Chemical Thermodynamics II

22 September2023 Dr. Aqeela Sattar Qureshi, Royal College , Mira Road
CHEMICAL THERMODYNAMICS
Semester : III
PAPER 1 , UNIT - I

Chemical Thermodynamics
• Chemical Thermodynamics deals with the application of
the laws of thermodynamics to chemical system
• FREE ENERGY FUNCTIONS
• The concept of free energy gives the amount of available
energy to perform useful work
• The free energy change is used –
 to predict the spontaneous nature of a chemical process
 to study physical and chemical equilibria
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road

FREE ENERGY FUNCTIONS
• HELMHOLTZ FREE ENERGY (A)
• Introduced by German Physicist Hermann von
Helmholtz (1821-1894) to define equilibrium at
constant temeperature
• Symbol ‘A’ is taken from German word ‘Arbeit’
which means work
• Work function is defined as A = E – T S

HELMHOLTZ FREE ENERGY (A)
• Work function is defined as A = E – T S
• ‘A’ is an extensive property
• ‘’E’ and ‘S’ are state functions, independent of
history , mechanism, path etc so A is also a state
function
• For an isothermal change from state 1 to state 2
• A1 = E1 – T S1 and A2 = E2 – T S2
• A2 - A1 = E2 – T S2 - E1 + T S1
• Δ A = Δ E – T ΔS

HELMHOLTZ FREE ENERGY (A)
max
max
rev
rev
rev
rev
rev
rev
W
A
or
W
A
work
maximum
to
equal
is
associated
work
,
reversibly
out
carried
is
process
Since
W
A
(3)
and
(2)
equation
Comparing
q
E
W
i.e
W
q
E
mics
thermodyna
of
law
first
by
But
(2)
-
-
-
q
E
A
(1)
eqn
in
ng
Substituti
q
S
T
T
q
S
e
temperatur
constant
at
process
reversible
a
For
(1)
-
-
-
-
S
T
E
A































)
3
(
Thus decrease
in Helmholtz
free energy
gives the
maximum
work that can
be done by
the system

GIBBS FREE ENERGY (G)
• Introduced by American Physicist J. W. Gibbs
(1839-1903) , it relates to net work done by the system
• Gibbs free energy is defined as G = H– T S
• ‘G’ is an extensive property
• ‘G’ is also a state function
• For an isothermal change from state 1 to state 2
• G1 = H1 – T S1 and G2 = H2 – T S2
• G2 - G1 = H2 – T S2 - H1 + T S1
• Δ G = Δ H – T ΔS

V
P
W
G
(3)
and
(2)
equation
Comparing
q
E
W
i.e
W
q
E
mics
thermodyna
of
law
first
by
But
V
P
q
E
G
q
V
P
E
G
V
P
E
H
But
q
H
G
(1)
eqn
in
ng
Substituti
q
S
T
T
q
S
e
temperatur
constant
at
process
reversible
a
For
(1)
-
-
-
-
S
T
H
G
rev
rev
rev
rev
rev
rev
rev
rev




















































)
3
(
)
2
(

net
exp
max
exp
max
exp
max
max
max
rev
rev
W
W
W
W
W
G
V
P
W
by
given
is
pressure
constant
against
gas
of
expansion
to
due
done
work
But
V
P
W
G
-
OR
V
P
W
G
W
W
work
maximum
to
equal
is
associated
work
,
reversibly
out
carried
is
process
Since
V
P
W
G





























)
(
Thus decrease in Gibbs free energy gives the
net work that can be done by the system

Relation between Gibb’s free energy
and Helmholtz free energy
• Gibbs free energy change ∆G is given by,
∆G = ∆H – T∆S -- (1)
• Helmholtz free energy is given by ,
∆A =∆E – T∆S -- (2)
• But enthalpy change for a chemical reaction at constant
pressure is given by,
∆H = ∆E + P∆V --(3)
• Substituting (3) in equation (1) we get,
• ∆G = ∆E + P∆V – T∆S ie. ∆G = ∆E – T∆S + P∆V
• Since , ∆A = ∆E – T∆S
• from equation (2), we get ∆G = ∆A + P∆V

Significance of Gibb’s Free Energy
• The sign of ∆G helps to decide the
nature of process
 ∆G < 0 process is spontaneous
 ∆G > 0 process is non-spontaneous
 ∆G = 0 process has reached equilibrium

