The effect of Me4NBr, Et4NBr, Bu4NBr, and (EtOH)3EtNBr on the temperature of maximum density of water

Article abstract of DOI:10.1007/s10953-008-9340-9

The densities of aqueous solutions of Me₄NBr, Et₄NBr, Bu₄NBr, and Et(OH)₃EtNBr were measured in the concentration range 0.002 to 0.05 mol·kg^-1. The temperature of the determinations ranged from 275.15 to 279.15 K in 0.5 K steps, and the uncertainty of the densities was around ±1×10^-6 g·cm^-3. Eleven concentrations were used for each of the salts. It was found that all the solutes follow Despretz' law. The absolute value of the Despretz's constants increases with increasing number of carbon atoms in the cation, except for Et(OH)₃EtNBr which has the highest value. The ionic contributions to the Despretz's constants were calculated. The volumetric data obtained allows the calculation proposed by Kalgud and Pokale. The effective ionic radii were calculated using a semi-empirical equation, as proposed previously by several workers. The nonlinearity of the plot of the ionic Despretz constants versus effective ionic radius is confirmed.

Full text of DOI:10.1007/s10953-008-9340-9

J Solution Chem (2008) 37: 1657–1669
DOI 10.1007/s10953-008-9340-9
The effect of Me4NBr, Et4NBr, Bu4NBr,
and (EtOH)3EtNBr on the Temperature of Maximum
Density of Water
Luis H. Blanco · Alexandra Torres
Received: 22 April 2008 / Accepted: 15 July 2008 / Published online: 21 October 2008
© Springer Science+Business Media, LLC 2008
Abstract The densities of aqueous solutions of Me4NBr, Et4NBr, Bu4NBr, and
Et(OH)3EtNBr were measured in the concentration range 0.002 to 0.05 mol·kg−1. The
temperature of the determinations ranged from 275.15 to 279.15 K in 0.5 K steps, and
the uncertainty of the densities was around 1 × 10−6 g·cm−3. Eleven concentrations were
used for each of the salts.
It was found that all the solutes follow Despretz’ law. The absolute value of the De-
spretz’s constants increases with increasing number of carbon atoms in the cation, except
for Et(OH)3EtNBr which has the highest value. The ionic contributions to the Despretz’s
constants were calculated.
The volumetric data obtained allows the calculation proposed by Kalgud and Pokale. The
effective ionic radii were calculated using a semi-empirical equation, as proposed previously
by several workers. The nonlinearity of the plot of the ionic Despretz constants versus ef-
fective ionic radius is confirmed.
Keywords Water · Tetraalkylammonium salts · Maximum density
1 Introduction
The existence of a temperature of maximum density for water is one of the so-called “anom-
alies” that make the substance unique in nature [1, 2]. The effect of dissolved substances on
this property has received attention since the nineteen century when the French physicist
L.H. Blanco ( ) · A. Torres
ꢀ
Laboratorio de Investigaciones Básicas, Departamento de Química, Universidad Nacional de Colombia,
Bogotá, Colombia
e-mail: lhblancoc@unal.edu.co
Present address:
A. Torres
Grupo de Biocalorimetría, Departamento de Biología - Química, Universidad de Pamplona,
km 1 vía Bucaramanga-Pamplona, Pamplona, Colombia
e-mail: datorres@unipamplona.edu.co

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Despretz [3] studied it. Since then, there have been a number of studies by several workers,
some of the more recent ones being from this laboratory [4, 5].
The experimental technique most frequently used for the measurements is dilatometry
[4, 6]. In this work we made direct measurements of density as a function of temperature.
For this purpose, a version of a magnetic float densimeter was built, following the design of
Vargas and Blanco [7].
2 Experimental Section
A description of the technique and equipment has been reported elsewhere [5, 7].
Water was purified according to recommendations in the literature [8]. The conductivity
of the purified water was always less than 4 µS. The KCl used for calibration purposes was
Merck analytical grade with purity 99.99%. It was dried at 373 K for 12 h and kept in a
desiccator until used.
The symmetric tetraalkylammonium bromides used were obtained as follows: Me4NBr,
Merck, purity > 99%; Et4NBr, ICN Pharmaceuticals Inc. purity > 98%; and Bu4NBr, Sigma
purity > 99%. They were further purified according to recommendations in the literature
[9, 10]. The salts were crystallized from ethanol solutions. Full precipitation was achieved
using diethyl ether. After this, they were kept under vacuum until used.
The salt (EtOH)3EtNBr was prepared according to the method of Wen and Saito [10].
A mixture of triethanolamine in excess and ethylbromide was heated in anhydrous methanol
under reflux for 24 h. The resulting salt was purified by repeated crystallizations from
ethanol and ethanol + chloroform mixture; it was subsequently kept dry under vacuum.
All the bromides were analyzed after purification and before use for their halide content,
by potentiometric titration with AgNO3. The purities were better than 99.9% in all cases.
The solutions were prepared by weight using a Mettler AT 261 balance, which had a
sensitivity of 1 × 10−5 g between 0 and 50 g, and of 1 × 10−4 g between 50 and 210 g.
The concentration range was varied from 0.00200 to 0.05000 mol·kg−1
.
The densimeter was calibrated [7] using platinum rings and checked using solutions of
known density [11]. This procedure is fully described by Torres [5]. The temperature was
kept constant to within 0.001 K and densities were measured to 1 × 10−6 g·cm−3 in the
range of temperature from 275.15 to 279.15 K. Measurements were done at intervals of
0.5 K.
3 Results and Discussion
Tables 1 to 4 show the density data obtained for the four salts at the selected temperatures.
The data were fitted by equations using the least-squares method, and from them the tem-
peratures of maxima density were calculated.
According to the traditional treatment, Despretz’s law is written as:
ꢀθobs = Kmm
(1)
where ꢀobs = θ − θw. θ and θw are the temperatures of maximum density of the solution
and of water, Km is Despretz’s constant and m the concentration of the solutions in molality
units.

