J Solution Chem (2010) 39: 701–708
DOI 10.1007/s10953-010-9538-5
Dielectric Constants of Water, Methanol, Ethanol,
Butanol and Acetone: Measurement and Computational
Study
M. Mohsen-Nia · H. Amiri · B. Jazi
Received: 10 June 2009 / Accepted: 8 December 2009 / Published online: 26 May 2010
© Springer Science+Business Media, LLC 2010
Abstract The dielectric constants (relative permittivities) of water, methanol, ethanol, butanol and acetone were measured at 91.3 kPa and (283.15 and 293.15) K and are reported
here. The dielectric constants were determined by using a new setup based on a low-pass
filter. The obtained dielectric constant values are compared with those reported in the literature, and are consistent with those reported in the literature. The obtained dielectric constant
data were also compared with those calculated by the Kirkwood model. The comparisons indicated that Kirkwood model can be successfully used for calculation of dielectric constants
of the pure fluids.
Keywords Dielectric constant · Low-pass-filter · Capacitor · Kirkwood model
1 Introduction
Because intermolecular forces in a dielectric medium are electrical in nature, the dielectric
constant of a solvent influences equilibrium constants and reaction rate constants. Dielectric
constants are related to many important physical and biological applications, and thus the
dielectric constant of a solvent is an important physicochemical parameter. The dielectric
constant measures the solvent’s ability to reduce the strength of the electric field surrounding a charged particle that is immersed in it. This reduction is then compared to the field
strength of the same charged particle in a vacuum. Therefore, when a finite electric potential
is applied on capacitor plates, the dielectric constant of the dielectric can be obtained in the
following form:
εr = C/C0
M. Mohsen-Nia () · H. Amiri
Thermodynamic Research Laboratory, University of Kashan, Kashan, Iran
e-mail: m.mohsennia@kashanu.ac.ir
B. Jazi
Department of Physics, University of Kashan, Kashan, Iran
(1)
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J Solution Chem (2010) 39: 701–708
where C0 and C are the capacitance of this capacitor when its is measured, respectively,
in a vacuum and with a dielectric medium between its plates. For time-variant electromagnetic fields, this quantity becomes frequency dependent and in general is called the relative
permittivity.
Historically, Jennings presented a method for the measurement of the dielectric constant
of liquids [1]. A concentric cylinder capacitor was used for capacitance measurements of
water at temperatures between 273 and 373 K by Fernandez et al. [2]. Goodwin et al. developed a reentrant-type resonator, with a single-lobe extension inside the cavity [3]. It was
used to measure dipole moments of polar gases. Kaatze studied the dielectric properties of
water in its different phases [4]. Gary et al. presented a new radio-frequency resonator for
measuring the static dielectric constants for liquid water [5]. Considering the lack of theoretical models for accurate prediction of dielectric constant of solvents and aqueous solutions,
developing suitable techniques for the accurate experimental measurements of the dielectric
constant of solvents is still of great interest [5].
Dielectric constant data have been reported as a function of temperature for a number of
pure liquids and dilute solutions by Buckley et al. [6]. Dunn and Stokes studied the pressure and temperature dependence of the electrical permittivities of formamide and water [7].
A relatively small number of studies on the measurement of the dielectric constant of solvents as a function of temperature (T ) and pressure (p) have been reported in the literature
[8–12]. The static dielectric constant of liquid water near its saturated vapor pressure has
been measured by Hamelin et al. [13]. Hamelin et al. studied resonators for accurate dielectric measurements in conducting liquids [14]. Marcus and Hefter studied the electric field
dependences of the dielectric constant of liquids [15].
The dielectric constant is of central importance in the thermodynamics of electrolyte
solutions. Excess thermodynamic properties of electrolyte solutions arise from various intermolecular interactions, especially those involving the ions. Experimental dielectric constant data for liquid mixtures and electrolyte solutions have been published by several researchers [16, 17]. The dielectric constants of some organic solvent–water mixtures were
measured by Åkerlöf [8]. Hasted measured the dielectric constants of a series of concentrated aqueous ionic solutions [18]. Akhadov compiled data for binary mixtures published prior to 1980 [19]. A general model has been developed for calculating the static dielectric constant of mixed-solvent electrolyte solutions by Wang and Anderko [17].
The accuracy of most high temperature dielectric constant data is better than 1%, whereas
in the lower temperature limit (below 70°C) the accuracy of most of the data is around
0.1% [9].
Based on the dielectric constant of the solvent, solvents may be roughly classified
into two categories: polar and non-polar. Dielectric constant measurements are often
used for evaluation of the polarity characteristics of liquids. Solvents with a dielectric constant of less than 15 are generally considered non-polar [20]. Water is an excellent polar solvent that is often referred to as the “Universal Solvent”. Water serves
not just as a filling material in biological tissues but constitutes the basis for normal
metabolic activity [21]. In this work, the dielectric constant of water and some solvents with applications in chemical industries (methanol, ethanol, butanol, and acetone)
were measured at 91.3 kPa and (293.15 and 283.15) K with a simple method. The
obtained results were compared with those calculated by the Kirkwood equation. This
comparison indicates consistency of the measured and calculated dielectric constant results.