Variation of Gibb’s free energy
with Temperature and Pressure
• Gibb’s free energy is defined as G = H – TS - - (1)
• By definition H = E + PV
• Therefore G = E + PV – TS
•For infinitesimal change, equation (1) can be
written as, dG = dE + PdV + VdP – SdT - TdS -- (2)
• From the first law of thermodynamics,
dE = dq + dW
• If work is of expansion type, then dw = - PdV
• . . . dE = dq - PdV or dq= dE + PdV ---- (3)

Variation of Gibb’s Free Energy
• According to definition of entropy
• dS= dqrev / T or dqrev = T.dS
where, dS is infinitesimal entropy change for a reversible
process substituting (3)
• TdS = dE + PdV --- (4)
• Substituting in eqn (2)
• dG = dE + PdV + VdP – SdT - TdS -- (2)
• dG = TdS + VdP – SdT - TdS
dG = VdP – S.dT ----- (5)

Variation of Gibb’s Free Energy
The rate of change of Gibb’s
free energy with
temperature at constant
pressure is equal to
decrease in entropy of the
system.
The rate of change of Gibb’s
free energy with respect to
pressure at constant
temperature is equal to
increase in volume
occupied by the system.
V
dP
dG
i.e
VdP
dG
0
dT
,
e
temperatur
constant
At
S
dT
dG
i.e
SdT
-
dG
0
dP
,
pressure
constant
At
SdT
VdP
dG
T
P
























GIBB’S HELMHOLTZ EQUATION
dT
S
S
S
S
dT
G
d(G
dT)
(-S
-
dT
-S
dG
dG
dT
S
-
dG
and
dT
S
-
dG
dT
amount
small
by
changed
is
e
temperatur
when
energy
free
in
changes
the
be
dG
and
dG
Let
SdT
-
dG
0
dP
,
pressure
constant
At
SdT
VdP
dG
as
be written
can
pressure
and
e
temperatur
h
energy wit
free
s
Gibb’
of
Variation
1
2
2
1
1
2
1
2
1
2
2
2
1
1
2
1
)
(
)
(
) 


















(1)
-
-
-
S
dT
G
d
dT
S
-
G
d
dT
S
S
S
S
dT
G
d(G 1
2
2
1
1
2













 )
(
)
(
)

change.
energy
free
of
t
coefficien
e
Temperatur
as
knwon
is
dT
G
d
term
The
equation
Helmholtz
Gibbs
as
known
is
equation
Above
dT
G
d
T
H
G
(1)
equation
in
S
-
of
value
ng
Substituti
S)
T(-
H
G
i.e
S
T
-
H
G
by
given
is
energy
free
in
change
e
temperatur
cosnstant
At
P
P





 





 















   
 
  (1)
-
-
-
dT
G
d
T
1
T
G
T
G
dT
d
dT
G
d
T
1
T
G
T
G
dT
d
dT
G
d
T
1
T
1
dT
d
G
T
G
dT
d
pressure.
constant
at
e
temperatur
to
respect
with
T
G
ating
differenti
by
obtained
is
equation
Helmholtz
Gibbs
of
form
Another
P
P
P





 










 
















 





2
2
1

)
2
(
2
2








 










 









 




P
2
2
P
2
2
P
dT
G
d
T
1
T
H
T
G
dT
G
d
T
T
T
H
T
G
T
by
equation
above
Dividing
dT
G
d
T
H
G
is
equation
Helmholtz
Gibbs

PARTIAL MOLAL QUANTITY
 
 
equation
Helmholtz
Gibbs
of
form
another
is
equation
above
The
T
H
T
G
dT
d
T
H
T
G
T
G
T
G
dT
d
(2)
and
(1)
equation
Comparing
2
2
2