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Table 5 Variation of
−1
3/2
3/2
m/mol·kg
ꢀθ + 1.074m
(K)
ꢀθ + 1.074m
(K) with
molality, m, for aqueous
0.001999
0.005000
0.01000
0.01500
0.02000
0.02500
0.03000
0.03500
0.04000
0.04490
0.05000
−0.004
−0.016
−0.071
−0.135
−0.157
−0.236
−0.339
−0.383
−0.472
−0.453
−0.517
solutions of Et NBr
4
Table 6 Variation of
−1
3/2
3/2
m/mol·kg
ꢀθ + 1.074m
(K)
ꢀθ + 1.074m
molality, m, for aqueous
solutions of Me NBr
(K) with
0.002000
0.005000
0.009999
0.01500
0.02000
0.02500
0.03000
0.03500
0.04000
0.04500
0.05000
−0.054
−0.050
0.000
4
−0.115
−0.184
−0.197
−0.285
−0.418
−0.373
−0.421
−0.467
Several modifications of the original equation have been proposed [12], including a work
by Kaulgud and Pokale [13] that uses the equation proposed by Wakabayashi and Takaizumi
[14]:
ꢀθ + 1.074m3/2 = Kmm.
(2)
A plot of ꢀθ + 1.074m3/2 versus m should yield a straight line with a slope equal to De-
spretz’s constant Km. Blanco and Torres [4] found that the values of the constant differ
little from those calculated using Eq. 1. Tables 5 to 8 and Figs. 1 to 4 show the variation of
ꢀθ + 1.074m3/2 with molality for all of the systems studied, and Table 9 reports the cal-
culated constants. These values obtained are compared with those of Wada and Miura [15]
for the three salts that were studied in common. The values are quite similar in all cases.
However, the agreement is not complete, probably due to the fact that Wada and Miura used
higher concentrations in their work.
To calculate the ionic contributions to the constant, and following earlier workers such
as Wakabayashi and Takaizumi [14], we took a value of Km = 6.6 K·mol−1 for the Br− ion
from the report of Kaulgud and Pokale [13]. The calculated values are shown in Table 10.
Kaulgud and Pokale [13], following the method proposed by Leyendekkers in a series
of papers [16–21], used values of the “real” radii of ions in aqueous solutions at 298.15 K.

