Recommended Liquid–Liquid Equilibrium Data. Part 4. 1-Alkanol ...

librium line can be described by the equation used previously
for the solubility of hydrocarbons in water. This equation
adopted for the monomers can be written as follows:
lnN 1/n/1/T =−h 1/R, 1
where N 1 is number of moles of the monomer in solution
consisting of n total number of moles and h 1 is heat of solution
of the monomer. The monomers are in chemical equilibrium
with various associations of the alkanol. Hence, the
total amount of the alkanol dissolved in water is higher than
N 1 and corresponds to the total moles of alkanol n 1. Using
the definition:
= N 1/n 1. 2
One can rearrange Eq. 1 into the following form:
ln x 1/1/T =−h 1/R − ln /1/T, 3
where x1 is the mole fraction of an alkanol in water along the
three-phase equilibrium line. In analogy to the alkane
+water systems, it is assumed that h1 depends linearly on T
going through zero at some temperature T0 . Thus h1/R in Eq.
3 can be approximated with the following equation:
h1/R = C1T − T0, 4
where C 1 is an adjustable parameter depending on alkanol.
For the second term in Eq. 3, the following approximation
is used:
ln /1/T K = 2400. 5
The approximation of Eq. 5 is valid at sufficiently low
temperatures, say below 370 K. This can be seen from an
analysis of the association model used in this work for LLE
calculations. Equations 4 and 5 introduced into Eq. 3
give, after rearrangement,
ln x 1/1/T =−C 1T − T 1,min, 6
where T1,min is defined by
T1,min K = T0 K + 2400/C1, 7
where T1,min is a temperature at which the differential in Eq.
6 is equal to zero. Thus T1,min is a temperature corresponding
to the minimum of the solubility of the 1-alkanol. Equation
6 has the same form as the equation used for solubility
of alkanes, 166 but T1,min is no longer constant as it depends on
C1, which in turn depends on the number of carbon atoms of
the alkanol. This explains the change of T1,min observed in
alkanol+water systems.
Integration of Eq. 6 gives the following equation, which
describes the solubility of alkanols in water as a function of
temperature:
ln x1 =lnx1,min + C1fT1,min/T, 8a
where
fT1,min/T = T1,min/T −lnT1,min/T −1. 8b
The same type of equation was used previously 166 for
alkane+water systems but contrary to the alkane systems Eq.
LIQUID–LIQUID EQUILBRIUM. 4 1393
FIG. 3. Logarithm of mole fractions of alkanols in water ln x 1 vs temperature
T. Experimental points and approximating curves calculated with Eq.
11 with parameters defined by Eq. 12.
8a when applied for alkanols is valid only at temperatures
sufficiently distant from the critical temperature of solubility.
It was found that all investigated 1-alkanol+water systems
can be approximated simultaneously with Eq. 8a provided
that the adjustable parameters ln x 1,min and C 1 are treated as
linear functions of the number of carbon atoms, N c
ln x 1,min = d 1 + d 2N c, 9
C 1 = d 3 + d 4N c. 10
Equations 9 and 10 allow rewriting Eq. 8 in the form:
ln x1 = d1 + d2Nc + d3 + d4NcfT1,min/T. 11
The coefficients d1, d2, d3, and d4 in Eq. 11 as well as T0 in
definition 7 were determined by simultaneous regression of
the experimental data for normal 1-alkanols from 1-pentanol
to 1-hexadecanol at at temperatures from the freezing point
of water to approximately 60 K below the critical temperature
of solubility. Altogether 242 experimental points were
used in the regression. After the regression the most outlying
point was removed and the remaining points were regressed
once more. This procedure was repeated until the deviation
of the most outlying point in the remaining data set did not
exceed three times the estimated standard deviation. This
procedure removed 22 of 242 initial points. The following
values of the parameters were obtained:
d1 = 1.249, d2 = − 1.365, d3 = 7.7, d4 = 4.2,
T 0 /K = 246.4. 12
Equation 11 works well up to 60 K below the critical
temperature of solubility T 2c as is shown in Fig. 3 but the
data above the boiling point of water were reported only by
one source with exception of pentanol. For the higher alkanols
shown in Fig. 4, there are no measurements at high
temperatures. Therefore it is concluded that reliability of Eq.
11 is not sufficiently tested at T373 K.
It was found that Eq. 11 with parameters defined by Eq.
12 can also be applied for branched 1-alkanols provided
J. Phys. Chem. Ref. Data, Vol. 35, No. 3, 2006