Chemistry Reference
In-Depth Information
to have available values of the pure components (not necessarily very accurate and can
even be estimated), and to assume ideal behavior for the calculation of κ
T
of a mixture,
3
∑
o
κ
=
φ κ
(4.5)
T
i
Ti
,
i
=
1
where ϕ
i
is the volume fraction of component
i
.
4.2.3 d
aTa
T
reaTmenT
Many equations, either empirical or derived from models, are available to repre-
sent excess thermodynamic properties as a function of the liquid mole fraction and
of a number of adjustable parameters for use in Equations 4.3 and 4.4 (Prausnitz,
Lichtenthaler, and Gomes de Azevedo 1999). In the treatment of our experimental
data, we have examined the capability of many of these equations to fit data with
the smallest number of parameters and with the least standard deviation of the O.F.
(Lepori et al. 1998). For the majority of systems, either binary or ternary, examined
by us in the course of about two decades, the rational form (Myers and Scott 1963)
of the Redlich-Kister (RK) expression (Redlich and Kister 1948), and the Wilson
(Wilson 1964) equation in the extended form (Novák, Matouš, and Pick 1987), have
resulted in the most appropriate representations of
G
E
and
V
E
. For ternary systems,
the excess functions can be expressed as the sum of a contribution (subscript B),
which depends only on the parameters of the three binary systems, and a ternary
contribution (subscript T), which involves additional parameters,
E
B
E
T
E
YYY
=+
(4.6)
where
g
or
V
, and
g
=
G
/ RT.
In the case of the Wilson equation,
g
E
and
V
E
are formally different,
3
3
2
3
∑
ln
∑
∑
∑
g
E
=−
x
Λ
x
+
pxx
(
Λ
=
1
)
(4.7)
i
ijj
ij
ij
ii
B
i
=
1
j
=
1
i
=
1
ji
=
+
1
3
3
3
∑∑
∑
B
E
=
V
x
x
Λ
λ
x
Λ
(
Λ
ii
i
==
1
,
λ
0
)
(4.8)
i
j
ij j
j
ij
i
=
1
j
=
1
j
=
1
If the RK model is assumed, the same formal equation can be used to express
g
B
and
V
B
,