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Table 7 Variation of
−1
3/2
3/2
m/mol·kg
ꢀθ + 1.074m
(K)
ꢀθ + 1.074m
(K) with
molality, m, for aqueous
0.002000
0.005000
0.01000
0.01500
0.01999
0.02499
0.03000
0.03500
0.04000
0.04500
0.05000
−0.002
−0.037
−0.126
−0.247
−0.320
−0.407
−0.508
−0.654
−0.696
−0.720
−0.852
solutions of Bu NBr
4
Table 8 Variation of
−1
3/2
3/2
m/mol·kg
ꢀθ + 1.074m
(K)
ꢀθ + 1.074m
molality, m, for aqueous
solutions of (EtOH) EtNBr
(K) with
0.001000
0.002000
0.003500
0.004762
0.008000
0.009999
0.01250
0.01500
0.01700
0.02000
0.02500
0.03000
−0.006
−0.018
−0.052
−0.068
−0.139
−0.185
−0.239
−0.266
−0.308
−0.410
−0.541
−0.558
3
These radii are larger than the corresponding Pauling’s radii by an amount ꢀ. According to
Kaulgud and Pokale [13], the radii are larger that the Pauling ionic radii (r) by an amount
ꢀ that is defined by the positional correlation of the ion and the adjacent water molecules.
Using the measured densities at 277.15 K we calculated the limiting partial molar ionic
volumes using Conway’s method [22]. A plot of the partial molar volumes at infinite di-
lution V o versus molar mass allows the calculation of V o for the anion. Then, using the
additivity principle, V o is obtained for each cation. From these values it is possible to obtain
the effective radii for the cations. Several workers [23–31] have used the semi-empirical
equation:
Vioon = 2.5(r + ꢀ)3
(3)
that we also used here to get the values reported in Table 11. In reference [13], a plot of
Km(ion) versus (r + ꢀ) is presented. It was found that the values for the tetraalkylammonium
cations deviate from a linear tendency as shown in Fig. 5. The deviations were attributed
partially to the fact that no values for the volumes at 277.15 K were known at the time, even
though they expected there to be a small correction. According to our results, when using

J Solution Chem (2008) 37: 1657–1669
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3/2
−1
Fig. 1 Plot of ꢀθ + 1.074m
against molality (m/mol·kg ) for aqueous solutions of Me NBr
4
3/2
−1
Fig. 2 Plot of ꢀθ + 1.074m
against molality (m/mol·kg ) for aqueous solutions of Et NBr
4
values of volumes determined at temperatures in the neighborhood of the temperature of
maximum density, the tetraalkylammonium cations still deviate from a straight line.
In Fig. 5 the filled triangles represent the experimental results reported in Ref. [13] and
the open ones are the results of this work. There is a small difference as had been predicted

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3/2
−1
Fig. 3 Plot of ꢀθ + 1.074m
against molality (m/mol·kg ) for aqueous solutions of Bu NBr
4
3/2
−1
Fig. 4 Plot of ꢀθ + 1.074m
against molality (m/mol·kg ) for aqueous solutions of (EtOH) EtNBr
3
earlier [4, 13]. In Ref. [13], density data at 298.15 K were used because at that time data
were not available at lower temperatures. We used our data in the vicinity of 277.15 K and
thus, the values of the calculated radii are slightly lower that those reported earlier. As we
had pointed out before [4], the simplest prediction of the effect of the tetraalkylammonium

J Solution Chem (2008) 37: 1657–1669
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Table 9 Despretz constants
(K·mol ·kg)
Me NBr
4
Et NBr
4
Bu NBr
4
(EtOH) EtNBr
3
−1
a
b
c
K
−10.10
−9.86
−9.9
−11.47
−11.23
−11.0
−17.93
−17.69
−15.9
−20.48
−20.30
–
m
a
Calculated using Eq. 1
K
K
m
m
b
c
Calculated using Eq. 2
From [15]
Table 10 Despretz constants
−1
+
+
+
+
Ion
Et N
4
Me N
4
Bu N
4
(EtOH) EtN
3
K
(K·mol ·kg) for individual
m
ions
K
m
−4.85
−3.48
−11.31
−13.86
Table 11 Effective ionic radii of
alkylammonium cations
a
b
Ion
r
(nm)
(r + ꢀ) (nm)
(r + ꢀ) (nm)
Pauling
+
+
+
Me N
0.305
0.369
0.468
0.3194
0.3816
0.4722
0.3366
0.3956
0.4843
4
Et N
4
a
This work
Bu N
4
b
From [13]
Fig. 5 Variation of the Despretz
constant K with the effective
m
ionic radii (r + ꢀ). Symbols:
(", 2) cations; (!), anions;
(1), tetraalkyl ammonium salts
calculated according to their size,
(Q) Experimental values from
Kaulgud and Pokate [13];
(P) this work
cations on the TMD is that they should increase its value, because the cations are supposed
to be water structure makers. In fact this does not happen: as shown in this work, among oth-
ers, and ꢀθ is negative in all cases. Some authors, for instance Darnell and Greyson [12],
propose that at lower temperatures near the TMD the structural effect is the opposite. That
is, it changes sign. This is not in agreement with experimental observations [13]. Earlier
reports in the literature [4, 13] show that the change in sign does not happen. This work

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J Solution Chem (2008) 37: 1657–1669
shows clearly that the values of the calculated radii support the conclusion that the tetra-
butylammonium cations enhance the water structure at temperatures in the neighborhood of
the TMD.
Acknowledgements We thank the Universidad Nacional de Colombia, Fundación para la Promoción de
la Investigación y la Tecnología del Banco de la República and the Universidad de Pamplona for financial
support.
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