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Thermodynamics properties of glycerol-water solution

Article  in  Ukrainian Journal of Physics · March 2007

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LIQUIDS AND LIQUID CRYSTALS

THERMODYNAMICS
PROPERTIES OF GLYCEROL–WATER SOLUTION
I.I. ADAMENKO, S.O. ZELINSKY, V.V. KOROLOVICH
UDC 532 Taras Shevchenko Kyiv National University
c
°2007 (6, Academicain Glushkov Ave., Kyiv 03127, Ukraine;
e-mail: iadamenko@univ.kiev.ua, sergiy@univ.kiev.ua)

The influence of structural features of water on the thermodynamic pressure technologies for fabricating compact powders,
properties of associated liquids has been studied, with the glycerol– because they preserve their liquid phase state up to
water solutions being taken as an example. The P − V − T data
for those solutions are experimentally measured in the pressure
pressures of the order of 5 GPa [2], as well as in
interval 0.1–103.1 MPa and in the temperature range 293–380 K. cryomedicine.
The modulus of elasticity, the coefficient of thermal expansion,
We aimed at studying the thermodynamic properties
the increments of the entropy, Gibbs energy, and the enthalpy
are calculated numerically. The temperature dependences of the of solutions glycerol–water by measuring P − V − T data
parameters of the semiempirical Tait equation have been analyzed, experimentally in the pressure interval 0.1–103.1 MPa
and the recommendation to use this equation for the description and the temperature range 293–380 K making use of a
of data obtained is made.
bellows piezometer. We studied glycerol–water solutions
with four concentrations: 0.27, 0.31, 0.33, and 0.35
mole fraction of glycerol (m.f. Gly). The results of our
It is known that there is no theory of real solutions
researches revealed that the concentration dependence of
in molecular physics which adequately describes the
the solution density demonstrated a peculiarity, namely,
relevant experimental thermal data. The existing
a jump-like reduction at a concentration of about
theories of two-component liquid systems are developed
0.33 m.f. Gly in the temperature interval concerned [3].
in the case where the difference between the dimensions
This concentration is close to the accepted threshold
of molecules is small, as well as the energy of interaction
which divides glycerol–water solutions into two groups:
between different components; in this case, the potential
glycerol-rich (the concentration from 0.4 to 1.0 m.f. Gly)
energy is an even additive function [1]. The development
and water-rich ones (the water concentration from 1.0 to
of the statistical theory of liquid solutions becomes
0.6 m.f.) [4, 5].
substantially complicated if this difference grows and if
the solution components are associated liquids, for which The dependence of the solution density on pressure
the potential of intermolecular interaction is not an even is monotonous within the whole studied interval of
additive function any more. temperatures (Fig. 1). From this figure, one can see that
We studied the solutions glycerol–water, where the adding 0.27 m.f. Gly to water at 0.1 MPa results in
molecules of their components substantially differ from the increase of the solution density by approximately
one another by shape, dimensions, and interaction 18%. If the pressure grows under isothermal conditions,
energy magnitude. Experimental researches of solutions the density of water increases more rapidly than the
are of fundamental and applied significance, because, density of solutions, which testifies that the glycerol–
on the one hand, they assist in the development water solutions under investigation are less compressible
of the statistical theory of molecular liquid solutions and more dense-packed in comparison with water.
and, on the other hand, allow one to solve important The method of numerical differentiation was applied
engineering problems. For instance, glycerol–water to the measured P − V − T data in order to calculate
solutions are used as a working liquid in hydrostatic the following thermodynamic quantities:

