Chemistry Reference
In-Depth Information
TABLE 4.2
Parameters of Equations 4.10 and 4.11 for
V
m
E
of Systems I, II,
and III at 298.15 K
a
a
0
a
1
a
2
a
3
a
4
d
I, Et+THF
-0.0844
-0.2544
0
0
0
0
I, Et+cyH
2.2329
2.2858
0.8137
0.4951
0
0.9697
I,II,III, THF+cyH
2.1217
-0.2426
0.1538
-0.0748
0
0
II, MEt+THF
0.4948
-0.0954
0.0562
0
0
0
II, MEt+cyH
3.5685
3.6412
1.7023
0
-0.8728
0.9348
III, TCM+THF
-1.4061
-0.2420
0.3276
0.3793
0
0
III, TCM+cyH
2.2357
-0.1737
0.0526
0
0
0
b
00
b
10
b
11
b
22
b
33
d
T
I
0.24770
1.5576
-1.4841
3.1869
-2.0987
0.99593
II
4.1144
-3.7071
-4.1203
0
0
0.469216
III
-7.7156
4.7686
5.1233
0
0
0
Sources:
From L. Lepori and E. Matteoli, 1998, Excess Volumes of the Ternary System
Ethanol + Tetrahydrofuran + Cyclohexane at 298.15 K,
Fluid Phase Equilibria
,
145, 69; G. Conti, P. Gianni, L. Lepori, and E. Matteoli, 2003, Volumetric Study of
(2-Methoxyethanol + Tetrahydrofuran + Cyclohexane) at 298.15 K,
Journal of
Chemical Thermodynamics
, 35, 503; P. Gianni, L. Lepori, and E. Matteoli, 2010,
Excess Gibbs Energies and Volumes of the Ternary System Chloroform +
Tetrahydrofuran + Cyclohexane at 298.15 K,
Fluid Phase Equilibria
, 297, 52.
a
Values of parameters not reported in the table are zero. Units are cm
3
mol
-1
for
a
and
b
;
d
are dimensionless. The following values of pure components have been used:
V
°
(cm
3
mol
-1
), 58.74, 79.18, 83.10, 81.74, 108.75 for Et, MEt, TCM, THF, cyH, respec-
tively; κ
T
° (MPa
-1
), 0.00114 for cyH, 0.001 for Et, MEt, TCM, THF.
4.3
FUNDAMENTAL AND OPERATIVE EQUATIONS
4.3.1 K
irKwood
-B
uFF
i
inTegrals
In this section, we illustrate the procedure to obtain KBI having available analytical
parametric expressions of
G
E
(or ln γ
i
) and
V
E
as functions of the mole fractions
x
1
,
x
2
,
x
3
. The fundamental equation, which relates
G
ij
to thermodynamic properties in
the isothermal-isobaric ensemble (in mole units) can be expressed as
ij
A
δ
ij
G
=
−
(4.12)
ij
cc
A
c
ij
j
where
A
is a matrix whose elements are defined by (see Section 1.2.4 in Chapter 1)
κµ
VVV
RT
′
+
Tij
i
j
A
=
(4.13)
ij
κ
T
