WOLFRAM|DEMONSTRATIONS PROJECT

Simple Distillation Residue Curves for a Mixture of Pentane and Dichloromethane at 750 mmHg

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initial pentane mole fraction in the still
0.5
The vapor-liquid equilibrium behavior of the binary mixture composed of pentane and dichloromethane at 750 mmHg can be represented by the following empirical equation:
y=
ax
1+(a-1)x
+bx(1-x)
, where
a=4.2
and
b=-1.2
.
This mixture exhibits a minimum boiling azeotrope at approximately 52.08% pentane mole fraction.
The simple distillation residue curve is given by the following implicit relation:
ξ=
1
(a-1+b)
ln
x
0
(1-x)
x(1-
x
0
)
+
2
(a-1)
(a-1+b)(a-1+ab)
ln
(1-x)(a-1+b[1+(a-1)
x
0
])
(1-
x
0
)(a-1+b[1+(a-1)x])
,
where
ξ
is the warped time,
x(ξ)
is the pentane mole fraction in the still at
ξ
, and
x
0
is the initial pentane composition in the still. The warped time
ξ
is related to clock time
t
by
dξ=
V
H
dt
, where
V
is the vapor rate from the still in mole/s and
H
is the liquid hold-up in the still in moles.
If the initial composition is
x
0
=0.5208
, the azeotropic composition, then
x(ξ)=0
.5208 ∀ ξ. Indeed, this mixture forms a positive azeotrope at 52.08% pentane mole fraction.
If the initial composition in the still is rich in pentane (i.e.,
x
0
>0.5208
), then the only component that is left in the still at large values of the warped time is pentane (i.e.,
x(ξ)->1
as
ξ→∞.
).
If the initial composition in the still is rich in dichloromethane (i.e.
x
0
<0.5208
), then the only component that is left in the still at large values of the warped time is dichloromethane (i.e.,
x(ξ)0
as
ξ→∞.
).