J ournal of Chemical and Engineering Data, Vol. 43, No. 5, 1998 753
Ta ble 3. Sa tu r a tion Mola lities m Sa t in Wa ter a n d
bined standard uncertainties are then multiplied by 2 to
(
2,2,4-Tr im eth ylp en ta n e + Wa ter ) P a r tition Coefficien ts
arrive at a final set of results with somewhat larger
estimates of total error. Thus, the values of the equilibrium
constant K(1) are (39.6 ( 7.5) for hexane, (35.3 ( 9.0) for
heptane, (23.3 ( 7.6) for cyclohexane, (27.2 ( 5.6) for 2,2,4-
trimethylpentane, and (17.9 ( 6.9) for toluene. The values
of the saturation molalities msat in water are (3.91 ( 0.27)
KIso/w of 1-Dod eca n ol, 1-Dod eca n oic Acid , a n d Dod ecyl
Dod eca n oa te a t T ) 298.15 K
a
1
Kiso/wb
substance
msat/mol kg-
-
-
5
5
4
1
1
-dodecanol
-dodecanoic
acid
(3.91 ( 0.26) × 10
(7.61 ( 0.15) × 10
(3.44 ( 0.21) × 10
4 c
(3.11 ( 0.26) × 10
-5
-1
-5
×
10 mol kg for 1-dodecanol, (3.11 ( 0.27) × 10 mol
(3.897 ( 0.083) × 10-
6
(2.03 ( 0.15) × 10
6
dodecyl
dodecanoate
-
1
-
6
kg for 1-dodecanoic acid, and (3.90 ( 0.12) × 10 mol
-
1
kg for dodecyl dodecanoate. The values of the partition
4
a
coefficient Kiso/w are (7.61 ( 0.27) × 10 for 1-dodecanol,
These uncertainties are based on two estimated standard
deviations of the mean. Final uncertainties are given in the text
4
(6.88 ( 0.47) × 10 for 1-dodecanoic acid, and (2.03 ( 0.16)
b
6
(
see Results and Discussion). The molalities of the solutes in the
× 10 for dodecyl dodecanoate.
-
5
-1
aqueous phases were 1-dodecanol, (1.87 ( 0.04) × 10 mol kg
;
The aforementioned thermochemical cycle is now de-
scribed. The chemical reference reaction in water that will
be used is
-
5
-1
1
-dodecanoic acid, (2.64 ( 0.07) × 10 mol kg ; dodecyl dode-
-6 -1
canoate, (2.94 ( 0.20) × 10 mol kg . c The value given in this
table was obtained from the molality of aqueous 1-dodecanoic acid
at pH ) 4.9. This measured molality is the sum of the molalities
of both the ionized and nonionized forms of 1-dodecanoic acid. The
1
-dodecanol(aq) + 1-dodecanoic acid(aq) )
dodecyl dodecanoate(aq) + H O(l) (3)
4
value Kiso/w ) (6.88 ( 0.42) × 10 pertains to the transfer of the
2
nonionized form of 1-dodecanoic acid to 2,2,4-trimethylpentane (see
Results and Discussion).
The charges on all of the substances in reaction 3 are zero
and therefore are omitted. The equilibrium constant K
for this reaction is
m
by GC is equal to the total molality of both the ionized and
nonionized forms of this acid. Thus, the measured value
4
K
iso/w ) (3.44 ( 0.21) × 10 pertains to this mixture of
Km ) {m(dodecyldodecanoate)‚m°/
species; formally it is an apparent equilibrium constant.
However, it is desired to obtain a value of Kiso/w that
pertains only to the nonionized form of 1-dodecanoic acid.
