Fugacity: It is derived from Latin, expressed as fleetness or escaping ...

(
nM )
(
nM ) (
nM )
(
nM )
(
nM )
dT
dP dn1
dn
T
P,
n , n
P
T , n , n
n1
n2
n(
M )
(
nM )
T
1
2
P,
n , n
1
2
n(
M )
dT
P
From the definition of partial molar properties
1
2
T , n , n
1
2
T , P1
, n2.
n3
(
nM )
dP
ni
T , P,
n
n(
M ) n(
M )
(
nM )
dT
dP M idni
----------(3)
T
P
P,
n , n
Subtracting equation (2) from equation (3)
n(
M )
T
n(
M )
dT
P
dP
P,
n , n
1
2
1
2
T , n , n
1
2
T , n , n
1
2
n d M
Equatin (4) is the fundamental form of Gibbs Duhem equation
i
i
j
dn
0 ------------------(4)
i
T , P,
n1
, n3
Special Case
At constant temperature and pressure dT and dP are equal to zero. The equation becomes
i i 0 M d x
For binary solution at constant temperature and pressure the equation becomes
x d M x d M 0
1
1
2
2
x d M 1
x ) d M 0 ------------(5)
1
1
( 1 2
dividing equation(5) by dx1
x
1
d M
dx
1
1
( 1
x
1
)
d M
dx
1
2
0
The above equation is Gibbs Duhem equation for binary solution at constant temperature
and pressure in terms of Partial molar properties.
Any Data or equation on Partial molar properties must satisfy Gibbs Duhem
equation.
2