J Solution Chem (2010) 39: 701–708
703
2 Experimental
2.1 Materials
Pure grade compounds, methanol, ethanol, butanol and acetone, were supplied by Merck Co.
Inc., Germany. However, the purity of each compound was checked by gas chromatography,
and the results confirmed that mass fraction purities were >0.99. They were used without
further purification. Double distilled water was used.
2.2 Apparatus and Procedure
Dielectric constants of fluids were determined by a low-pass filter method. Figure 1 presents
the experimental setup for measuring the dielectric constant of a liquid sample. The setup
is based on operation of a RC low-pass filter. A variable rotary capacitor connected to a
signal generator, with tunable ranges for voltage amplitude and frequency, was operated
in the 0 ≤ Vm ≤ 10 and 0 ≤ f ≤ 1 MHz ranges, respectively. Here a signal with Vm =
0.01 V and f = 60 Hz is applied on the capacitor plates. Two AC voltmeters are used
for controlling the input and output root-mean-square voltage amplitudes. The experimental
dielectric constant data were determined by using a glass cell with a water jacket to maintain
a constant temperature. The cell temperature was controlled with a temperature-controlled
bath with an precision of ±0.01 K [Lauda ecoline re 206, thermostat]. The variable rotary
capacitor was located in the glass cell containing the studied fluids.
The simple circuit containing a source of electrical potential difference or voltage ami
plitude, Vrms
, a conductive path, an electrical resistance R, and an electrical capacitance C
is shown in Fig. 2. Considering this figure, the voltage gain is the ratio of the output rooto
i
mean-square voltage amplitude, Vrms
, to the input root-mean-square voltage amplitude,Vrms
,
which can be presented in the following form [22]:
GV =
o
Vrms
1
=
1
i
Vrms
(R 2 C 2 ω2 + 1) 2
Fig. 1 The setup used for measurements of the dielectric constant (relative permittivity)
(2)
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J Solution Chem (2010) 39: 701–708
Fig. 2 A simple circuit
containing a source of electrical
i ,
potential difference, Vrms
a conductive path, an electrical
resistance, R, and an electrical
capacitance, C
where, ω = 2πf and f is the frequency. Equation 2 can then be rearranged as:
1
C=
2πf R
1
−1
G2V
(3)
By considering Eqs. 1 and 3, the dielectric constant of the studied fluids can be obtained at
the applied frequency and voltage amplitude. The effects of the shape of bodies around the
sample must be removed in capacitance measurements with our variable rotary capacitor.
Therefore, Eq. 1 can be rewritten in the following form [23]:
εr =
C(2) − C(1)
C0 (2) − C0 (1)
(4)
where, the numbers 1 and 2 in parentheses refer to two different geometric configurations
of the variable rotary capacitor. Each measurement was repeated at least five times. The
average value was taken as the measured dielectric constant. The maximum deviations from
the average value were less than 0.05%.
3 Results and Discussion
3.1 Dielectric Constant Measurements
The experimental dielectric constants of water, methanol, ethanol, butanol, and acetone at
91.3 kPa and at 283.15 and 293.15 K are given in Table 1. The obtained dielectric constant
data were compared with those available in the literature [24] to check the reliability of our
setup. The comparison presented in Table 1 indicates the accuracy of our measurements.
According to the obtained results, the dielectric constants of these fluids decrease with increasing temperature.
Table 1 Comparison of the obtained dielectric constant data with values reported in the literature
Components
εlit. [24]
εexp .