ISSN 0503-1265. Ukr. J. Phys. 2007. V. 52, N 9 855

I.I. ADAMENKO, S.O. ZELINSKY, V.V. KOROLOVICH

Fig. 2. The same as in Fig. 1, but for the isothermal modulus of

elasticity
Fig. 1. Pressure dependences of the density for water and glycerol–
water solutions with various glycerol concentrations and at a
temperature of 301 K The temperature dependence of the elasticity
modulus for water is known to have a maximum
at the pressure P = 0.1 MPa and a temperature
the isothermal modulus of elasticity
µ ¶ of 320 K. Similar temperature dependences of KT
∂P are also observed for glycerol–water solutions with
KT = ρ , (1)
∂ρ T concentrations ranging from 0.27 to 0.31 m.f. Gly. At
a solution concentration of 0.33 m.f. Gly, this maximum
the isobaric coefficient of thermal expansion
µ ¶ disappears (Fig. 3). In the case of water, the maximum
1 ∂ρ in the temperature dependence of KT at P = 0.1 MPa
αP = − , (2)
ρ ∂T P and near the temperature T = 320 K is associated with
the disappearance of an ice-like water structure. It is
and the isothermal increments of the isobaric-isothermal natural to assume that this structural feature of water
Gibbs potential, would manifest itself in the glycerol–water solutions with
ZP concentrations up to 0.31 m.f. Gly as well.
1
∆G = dP, (3) Dielectric spectroscopy of water-rich solutions
ρ
P0 glycerol–water showed that they are characterized by
a high degree of inhomogeneity. This is connected
entropy,
with the fact that some part of water molecules can
ZP µ ¶ be included into glycerol–water domains, another part
1 ∂ρ
T ∆S = T , dP (4) can form aggregates with loosen packing of the Ice I
ρ2 ∂T P type, and the rest of them remains free to form
P0
interphase water. Using data on the latent heat of
and enthalpy, ice melting, it was shown that, in the glycerol–water
ZP µ µ ¶ ¶ solution with a concentration of 0.1 m.f. Gly, water
1 T ∂ρ is distributed among those states as follows: 0.5 m.f.
∆H = + 2 dP. (5)
ρ ρ ∂T P is in the ice-like structure, 0.15 m.f. in “domains”,
P0
and 0.25 m.f. forms interphase water [5]. One may
Figure 2 demonstrates the dependence of the expect that the variation of pressure would change
isothermal modulus of elasticity KT on pressure. It is this relationship for the water molecule distribution
evident that this quantity increases with the growing among “various states”, which would manifest itself
pressure, being approximately 2.5 times as large as that in the thermodynamic properties of glycerol–water
for water. solutions.

856 ISSN 0503-1265. Ukr. J. Phys. 2007. V. 52, N 9

 THERMODYNAMICS PROPERTIES OF GLYCEROL–WATER SOLUTION

b
Fig. 3. Temperature dependences of the isothermal modulus of
elasticity for water and glycerol–water solutions with various
glycerol concentrations at atmospheric pressure (a) and at P =
98.1 MPa (b)

In particular, the maximum in the temperature

dependences of the isothermal elasticity moduli of water
and aqueous solutions of glycerol under consideration
diminishes as the pressure grows and, at a pressure of
98.1 MPa, practically disappears in the 0.31-m.f. Gly
solution.
The dependence of the thermal expansion coefficient
αP on temperature is ascending for pure water (Fig. 4,a).
At the same time, the isobars of the thermal expansion
coefficient of water intersect one another: if the
pressure grows, the parameter αP of water increases at
temperatures below 325 K but decreases at T > 325 K,
as αP ’s of all other associated and non-associated liquids
do. The coefficient of thermal expansion for solutions Fig. 4. Temperature dependences of the isobaric coefficients of
with concentrations of 0.27 and 0.35 m.f. Gly also thermal expansion for water (a) and the glycerol–water solutions
increases as the temperature grows, but the αP -isobars with concentrations of 0.27 (b) and 0.35 m.f. Gly (c)

ISSN 0503-1265. Ukr. J. Phys. 2007. V. 52, N 9 857

I.I. ADAMENKO, S.O. ZELINSKY, V.V. KOROLOVICH

Fig. 5. Baric dependences of the Gibbs potential increment at

T = 301 K for water and glycerol–water solutions with various Fig. 6. Temperature dependences of the parameter B for water
glycerol concentrations and glycerol–water solutions with various glycerol concentrations