 2

)
....
,
i
n
......
,
3
n
,
2
n
,
1
n
,
P
,
T
(
f
X
t.
constituen
various
of
amount
and
pressure
e,
temperatur
on
depend
will
x'
'
then
study
for
selected
system
of
property
extensive
any
is
x'
'
If
ly.
respective
i
....
3
,
2
,
1
ts
constituen
of
moles
of
no.
the
be
i
n
3
n
,
2
n
1
n
Let
t
constituen
ith
of
consisting
system
open
an
Consider


i
....n
n
,
P,n
T,
i
2
.
....n
n
,
P,n
T,
1
.
....n
n
,
P,n
T,
i
....n
n
,
P,n
T,
i
2
.
....n
n
,
P,n
T,
1
.
....n
n
,
P,n
T,
.
,....n
,n
T,n
.
,....n
,n
P,n
dn
n
x
dn
n
x
dn
n
x
dx
Pressure,
and
e
Temperatur
constant
At
dn
n
x
dn
n
x
dn
n
x
dP
P
x
dT
T
x
dx
as
be written
can
dx'
'
system
the
in
change
small
a
For
1)
-
i
(
3
1
i
3
1
i
3
2
1)
-
i
(
3
1
i
3
1
i
3
2
i
2
1
i
2
1
i
n
......
,
2
n
,
1
n
,
P
,
T
(
f
X






















































































.......
.......
2
1
2
1
)

system.
of
n
compositio
the
affect
not
does
mole
added
the
that
system
of
quantity
large
a
such
to
added
is
pressure
and
e
temperatur
constant
at
component
particular
of
mole
one
when
...
system
of
volume
,
enthalpy
energy,
free
as
such
property
in
change
the
gives
it
that
is
quantity
molar
partial
of
ce
significan
physical
The
dn
x
dn
x
dn
x
dx
property.
the
of
symbol
the
over
bar
by writing
d
represente
is
It
quantity.
molal
partial
as
known
is
n
x
term
The
dn
n
x
dn
n
x
dn
n
x
dx
i
i
2
1
i
....n
n
,
P,n
T,
i
2
.
....n
n
,
P,n
T,
1
.
....n
n
,
P,n
T, 1)
-
i
(
3
1
i
3
1
i
3
2















































......
....
2
1
2
1

dn
V
........
dn
V
dn
V
dV
dn
n
V
dn
n
V
dn
n
V
dV
,
be
l
volume wil
in
change
small
pressure
and
e
temperatur
constant
At
volume.
molal
partial
as
known
is
n
V
uantity
q
the
then
property
extensive
the
is
volume
If
i
i
2
2
1
1
i
...n
,n
n
P,
T,
2
2
...n
,n
n
P,
T,
2
1
...n
,
n
P,
T,
1
i
3
1
i
3
1
i
2
















































......
...

CHEMICAL POTENTIAL
dn
........
dn
dn
dG
'
'
by
d
represente
is
and
potential
chemical
as
known
also
is
t
I
.
G)
(
energy
free
molal
partial
as
known
is
n
G
uantity
q
dn
n
G
dn
n
G
dn
n
G
dG
,
be
ll
energy wi
free
in
change
small
pressure
and
e
temperatur
constant
At
)
n
.....
n
,
n
,
n
,
P
,
T
(
f
G
e
i.
property
extensive
an
is
system
a
of
energy
ree
F
i
i
2
1
i
...n
,n
n
P,
T,
2
2
...n
,n
n
P,
T,
2
1
...n
,
n
P,
T,
1
i
3
2
1
i
3
1
i
3
1
i
2



 
















































2
1
......
...

Gibbs Duhem Equation
dn
........
dn
dn
dG
'
'
by
d
represente
is
and
potential
chemical
as
known
also
is
t
I
.
G)
(
energy
free
molal
partial
as
known
is
n
G
uantity
q
dn
n
G
dn
n
G
dn
n
G
dG
,
be
ll
energy wi
free
in
change
small
pressure
and
e
temperatur
constant
At
)
n
.....
n
,
n
,
n
,
P
,
T
(
f
G
e
i.
property
extensive
an
is
system
a
of
energy
ree
F
i
i
2
1
i
...n
,n
n
P,
T,
2
2
...n
,n
n
P,
T,
2
1
...n
,
n
P,
T,
1
i
3
2
1
i
3
1
i
3
1
i
2



 
















































2
1
......
...

