Engineering Chemistry S Datta

THERMODYNAMICS 89
Chemical Potential (µ)
Free energy per mole at a given temperature T and pressure (P) is called the chemical
potential µ or G .
Therefore, chemical potential, µ = G n
(for a pure substance).
For a species i which is component of a mixture we can express its chemical potential µ i
as follows.
µ i
=
F
HG
∂G
∂n
I K J
T, P,
n j
where n j
represents the constant composition of a mixture.
It is to be noted that free energy is an extensive property but chemical potential is an
intensive property.
Just like temperature, pressure or electric potential it tends to equalise within all parts
of a system. Chemical potential also has such a tendency, that is why the study of chemical
potential has become important.
Thus, chemical potential of water in ice must be same in both the phases. It can be
proved easily. For the equilibrium,
Ice
(I)
Water
(II)
If dn moles are transferred from phase I to phase II,
dG = µ(II) dn – µ(I) dn
But for equilibrium, dG = 0, ∴ µ(I) = µ(II)
Maxwell’s Relations
1. dE = TdS – PdV
2. dH = TdS + VdP
3. dA = – PdV – SdT
4. dG = VdP – SdT.
Applying the cross-derivative rule, we have
∂T
F ∂PI (i) = –
∂V S
HG
∂ K J
F ∂TI ,
(ii)
S V
HG
∂ K J =
P S
(iii)
F I
HG K J
F ∂PI HG
∂ K J
T V
=
F
HG
I K J
∂S
,
∂V T
(iv)
F
HG
I K J
F
HG
F
∂V
= –
∂T P
I K J
∂V
,
∂S P
∂SI HG
∂ K J .
P T
These four derivatives are very well known relations, which have extensive applications
in both physical and chemical phenomena.
Chemical potential of an ideal gas at temperature, T.
We have,
dG = – Sdt + VdP
= O + VdP (at constant, T)
z2
1
∴ ∆G = G 2
– G 1
= VdP