Chemistry Reference
In-Depth Information
This concept is also often applied to the volume of the solution even though abso-
lute molar volumes of mixing can be determined quite easily. Other standard states
are possible. The most common alternative involves an infinitely dilute solute, also
known as the Henry's law standard state.
A series of excess quantities may then be defined using the properties of ideal
solutions such that
=
∑
E
id
E
X
=
∆
X
−
∆
X
x X
(1.14)
m
mix m
mix m
i
i
i
where the excess mixing quantities are expressed in terms of the corresponding excess
partial molar quantities. These are the quantities (
X
=
G
,
V
,
H
,
S
) that are normally
available experimentally. The first law properties (
U
,
V
,
H
) can be obtained directly
and the corresponding mixing properties are zero for ideal solutions. Properties that
relate to the second law (
S
,
G
) have to be determined indirectly—from phase equilib-
ria, for example—and their mixing properties are not zero even for ideal solutions.
Expressions for the excess partial molar quantities and their derivatives with respect
to composition can then be expressed in terms of derivatives of the excess mixing
quantities. One finds
∂
∂
X
x
E
m
E
E
XX
=+−
(
1
x
)
(1.15)
i
m
i
i
pT
,
and for derivatives of the chemical potentials in binary systems (see Section 4.3 in
Chapter 4 for ternary systems),
∂
∂
µ
i
E
∂
∂
2
G
x
E
m
=−
(
1
x
)
(1.16)
i
2
x
i
i
pT
,
pT
,
Obtaining the derivatives on the right-hand side requires a fitting equation for the
excess mixing quantities. The Wilson, Redlich-Kister, and nonrandom two liquid
(NRTL) model equations are some of the most commonly used (Poling, Praunitz,
and O'Connell 2000). Some additional practical considerations are also provided in
Section 1.3.9 and Section 4.2 in Chapter 4.
1.1.3 m
ore
on
c
hemical
P
oTenTials
Chemical potentials are central for an understanding of material/phase equilib-
rium and phase stability. FST can be used to study metastable phase and phase
instabilities. However, the vast majority of the studies using the FST of solutions
involve a single stable phase with multiple components. Here, we are concerned
with the relationships among the chemical potentials, and their derivatives, and
the local solution distributions. Thermodynamically, from Equations 1.2 and 1.3,
we have:
