Chemical Thermodynamics II

D
Dr. Aqeela SattarAssociate Professor
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
HELMHOLTZ FREE ENERGY (A)
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
GIBBS FREE ENERGY (G)
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
(
GIBBS FREE ENERGY (G)
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Significance of Gibb’s Free Energy
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
• 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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
• 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
with Temperature and Pressure
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
• 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
with Temperature and Pressure
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
)
(
)
(
) 

















GIBB’S HELMHOLTZ EQUATION
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
(1)
-
-
-
S
dT
G
d
dT
S
-
G
d
dT
S
S
S
S
dT
G
d(G 1
2
2
1
1
2













 )
(
)
(
)
GIBB’S HELMHOLTZ EQUATION
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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





 





 














GIBB’S HELMHOLTZ EQUATION
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
   
 
  (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
GIBB’S HELMHOLTZ EQUATION
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
)
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
 
 
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
)
....
,
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

PARTIAL MOLAL QUANTITY
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
)
PARTIAL MOLAL QUANTITY
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
PARTIAL MOLAL QUANTITY
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
















































......
...
PARTIAL MOLAL QUANTITY
CHEMICAL POTENTIAL
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
......
...
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
)
)
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






















































Gibbs Duhem Equation
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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



















Gibbs Duhem Equation
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
Gibbs Duhem Equation
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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


22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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



22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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
















22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
(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
CONCEPT OF FUGACITY AND ACTIVITY
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
)
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
CONCEPT OF FUGACITY AND ACTIVITY
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
(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




















CONCEPT OF FUGACITY AND ACTIVITY
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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














CONCEPT OF FUGACITY AND ACTIVITY
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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


22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isotherm
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
(
.....)
(
.....)
(
.....
.....



























22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isotherm
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












22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isotherm
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

























22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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'
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isochore
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





























































































22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isochore
)
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isochore
(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



























22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isochore
 





 































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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isochore
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isochore
)
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
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Van’t Hoff’s Reaction Isochore
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 )
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
Recommended Reading :
22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
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Chemical Thermodynamics II

  • 1. 22 September2023 Dr. Aqeela Sattar Qureshi, Royal College , Mira Road CHEMICAL THERMODYNAMICS Semester : III PAPER 1 , UNIT - I
  • 2. 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
  • 3. 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 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
  • 4. 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 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
  • 5. HELMHOLTZ FREE ENERGY (A) 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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
  • 6. 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 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
  • 7. GIBBS FREE ENERGY (G) 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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 (
  • 8. GIBBS FREE ENERGY (G) 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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
  • 9. 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 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road
  • 10. Significance of Gibb’s Free Energy 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road • 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
  • 11. Variation of Gibb’s free energy with Temperature and Pressure 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road • 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)
  • 12. Variation of Gibb’s Free Energy with Temperature and Pressure 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road • 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)
  • 13. Variation of Gibb’s Free Energy with Temperature and Pressure 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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                       
  • 14. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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 ) ( ) ( )                  
  • 15. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road (1) - - - S dT G d dT S - G d dT S S S S dT G d(G 1 2 2 1 1 2               ) ( ) ( )
  • 16. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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                            
  • 17. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road         (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
  • 18. GIBB’S HELMHOLTZ EQUATION 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road ) 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
  • 19. PARTIAL MOLAL QUANTITY 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road     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
  • 20. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road ) .... , 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  PARTIAL MOLAL QUANTITY
  • 21. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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 ) PARTIAL MOLAL QUANTITY
  • 22. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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 PARTIAL MOLAL QUANTITY
  • 23. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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                                                 ...... ... PARTIAL MOLAL QUANTITY
  • 24. CHEMICAL POTENTIAL 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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 ...... ...
  • 25. Gibbs Duhem Equation 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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 ...... ...
  • 26. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road ) ) 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                                                       Gibbs Duhem Equation
  • 27. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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                    Gibbs Duhem Equation
  • 28. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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 Gibbs Duhem Equation
  • 29. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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
  • 30. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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  
  • 31. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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   
  • 32. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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                
  • 33. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road (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 CONCEPT OF FUGACITY AND ACTIVITY
  • 34. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road ) 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 CONCEPT OF FUGACITY AND ACTIVITY
  • 35. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road (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                     CONCEPT OF FUGACITY AND ACTIVITY
  • 36. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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               CONCEPT OF FUGACITY AND ACTIVITY
  • 37. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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  
  • 38. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isotherm 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 ( .....) ( .....) ( ..... .....                           
  • 39. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isotherm 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            
  • 40. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isotherm 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                         
  • 41. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road 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'
  • 42. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore 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                                                                                             
  • 43. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore ) 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
  • 44. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore (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                           
  • 45. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore                                         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
  • 46. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore 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
  • 47. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore ) 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
  • 48. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Van’t Hoff’s Reaction Isochore 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                      
  • 49. 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 ) 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road Recommended Reading :
  • 50. 22 September2023 Dr. AqeelaSattar Qureshi, Royal College , Mira Road