)
)
1
(
)
)
(
)
2
(
2
1
2
1
2
1
2
2
1
1
2
1
2
1
i
i
2
1
i
i
2
1
i
i
2
1
i
i
i
i
2
2
1
1
i
i
2
1
N
P,
T,
i
i
2
1
d
n
....
d
n
d
(n
dG
dG
dG
by
replaced
be
can
eqn
above
in
bracket
first
the
eqn
From
d
n
....
d
n
d
(n
dn
....
dn
dn
(
dG
d
n
dn
....
d
n
dn
d
n
dn
dG
give,
will
(2)
eqn
of
ation
differenti
Complete
n)
compositio
definite
N
n
........
n
n
(G)
be
will
(1)
eqn
of
n
integratio
the
n
compositio
definite
has
system
the
If
(1)
-
-
-
dn
........
dn
dn
dG























































2
1
2
1
2
1
2
1
2
1
0
0
0
)













d
n
n
d
d
n
d
n
d
n
d
n
is
equation
Duhem
Gibbs
mixture
binary
a
For
on.
distillati
as
such
equilibria
liquid
-
Gas
of
study
the
in
useful
is
equation
Duhem
Gibbs
d
n
as
be written
also
can
equation
above
The
equation.
Duhem
Gibbs
as
known
is
equation
above
The
d
n
....
d
n
d
n
d
n
....
d
n
d
(n
dG
dG
1
2
2
1
2
1
i
i
i
i
2
1
i
i
2
1




















energy.
free
to
equal
is
potential
chemical
substance
pure
any
of
mole
1
for
Thus
G
,
1
n
when
2)
eqn
N
(G)
be
will
equation
Duhem
Gibbs
then
substance
pure
i.e
t
constituen
1
only
of
consists
system
a
If
ve
d
then
ve
d
if
i.e
t
constituen
2nd
of
potential
chemical
the
affects
t
constituen
1st
of
potential
chemical
that
indicates
equation
Above
d
n
n
d
N
P,
T,
1
2















(
.
2
1
2
1

V
dP
dG
i.e
VdP
dG
0
dT
,
e
temperatur
constant
At
S
dT
dG
i.e
SdT
-
dG
0
dP
,
pressure
constant
At
SdT
VdP
dG
T
P























Effect of Temperature and
Pressure on Chemical Potential

i
T
i
i
T
i
i
T
dn
dV
dn
dG
P
d
d
dn
dV
dP
dG
n
d
d
n
'
w.r.t
equation
above
ating
Differenti
V
dP
dG























'
Effect of Pressure on Chemical Potential
i
i
V
P
d
d



i
P
i
i
P
i
i
P
dn
dS
dn
dG
T
d
d
dn
dS
dT
dG
n
d
d
n
'
w.r.t
equation
above
ating
Differenti
S
dT
dG


























'
Effect of Temperature on Chemical Potential
i
i
S
T
d
d




CONCEPT OF FUGACITY AND ACTIVITY
 
1
2
1
2
ln
ln 2
1
P
P
RT
G
P
RT
G
G
dP
P
RT
dG
equation,
above
g
Integratin
dP
P
RT
dG
P
RT
V
,
RT
PV
,
gas
ideal
an
For
VdP
dG
e
temperatur
constant
At
SdT
-
VdP
dG
by
given
is
pressure
and
e
temperatur
h
energy wit
free
of
variation
The
P
P
P
P
G
G
2
1
2
1

















(2)
-
-
-
B
lnf
RT
G
by
given
is
fugacity
and
energy
free
between
relation
The
'
f
'
symbol
the
by
d
represente
is
It
substance.
the
of
tendency
escaping
the
measure
to
used
is
fugacity
term
The
tendency.
escaping
as
known
is
property
This
state.
another
into
pass
to
tendency
has
state
given
a
in
substance
every
that
suggested
He
fugacity.
and
activity
as
known
parameters
mic
thermodyna
new
two
introduced
Lewis
N.
G.
gases
real
for
n
calculatio
energy
free
explain
to
order
In
gases.
ideal
for
only
valid
is
Equation
P
P
RT
G







)
1
(
)
1
(
ln
1
2

)
4
(
ln
ln
ln
ln
0
0
0
0












f
f
RT
G
-
G
f
RT
f
RT
G
-
G
(2)
equation
from
(3)
equation
g
Subtractin
(3)
-
-
-
B
f
RT
G
state
standard
in
fugacity
and
energy
free
the
be
f
and
G
Let
condition.
standard
under
done
was
G
of
ts
measuremen
all
Hence
.
calculated
be
cannot
B
known,
not
is
G
of
value
absolute
Since
constant
a
is
B
where
(2)
-
-
-
B
lnf
RT
G
0
0
0
0

