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Simple Distillation Residue Curves for a Mixture of Ethanol and Isopropanol at 750 mmHg

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initial ethanol mole fraction in the still
0.5
The vapor-liquid equilibrium behavior of a binary mixture composed of ethanol and isopropanol at 750 mmHg can be represented by the following equation:
y=
αx
1+(α-1)x
, where the relative volatility,
α=1.9
, is assumed constant.
The simple distillation residue curve is given by the following implicit relation:
ξ=
1
(α-1)
ln
x
0
(1-x)
x(1-
x
0
)
+ln
1-x
1-
x
0
,
where
ξ
is the warped time,
x(ξ)
is the ethanol mole fraction in the still at
ξ
, and
x
0
is the initial ethanol composition in the still. Warped time is related to clock time
t
by
dξ
=
V
H
dt
, where
V
and
H
are, respectively, the vapor rate and the liquid hold-up in the still, expressed in moles per second and moles.
Since the mixture does not have an azeotrope, the light component (i.e., ethanol) will preferentially boil off and thus we have
x(ξ)0
as
(ξ→∞)
.
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