To do this it is necessary to know the pK of 1-dodecanoic
acid. The value pK ) 4.9 for 1-dodecanoic acid from the
known pK’s of 1-hexanoic, 1-heptanoic, and 1-octanoic acids
{
m(1 - dodecanol)‚m(1 - dodecanoic acid)} (4)
The standard molality (m° ) 1 mol kg-1) has been used in
the above equation to keep the equilibrium constant
dimensionless. The partition coefficients Kiso/w pertain to
the following reactions:
(Martell et al., 1993). Thus, at the pH ) 4.9 at which the
experiments were performed, the fractions of the ionized
and nonionized forms of this acid are equal. This informa-
1
- dodecanol(aq) ) 1 - dodecanol(iso)
(5)
tion is used to calculate a value of Kiso/w ) (6.88 ( 0.42) ×
1 - dodecanoic acid(aq) ) 1 - dodecanoic acid(iso) (6)
4
1
0 , which pertains to the transfer of the nonionized form
of 1-dodecanoic acid to 2,2,4-trimethylpentane.
dodecyl dodecanoate(aq) ) dodecyl dodecanoate(iso)
The uncertainties assigned thus far are based on the
random errors in the measurements expressed as two
estimated standard deviations of the mean. Since these
uncertainties allow for only random errors, it is desirable
to consider possible systematic errors in the measurements.
It is judged that the determinations of the molalities m of
water are reliable to within 0.03‚m. The use of internal
standards also helps to minimize errors, and it is judged
that the systematic errors in the measured molalities of
(7)
In this case, “iso” denotes 2,2,4-trimethylpentane. Also,
needed in the thermochemical cycle is the standard molar
Gibbs free energy change ∆ G° for reaction 1 in 2,2,4-
r
m
trimethylpentane and the solubility of water in 2,2,4-
trimethylpentane:
H O(l) ) H O(iso)
(8)
2
2
1
-dodecanol, dodecyl dodecanoate, and 1-dodecanoic acid
∆rG° for reaction 3 can then be calculated with
are <0.01‚m. The final values of the equilibrium constants
for reaction 1 are based on results in which the position of
equilibrium was approached from two different directions.
Thus, systematic errors due to lack of equilibrium are
already included in the present uncertainty intervals. A
similar situation holds for the values of the saturation
m
∆rG° (3) ) ∆ G° (1) + ∆ G° (5) + ∆ G° (6) -
m
r
m
r
m
r
m
∆ G° (7) - ∆ G° (8) (9)
r
m
r
m
The values of Kiso/w (see Table 3) were used to calculate
values of ∆ G° for reactions 5, 6, and 7. The value of the
molalities msat
. Here, however, the tactic used was to
r
m
approach the position of equilibrium from two different
temperatures. While the method of approaching equilib-
rium from two different temperatures was not used in the
measurement of the values of Kiso/w, it had already been
established from the solubility measurements that 3 days
equilibration time was adequate for the attainment of
equilibrium. Thus, total systematic errors in the reported
quantities are judged to be, respectively, <0.035‚K(1),
equilibrium constant for reaction 1 with 2,2,4-trimethyl-
pentane as the organic solvent (see Table 2) give ∆ G° for
r
m
reaction 1. The solubility of water as determined in the
equilibrium measurements with the solvent 2,2,4-trimeth-
ylpentane (see Table 2) was used to calculate ∆ G° for
r
m
reaction 8. This seems reasonable since the aqueous and
the organic phases had equilibrated for 30 days. Also, it
seems unlikely that the solubility of water in the 2,2,4-
trimethylpentane would be significantly affected by the
dilute solutes that were also present in the organic phase.
The thermochemical cycle gives ∆ G° ) -(36.9 ( 2.9) kJ
<0.01‚msat, and <0.014‚Kiso/w
.
These estimates of possible systematic error are com-
bined in quadrature together with the statistical uncer-
tainties in the measured values of these quantities, ex-
pressed as one estimated standard deviation of the mean,
to obtain combined standard uncertainties. These com-
r
m
-
1
mol for reaction 3; the corresponding equilibrium con-
+
6.5
2.0
6
stant K
m
) (2.9- ) × 10 . Therefore, in aqueous solution,
the formation of dodecyl dodecanoate is favored over