Chemistry Reference
In-Depth Information
vector allows one to calculate the experimental mole fraction of each component
in the vapor phase,
3
∑
(
)
y
=
1
r
AA
(4.1)
i
ij
j
i
j
=
1
where
r
ij
are calibration constants that relate the peak area to the number of moles.
Correspondingly,
y
i
can be calculated as
3
∑
=
(
)
calc
calc
o
calc
o
y
γ
x p
Φ
γ
x p
Φ
(4.2)
i
i
ii
i
j
j
j
j
j
=
1
where
p
o
is the vapor pressure of the pure compound and Φ is a factor that takes
into account vapor nonideality (Van Ness 1995). γ
calc
is obtained from a parametric
expression of ln γ (or, if not available, from
G
E
by differentiation).
By means of a least square routine which minimizes the objective function (O.F.),
m
∑
=
∑
(
)
2
exp
calc
OF
.. =
ln
y
−
ln
y
(4.3)
ik
ik
i
1
k
the values of the parameters of the ln γ or
G
E
expression are obtained. The procedure
is applied first to each single binary system (
m
= 2), then to the ternary points, in
which case the binary parameters are kept fixed.
4.2.2
V
e
and
κ
T
d
eTerminaTion
For
V
E
, the same degree of accuracy as
G
E
is not necessary. Excess volumes have
been determined by measuring the density of mixtures with the commonly used
vibrating tube technique. Experimental
V
E
data are fitted to parametric equations,
similar to those used for
G
E
, by minimizing the O.F.,
∑
V
(
)
E
,
exp
E
,calc
O.F.
=
−
V
(4.4)
k
k
k
As for the
G
E
data, the binary systems are studied first, and their parameters are then
used as constants in the treatment of the ternary data. Usually, for a ternary mixture
of strongly interacting components, the number of experimental points,
k
, is of the
order of one hundred both for
G
E
and
V
E
. The numbers of parameters required is
around 8 for
G
E
and around 14 for
V
E
.
Isothermal compressibility values of mixtures are very scarce in the literature, and
their determination requires instrumentation not commonly available in laboratories.
Fortunately, they play a very modest role in determining the KBI values, so it is enough