(6)
-
-
a
a
RT
G
a
RT
G
a
RT
G
G
G
a
RT
G
G
and
a
RT
G
G
be
will
states
two
the
for
(5)
equation
the
then
a
and
a
are
activities
when
energies
free
are
G
and
G
If
G
G
1,
a
If
a
RT
G
G
state.
standard
the
in
substance
same
the
of
fugacity
the
a
to
state
given
the
in
substance
the
of
fugacity
of
ratio
the
as
defined
is
activity
Thus
a'.
'
by
d
represente
is
and
activity
as
known
is
f
f
ratio
The
0
0
1
2
0
2
0
1
2
1
2
1
0
0
1
2
1
2
2
1
0
ln
)
ln
(
)
ln
(
ln
ln
)
5
(
ln





















a
RT
as
be written
can
a
RT
G
G
i.e
(5)
equation
G
and
1
n
substance,
of
mole
1
For
activity.
by
replaced
are
ion
concentrat
whenever
obtained
are
result
exact
more
Hence
solvent.
with
solutes
of
reactions
and
attraction
mutual
the
ion
considerat
into
take
activities
the
solutions
of
case
In
possible.
become
ns
calculatio
exact
pressure
of
place
in
used
are
activities
when
Thus,
pressure.
of
place
the
takes
activity
that
found
is
it
(6)
and
(1)
equation
From
(6)
-
-
a
a
RT
G
and
(1)
-
-
P
P
RT
G
0
ln
ln
ln
ln
0
1
2
1
2















Van’t Hoff’s Reaction Isotherm
substance.
indicated
of
potential
chemical
are
s
where
be
reaction
the
in
part
taking
substances
various
of
energy
free
molal
partial
the
Let
quantity
molal
partial
of
terms
in
exressed
be
must
system
of
property
mic
thermodyna
change,
can
n
compositio
ose
mixture wh
a
is
ion
considerat
under
system
the
Since
.....
mM
L
l
....
B
b
aA
reaction
general
the
Consider
,
M
,
L
,
B
,
A
'
.....
....











reactants.
and
product
of
pressures
partial
and
G
,
G
between
relation
the
gives
isotherm
reaction
Hoff
t
Van'
0



state
standard
in
substance
a
of
potential
chemical
is
where
a
RT
realtion
following
usign
activity
of
terms
in
expressed
be
can
state
any
in
substance
a
of
potetntial
chemical
The
b
a
m
l
G
G
G
G
energy
free
in
Change
b
a
G
m
l
G
be
will
reactants
and
product
of
energy
Free
0
0
B
A
M
L
reactant
product
B
A
reactant
M
L
product











)
2
(
ln
)
1
(
.....)
(
.....)
(
.....
.....




























state.
standard
their
in
are
reaction
the
in
involved
substances
the
all
n
change whe
energy
free
is
G
where
a
a
a
a
RT
G
G
a
a
a
a
RT
b
a
m
l
G
a
RT
b
a
RT
a
a
RT
m
a
RT
l
G
be
l
energy wil
free
in
change
then
(2)
equation
from
derived
expression
ing
correspond
by
replaced
are
(1)
equation
in
of
values
the
If
0
b
B
a
A
m
M
l
L
0
b
B
a
A
m
M
l
L
B
A
M
L
B
B
A
A
M
M
L
L
M
L
B
A



































)
3
(
....
....
ln
....
....
ln
..)]
(
..)
[(
.....]
)
ln
(
)
ln
(
[
...]
)
ln
(
)
ln
(
[
..
,
,
,
0
0
0
0
0
0
0
0













state.
standard
for
equation
Hoff
t
Van'
is
(5)
Equation
(5)
-
-
-
Kp
RT
G
G
m
equilibriu
at
process
chemical
a
For
isotherm.
rxn
Hoff
t
Van'
as
knwon
are
(4)
and
(3)
Equation
(4)
-
-
-
Kp
RT
G
G
Kp
a
a
a
a
system
gaseous
of
case
in
and
constant
m
equilibriu
as
known
is
reactants
&
product
of
activities
of
ratio
involving
term
The
-
-
-
a
a
a
a
RT
G
G
0
0
b
B
a
A
m
M
l
L
b
B
a
A
m
M
l
L
0
ln
0
ln
....
....
)
3
(
....
....
ln


