do not intersect (Fig. 4,b and c). The isobars of We calculated the values of the constants A and B
the thermal expansion coefficient of the 0.27-m.f. Gly in the Tait state equation for water and glycerol–water
solution glycerol–water have a characteristic feature of solutions. The values obtained for the constant A are
the small-cusp type at about T = 325 K. However, if the as follows: 0.136 for water, 0.091 for the 0.27-m.f. Gly
concentration of glycerol in the solution grows further, solution, and 0.082 for the 0.35-m.f. Gly solution; i.e. the
this feature disappears (Fig. 4,c). increase of the glycerol content in the solutions studied
The isothermal increment of the isobaric-isothermal gives rise to a reduction of the A value.
Gibbs potential for both water and the solutions At the same time, the increase of the glycerol content
concerned increases in the investigated temperature in the solutions is accompanied by the growth of the
interval (Fig. 5), with the corresponding increments of constant B (Fig. 6). The values of the parameter B
the Gibbs potential for solutions growing more slowly for solutions are larger than that for water, which
with the increasing pressure than that for water. For testifies that the energy of intermolecular interactions
the solutions, the increment of the Gibbs potential does in solutions is greater than that in pure water.
not depend on the concentration within the limits of
Basing on the physical meaning of the Tait constants
calculation errors.
A and B, one may assert that the addition of glycerol to
The isothermal increments of the entropy for water
water-rich glycerol–water solutions increases the energy
and glycerol–water solutions are identical to each other
of interaction and the steepness of the intermolecular
within the error limits of their determination, while the
repulsion potential.
isothermal increment of the enthalpy for water is larger
than those for glycerol–water solutions. The value of constant B depends on the temperature
(Fig. 6). In the case of water, the B(T ) dependence
To describe the P − V − T data obtained for water
has a maximum. The same behavior is also observed
and glycerol–water solutions, we took the semiempirical
for the temperature dependence of B in the solutions
Tait equation of state which includes a small number of
with concentrations of 0.27 and 0.31 m.f. Gly. If the
parameters and can be substantiated statistically [6]:
concentration of glycerol increases further, the maximum
µ ¶ in the temperature dependence B(T ) diminishes, and
1 ∂ρ A
2
= . (6) this dependence becomes monotonously descending, as
ρ ∂P B+P
it occurs for non-associated liquids.
The choice of this equation was caused by the fact The increase of quantities KT and B with the
that the character of the dependence of the isothermal temperature growing in the interval 293–325 K is not
derivative ρ2 (∂P/∂ρ)T on pressure turned out linear for typical of a wide class of liquids, being inherent to
the studied solutions. aqueous liquid systems only.

858 ISSN 0503-1265. Ukr. J. Phys. 2007. V. 52, N 9

 View publication stats

THERMODYNAMICS PROPERTIES OF GLYCEROL–WATER SOLUTION

The researches carried out for glycerol–water 1. N.A. Smirnova, Molecular Theory of Solutions (Khimiya,
solutions showed that, for water-rich solutions, there Leningrad, 1987) (in Russian).
exists the threshold concentration, at which the 2. V.A. Sidorov and O.B. Tsiok, Fiz. Tekhn. Vysok. Davlen. 1,
temperature dependences of the isothermal elasticity N3, 74 (1991).
modulus KT and the Tait constant B change their 3. I. Adamenko, L. Bulavin, V. Ilyin, S. Zelinsky, and K. Moroz,
J. Mol. Liq. 127, 90 (2006).
behavior. If the glycerol concentration is lower than the
threshold one, the temperature dependences of KT and 4. A. Puzenko and Y. Hayash, J. Phys. Chem. B 109, 6031 (2005).
B have maxima. At higher concentrations of glycerol, 5. A. Puzenko, Y. Hayash, and J.Y. Feldman, J. Phys. Chem. B
109, 9174 (2005).
the maxima in the temperature dependences of KT
and B are not observed. Therefore, one may assert 6. V. Sysoev, Ukr. Fiz. Zh. 3, 34 (1975).
that, if the glycerol concentration in glycerol–water Received 20.03.07.
solutions is equal to or lower than the threshold one, the Translated from Ukrainian by O.I. Voitenko
appearance of structural skeleton formations of the “Ice
I” type made up of water molecules becomes possible. ТЕРМОДИНАМIЧНI ВЛАСТИВОСТI РОЗЧИНIВ
At higher glycerol concentrations, such structural ГЛIЦЕРИН–ВОДА
formations do not exist. Our researches demonstrated
that the increase of pressure gives reduction of the I.I. Адаменко, C.O. Зелiнський, В.Ф. Королович
threshold concentration and, therefore, favors the Резюме
destruction of such structural skeleton formations of
Дослiджено вплив структурних особливостей води на термоди-
water molecules of the “Ice I” type in glycerol–water
намiчнi властивостi асоцiйованих рiдин на прикладi розчинiв
solutions. глiцерин–вода. Експериментально отриманi P –V –T -данi для
The analysis of the results of our calculations also цих розчинiв в iнтервалi тискiв 0,1–103,1 МПа та температур
showed that, for water and the glycerol–water solutions 293–380 К. Розраховано пружний модуль, коефiцiєнт теплового
розширення, прирости ентропiї, iзобаро-iзотермiчного потен-
concerned, the Tait equation describes the temperature цiалу Гiббса та ентальпiї. Рекомендовано рiвняння стану Тейта
and baric dependences of the solution density with an та проаналiзовано залежнiсть його параметрiв вiд температу-
error of 0.5%. ри.

ISSN 0503-1265. Ukr. J. Phys. 2007. V. 52, N 9 859