February 7, 2014
Some T erminology...
M=
C
X
i=1
y
i
¯
M
i
Gibbs-Duhem 
Equation:
?
@M
@ P
?
T,y
dP +
?
@M
@ T
?
P,y
 C
X
i=1
y
i
d
¯
M
i
=0
“Partial Molar” property
M   -	

arbitrary thermodynamic      property (per mole)	

N
i	

-	

moles of species i 	

     
y
i	

-	

mole fraction of species i 
      
(liquid or gas)
Note at constant T and P, 
C
X
i=1
y
i
d
¯
M
i
=0
“Excess” propertyM
E
? M M
ideal
how much M deviates from 
the ideal solution behavior.
“Residual” property
M
ideal
=
C
X
i=1
y
i
M
i
how much M deviates from 
the ideal gas ( M
ig
 ) behavior.
M
ig
=
C
X
i=1
y
i
M
ig
i
M
R
? M M
ig
change in M due to adding a differential amount 
of species i.  For ideal mixtures, 
¯
M
i
=M
i
¯
M
i
? ?
@ NM
@ N
i
?
T,P,N
j
3 Thermo.key - February 7, 2014
Phase Equilibrium
G =G(T,P,N
1
,N
2
,...,N
C
)
Gibbs Energy 
(thermodynamic property)
Phase Equilibrium 
is achieved when 
G is minimized.
dG= SdT+VdP+
C
X
i=1
?
@ G
@ N
i
?
P,T,N
j
dN
i
µ
i
? ?
@ G
@ N
i
?
P,T,N
j
Chemical Potential	

(thermodynamic property, 
partial molar Gibbs energy)
In phase equilibrium,	

   T
(1)
 = T
(2)
 = ? = T
(N)
 	

   P
(1)
 = P
(2)
 = ? = P
(N)
For multiple 
phases in a 
closed system, 
G
system
=
N
X
p=1
G
(p)
dG
system
=
N
X
p=1
dG
(p)
For a nonreacting 
system, moles 
are conserved.
dG
system
=
N
X
p=2
"
C
X
i=1
?
µ
(p)
i
 µ
(1)
i
?
dN
(p)
i
#
T,P
dG
system
=
N
X
p=1
"
C
X
i=1
µ
(p)
i
dN
(p)
i
#
T,P
T o minimize G, dG=0.  But each 
term in the summation for dG is 
independent, so each must be zero.
µ
(p)
i
=µ
(1)
i
=µ
(2)
i
= ···=µ
(N)
i
For phase equilibrium, the 
chemical potential of any 
species is equal in all phases.
SHR §2.2
¯
f
i
=Cexp
?
µ
i
RT
?
Solution:  Partial Fugacity
C is a temperature-
dependent constant.
¯
f
(p)
i
=
¯
f
(1)
i
=
¯
f
(2)
i
= ···=
¯
f
(N)
i
For phase equilibrium, the fugacity 
of any species is equal in all phases.
Problem:
µ
i
!1 P! 0 as
N
X
p=1
dN
(p)
i
=0 dN
(1)
i
= N
X
p=2
dN
(p)
i
4 Thermo.key - February 7, 2014
Chemical Potential, Fugacity, Activity
SHR §2.2.1 & Table 2.2
P
s
i
vapor pressure of species i.
y
i
x
i
vapor mole fraction of species i.
liquid mole fraction of species i.
For phase equilibrium, the chemical potential, fugacity, 
activity (but not activity coef?cient or fugacity 
coef?cient) of any species is equal in all phases.
ThermodynamicQuantity De?nition Description Limitingcaseofideal
gasandidealsolution
Chemicalpotential µ
i
? ?
?G
?N
i
?
T,P,N
j
Partialmolarfreeenergy, g
i
µ
i
= g
i
Partialfugacity f
i
= Cexp(
µ
i/(RT)) Thermodynamicpressure f
iV
= y
i
P
Fugacitycoef?cientofa
purespecies
f i
? f
i/P Deviationoffugacitydueto
pressure
f iV
= 1.0
f iL
=
P
s
i
/P
Fugacitycoef?cientofa
speciesinamixture
f iV
? f
iV
/(y
i
P)
f iL
? f
iL
/(x
i
P)
Deviationstofugacitydue
topressureandcomposition
f iV
= 1.0
f iL
=
P
s
i
/P
Activity a
i
? f
i
/f
o
i
Relativethermodynamic
pressure
a
iV
= y
i
a
iL
= x
i
Activitycoef?cient g iV
? a
iV/y
i
g iL
? a
iL/x
i
Deviationoffugacitydueto
composition.
g iV
= 1.0
g iL
= 1.0
¯
f
iL
=
¯
 iL
x
i
P
=  iL
x
i
f
o
iL
¯
f
iV
=
¯
 iV
y
i
P
=  iV
y
i
f
o
iV
¯
f
iL
=
¯
f
iV
) y
i
x
i
=
¯
 iL
¯
 iV
we will use this on 
the next slide...
¯
f
i
= f
i
for a pure species
5 Thermo.key - February 7, 2014
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