6
44 J ournal of Chemical and Engineering Data, Vol. 44, No. 3, 1999
Ta ble 3. Sa tu r a tion Mola lities m (sa t) in Wa ter a n d
the activity is the product of the molality m and the activity
coefficient γ, the equilibrium constant for reaction 1 is
(
(
Hexa n e + Wa ter ) a n d P a r tition Coefficien ts Kh /w of
-)-Men th ol, 1-Dod eca n oic Acid , a n d (-)-Men th yl
a
d od eca n oa te a t T ) 298.15 K
K ) (m{(-)-menthyl dodecanoate}‚m(H O)/
2
1
Kh/wb
substance
m(sat)/mol kg-
[m{(-)-menthol}‚m(1-dodecanoic acid)])‚
-
3
(
1
-)-menthol
(2.34 ( 0.12) × 10
732 ( 7
(
γ{(-)-menthyl dodecanoate}‚γ(H O)/
-
-
5 c
6
4 d
2
-dodecanoic acid (3.11 ( 0.26) × 10
(5.78 ( 0.33) × 10
5
(-)-menthyl
(9.83 ( 0.78) × 10
(4.18 ( 0.52) × 10
[γ{(-)-menthol}‚γ(1-dodecanoic acid)]) (3)
dodecanoate
Here, the standard state used is the hypothetical ideal
solution of unit molality. Since the molalities of (-)menthol,
a
The uncertainties are based on two estimated standard
deviations of the mean. Final uncertainties are given in the text
see Results and Discussion). The molalities of the solutes in the
1
-dodecanoic acid, and (-)-menthyl dodecanoate in the
b
(
-
1
-3
organic solvents are e0.016 mol kg and since they are
almost certainly nonionized in these solvents, it is reason-
able to assume that the ratio of the activity coefficients of
the products to reactants, that is, the second term on the
right-hand side of eq 3, will be close to unity. Thus, the
thermodynamic equilibrium constant of the reaction can
be written in terms of the molalities of the products and
reactants
aqueous phases were as follows: (-)-menthol, (7.37 ( 0.12) × 10
-
1
-6
-1
mol kg ; 1-dodecanoic acid, (10.03 ( 0.63) × 10 mol kg ; and
-
6
-1
(
-)-menthyl dodecanoate, (1.61 ( 0.25) × 10 mol kg . c This
d
value was determined in a previous study (Tewari, 1998). The
value given in this table was obtained from the molality of aqueous
1
-dodecanoic acid at pH ) 5.22. This measured molality is the sum
of the molalities of both the ionized and nonionized forms of
5
1
-dodecanoic acid. The value Kh/w ) (1.79 ( 0.25) × 10 pertains
to the transfer of the nonionized form of 1-dodecanoic acid to
hexane (see Results and Discussion).
K ) m{(-)-menthyl dodecanoate}‚m(H O)/
2
saturation molalities of (-)-menthol and (-)-menthyl dode-
canoate were determined by approaching the position of
equilibrium from two different temperatures. For each
compound, approximately 0.2 g of that substance and 45 g
[m{(-)-menthol}‚m(1-dodecanoic acid)] (4)
This equilibrium constant is symmetrical and dimension-
less.
The molalities of the reactants and products as deter-
mined in the equilibrium measurements are given in Table
3
of water were added to two 50-cm Erlenmeyer flasks which
were sealed with ground-glass stoppers. One of these flasks
was then placed in a constant-temperature shaker bath (25
rpm) at T ) 288.15 K; the other flask was placed in a
similar bath set at T ) 308.15 K. After 24 h both flasks
were placed in a single shaker bath at T ) 298.15 K and
allowed to equilibrate for an additional 6 days.
2
. The molalities of (-)-menthol, dodecanoic acid, and
(-)-menthyl dodecanoate are the averages of four or five
measurements. The molality of (-)-menthol from the
forward direction of reaction has been corrected for the
presence of the (+)-menthol impurity (mole fraction )
Approximately 35 g of the equilibrated aqueous phase
was then carefully transferred into a Teflon bottle. Then
0
.018) in the sample. Similarly, the molality of (-)-menthyl
dodecanoate in the reverse reaction mixture was corrected
2
.0 cm3 of hexane and 100 µL of the internal standard
for the (+)-menthyl dodecanoate impurity (mole fraction
solution in hexane were quantitatively added to the bottle.
The contents of the bottles were shaken and then centri-
fuged at 2000 rpm for 15 min. The molality of the substance
in the hexane layer was then analyzed by GC with the
procedure described above.
)
0.018). Although the mole fractions of these impurities
are small, these corrections were as large as 0.07K. The
molalities of water in hexane, heptane, toluene, cyclohex-
ane, and 2,2,4-trimethylpentane were taken from a previ-
ous study (Tewari, 1998). The molalities of water in
toluene, acetonitrile, and 2-methyl-2-butanol are the aver-
age of three measurements for each forward and reverse
reaction mixture. The reported equilibrium constants
K(combined) are the weighted averages of the results
obtained from the forward and the reverse directions of the
reaction.
For the measurement of Kh/w, approximately 0.5 g of the
3
compound was quantitatively dissolved in 2.0 cm of hexane
3
in a 50-cm Erlenmeyer flask and 40 g of water was added
to the flask. Using a procedure similar to that used in the
measurement of the saturation molalities, one of these
flasks was then placed in a constant-temperature shaker
bath (25 rpm) at T ) 288.15 K and the other flask was
placed in a bath set at T ) 308.15 K. After 48 h, both flasks
were placed in a single shaker bath at T ) 298.15 K and
allowed to equilibrate for an additional 6 days. The molality
of the solute in the aqueous phase was then determined
using the same methods used for the determination of the
saturation molalities. The initial molality of the solute in
the organic phase and the amounts of the two phases are
well-known from its preparation by gravimetric methods.
Therefore, by knowing the molality of the solute in the
aqueous phase, a correction can be applied in order to
calculate the final molality of each compound in the hexane
phase.
The results of the measurements of the saturation
molalities m(sat) in water and of the (hexane + water)
partition coefficients Kh/w of (-)-menthol, 1-dodecanoic acid,
and (-)-menthyl dodecanoate at T ) 298.15 K are given
in Table 3. In all cases, the results obtained by approaching
equilibrium from the two different initial temperatures
were either in agreement or near agreement with each
other.
The uncertainties given in Tables 2 and 3 are based only
on the random errors in the measurements expressed as
two estimated standard deviations of the mean. We now
consider possible systematic errors in the measurements.
We judge that reasonable estimates of the standard
uncertainties (Taylor and Kuyatt, 1994) due to possible
systematic errors in the values of the equilibrium constant
K for reaction 1 are 0.03K in the moisture determinations;
Resu lts a n d Discu ssion
The equilibrium constant K for reaction 1 is
0
.05K in the GC measurements of the molalities of
K ) a{(-)-menthyl dodecanoate}‚a(H O)/
2
(-)-menthol, 1-dodecanoic acid, and (-)-menthyl dode-
canoate; 0.01K for sample impurities; and 0.25|K(forward)
[a{(-)-menthol}‚a(1-dodecanoic acid)] (2)
-
K(reverse)| due to a possible failure to reach equilibrium.
where a is the activity of the indicated substance. Since
Similarly, estimates of the standard uncertainties in the