Page 54 - Bruno Linder Elementary Physical Chemistry

August 18, 2010 11:36 9in x 6in b985-ch05 Elementary Physical Chemistry

TheFreeEnergy Functions 39

the partial molar or molal volume of i as

∗ (5.25)
i
V =(∂V/∂n i) T,P n j =n i
The total volume of all species of a homogeneous system can be
written as

V =Σ in i V i ∗ (5.26a)
and in particular in a two-component system,

∗
V = n AV , +n BV , (5.26b)
∗
A
B
Similar considerations apply to the Gibbs free energy
G = n A G , +n B G , (5.27)
∗
∗
A
B
5.6. The Chemical Potential
The partial molar free energy is often called the chemical potential and is
denoted as

(5.28a)
µ i =(∂G/∂n i ) T,P,n j =n i

Comment: The partial Gibbs free energy transcends ordinary prop-
erties of partials. The chemical potential, µ i , can be defined also as
the partial Helmholtz free energy, the partial internal energy, as well
as the partial enthalpy, namely,

(5.28b)
µ i =(∂A/∂n i) T,V,n j =n i
(5.28c)
µ i =(∂U/∂n i ) S,V,n j =n i
(5.28d)
µ i =(∂H/∂n i) S,P,n j =n i
As can easily be shown (not in this course), they are all equal to
Eq. (5.28a). Thus, it makes sense to give these partials a special name;
the name is chemical potential. Thus, instead of writing the Gibbs free
energy in terms of the partial molar quantities, as in Eq. (6.10), it is
common practice to express the free energy of, say, a two-component
system, as

G = n A µ A + n B µ B (5.29)