Van’t Hoff’s Reaction Isochore
T
Kp
T
R
T
G
T
Kp
RT
T
G
pressure
constant
at
e
temperatur
w.r.t
(1)
eqn
ating
Differenti
(1)
-
-
-
Kp
RT
G
is
state
standard
for
isotherm
Hoff
t
Van'
-
-
-
a
a
a
a
RT
G
G
P
0
P
0
0
b
B
a
A
m
M
l
L
0











































.
ln
)
ln
(
ln
)
3
(
....
....
ln
equation.
Helmholtz
Gibbs
and
isotherm
Hoff
t
van'
using
obtained
be
can
relation
The
e.
temperatur
and
constant
m
equilibriu
between
relation
the
gives
equation
Hoff
t
Van'

Kp
RT
T
Kp
RT
T
G
T
T
by
equation
above
g
Multiplyin
Kp
R
T
Kp
RT
T
G
Kp
T
Kp
T
R
T
G
T
T
Kp
T
Kp
T
R
T
G
T
Kp
T
R
T
G
P
0
P
0
P
0
P
0
P
0
ln
ln
ln
ln
.
ln
ln
.
ln
ln
.
ln
2






























































































)
3
(
)
2
(
ln
ln
ln
ln
2
2








































































0
0
P
0
P
0
0
0
0
P
0
0
P
0
H
G
T
G
T
T
G
T
H
G
is
state
standard
for
equation
Helmholtz
Gibbs
G
T
Kp
RT
T
G
T
Kp
RT
G
(1)
equation
From
Kp
RT
T
Kp
RT
T
G
T

(5)
-
-
RT
H
T
Kp
T
Kp
RT
H
hence
negligible
is
H
and
H
between
difference
reaction
chemical
a
For
state.
std
their
in
are
substances
the
all
hen
pressure w
constant
at
reaction
of
enthalpy
is
H
equation
above
n
I
T
Kp
RT
H
G
T
Kp
RT
H
G
(3)
and
(2)
equation
Equating
0
0
0
0
0
0
2
2
2
2
ln
ln
)
4
(
ln
ln




























 





 































2
1
1
2
1
2
2
1
1
2
2
2
303
.
2
ln
1
1
ln
ln
1
ln
.
1
ln
ln
2
1
2
2
1
2
T
T
T
T
R
H
Kp
Kp
T
T
R
H
Kp
Kp
T
R
H
Kp
T
T
R
H
Kp
:
equation
Hoff
t
Van'
of
n
Integratio
equation.
Hoff
t
Van'
as
known
is
eqn
Above
(5)
-
-
RT
H
T
Kp
T
T
Kp
Kp
T
T
Kp
Kp
1
1

T
lnRT
n
T
Kc
T
Kp
e
temperatur
w.r.t
eqution
above
ating
Differenti
lnRT
n
lnKc
lnKp
equation
above
of
log
Taking
.(RT)
Kc
Kp
equation
following
using
by
obtained
be
can
volume
constant
at
reaction
of
heat
involving
(5)
eqn
of
form
other
The
(5)
-
-
RT
H
T
Kp
n


















ln
ln
ln
2

)
7
(
ln
ln
ln
ln
)
6
(
ln
ln
ln
ln
2
2
2
2











































RT
nRT
-
H
T
Kc
T
n
RT
H
T
Kc
RT
H
T
n
T
Kc
(5)
-
-
RT
H
T
Kp
(5)
eqn
and
(6)
equation
Equating
T
n
T
Kc
T
Kp
T
lnRT
n
T
Kc
T
Kp

Isochore
Hoff
t
Van'
or
equation
Hoff
t
Van'
as
known
is
equation
above
The
RT
E
T
Kc
(7)
equation
in
ng
Substituti
E
nRT
-
H
nRT
E
H
equation
following
the
by
volume
constant
at
reaction
of
heat
to
related
is
pressure
constant
at
reaction
of
heat
The
RT
nRT
-
H
T
Kc
2
2
ln
)
7
(
ln























Reference Books :
• Advanced Physical chemistry – Gurdeep Raj
• Thermodynamics – A core course – 2nd edn by R.C.
Srivastava
• An introduction to chemical thermodynamics – 6th edn
Rastogi & Misra
• Advanced physical chemistry - D. N. Bajpai (S. Chand )
Recommended Reading :

Chemical Thermodynamics II

Chemical Thermodynamics II

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