Chemistry Reference
In-Depth Information
The reduced covolumes,
b
and
b
HS
, are generalized functions of reduced tempera-
ture and multiplied by a characteristic volume,
V
*
.
Expressions for the hard-sphere
DCFI of Equation 9.4 are given by Mathias (O'Connell 1981) and Campanella,
Mathias, and O'Connell
(1987). Abildskov, Ellegaard, and O'Connell (2010a) give
the most recent correlations for the hard-sphere diameters and linear-density coef-
ficients as functions of reduced temperature. Ionic liquid (IL) characteristic parame-
ters for Equations 9.3 and 9.4 are listed, along with group-contribution characteristics
(Abildskov, Ellegaard, and O'Connell 2010a).
Comparisons of these correlations with experiment are given in the next sec-
tion. Experimental compressibilities are typically values manipulated from densities
measured at discrete pressures, so direct comparisons of densities of compressed
fluids are more reliable than compressibilities.
9.2.2 P
ure
c
omPonenT
and
s
oluTion
d
ensiTies
The pressure dependence of liquid densities can be obtained by isothermal integra-
tion of Equation 9.1 over a change in density from a reference state, ρ
0
,
p
0
,
T
, and {
x
},
such as ambient or saturated, to the desired state,
p
,
T
, and {
x
}. In terms of the DCFIs,
for which most applications have been made,
(
)
=
x
ρ
(
)
−
,
{}
{}
n
0
i
pT
,
ρ
x
pTx
kT
,
ρ
,
c
∑
V
kT
∫
i
x
d
ρ
i
i
κ
B
BT
i
=
0
1
x
ρ
i
(9.5)
x
ρ
n
n
i
c
c
∑
∑
∫
=
x
x
1
−
CT
(, )
ρ
d
i
ρ
i
j
ij
i
{}
Tx
,
0
i
=
1
j
=
1
x
ρ
i
A general integration procedure for these relations is described by O'Connell (1981,
1994, 1995), though for models of the forms 9.3 and 9.4, analytic relations exist. The
equations below are given by Abildskov, Ellegaard, and O'Connell
(2009).
For Equation 9.3, the pressure difference can be solved iteratively to obtain ρ,
(
)
=−
(
)
−
0
0
pT
,
ρ
pT
RT
,
ρ
()
(
)
(9.6)
0
1*
CbT
ρρ
−
1
−
()
+
−
()
+
−
()
2
3
4
ρρ
2
0
ρρ
3
0
ρρ
4
0
()
()
()
2
*
3
−
Cb
*
TV
*
bTV
*
b
TV
2
3
4
2
3
4
where the coefficients
b
i
(
T
) are combinations of those in Equation 9.3 and are listed
by Abildskov, Ellegaard, and O'Connell
(2009). It should be noted that predictions of
pressure/density differences, such as done here, are much more accurate than those