293.15 K
283.15 K
293.15 K
283.15 K
Water
79.99 ± 0.04
83.85 ± 0.04
80.20 ± 0.20
84.04 ± 0.20
Methanol
33.30 ± 0.02
35.40 ± 0.02
33.64 ± 0.06
35.74 ± 0.06
Ethanol
25.02 ± 0.02
26.47 ± 0.02
25.16 ± 0.04
26.79 ± 0.04
Butanol
17.68 ± 0.01
19.12 ± 0.01
18.19 ± 0.04
19.54 ± 0.04
Acetone
21.30 ± 0.02
22.30 ± 0.02
21.13 ± 0.04
22.21 ± 0.04
J Solution Chem (2010) 39: 701–708
705
Fig. 3 Plotting of P versus 1/T
for water (—F—), methanol
(—1—), ethanol (—F—),
butanol (—E—), and acetone
(—2—)
3.2 Computational Method
Based on an empirical modification of the Kirkwood theory for a pure fluid, the dielectric
constant, ε, is related to intermolecular interactions in the following form [17]:
4πρNA
μ2 g
(ε − 1)(2ε + 1)/9ε =
α+
(5)
3M
3kB T
where M, ρ, α, NA , μ and kB , respectively, are the molecular weight, density, molecular polarizability, Avogadro’s number, dipole moment of the molecule, and Boltzmann’s constant,
while g is a correlation factor that characterizes the relative orientations between neighboring molecules. Equation 5 can also be rewritten to explicitly relate the polarization per unit
volume of the fluid, P , to the dielectric constant [17]:
P = (ε − 1)(2ε + 1)/9ε
(6)
By combining Eqs. 5 and 6, we have:
P=
4πρNA
μ2 g
α+
3M
3kB T
(7)
By plotting P against 1/T , μ2 g may be obtained for pure fluids. The density ρ is also
a function of temperature, but the effect of temperature functionality of the density in a
limited temperature range has a negligible effect on the linear plotting of P versus 1/T .
Figure 3 shows the plot of P versus 1/T for the fluids studied in this work.
For determining the value of g from experimental data, we also used the available data for
the dielectric constant, ε, the density, ρ, and the dipole moment, μ, at different temperatures
[25]. For simplicity, the density data of the studied fluids in this work have been correlated
with a linear temperature-dependent model in the following form:
ρ = a + bT
(8)
where, a and b are correlation parameters that are presented in Table 2. The small values of
b in this table emphasize that the temperature variation of density data of the studied fluids
can be neglected over the investigated temperature range of 283.15 to 293.15 K.
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Table 2 The adjusted
parameters a and b of Eq. 8
Table 3 The accepted dipole
moment data μ [25] and the
corresponding correlation factor
g for the studied liquids from the
slope of linear plottings of P
versus 1/T as presented in Fig. 3
Component
a
(g·cm−3 )
B × 104
(g·cm−3 ·K−1 )
−1.82
Water
1.050
Methanol
1.040
−8.57
Ethanol
1.136
−11.60
Butanol
1.027
−7.54
Acetone
1.088
−10.10
Component
μ
g
Water
1.84
6.037
Methanol
1.68
5.653
Ethanol
1.70
5.631
Butanol
1.52
9.336
Acetone
2.91
4.773
Table 4 Comparison of the dielectric constants of water, methanol, ethanol, butanol and acetone with those
calculated by the Kirkwood model
Components
|εexp . −εcal. |
× 100
εexp .
εcal.
293.15 K
283.15 K
293.15 K
283.15 K
0.08
Water
80.10
83.92
0.14
Methanol
33.10
36.96
0.60
4.41
Ethanol
25.10
26.58
0.32
0.41
Butanol
17.90
19.37
1.24
1.30
Acetone
21.40
22.72
0.47
1.88
Table 3 reports the calculated Kirkwood correlation factor g for the water, methanol,
ethanol, butanol and acetone. Using the obtained values of g, the Kirkwood model (Eq. 5)
was used for calculating the dielectric constant of the fluids. The dielectric constants data
obtained in this work were then compared with those calculated by the Kirkwood model.
This comparison is presented in Table 4. According to this table, the maximum per cent
absolute deviation between the experimental and calculated dielectric constants is less than
0.12. Therefore, the Kirkwood model can be successfully used for calculating the dielectric
constant of the studied fluids. It should be noted that the approach used here is only applicable and valid over a limited temperature range such as used in this study, i.e. 283.15 to
293.15 K.
Molecular polarity is a physical property of compounds that relates other physical properties such as melting and boiling points, solubility, and intermolecular interactions between
molecules. The molecular polarity can be correlated with the dielectric constant. Molecules
with O–H bonds are capable of hydrogen bonding, in addition to London dispersion and
dipole-dipole interactions. When the size of the alkyl chain of an alcohol increases (as in
ethanol and butanol), London dispersion forces between molecules increase and may become greater than the stronger dipole-dipole and H-bonding intermolecular forces. There-
J Solution Chem (2010) 39: 701–708
707
fore, methanol with a single methyl group has only a weak London dispersion force and,
as expected, the measured dielectric constants of methanol at 283.15 and 293.15 are higher
than those measured for ethanol and butanol at these temperatures.
4 Conclusions
The experimental dielectric constants of water, methanol, ethanol, butanol and acetone were
measured at 91.3 kPa and 283.15 and 293.15 K. The data were determined at 60 Hz and 0.01
V by a low-pass filter method. The obtained dielectric constant data were compared with
those available in the literature. This comparison indicated that the measured data are accurate. According to the obtained results, the dielectric constant of the studied fluids increases
with decreasing temperature. In this work, the Kirkwood model was used for calculation
of the dielectric constants of the studied fluids. The measured dielectric constant data were
compared with those calculated by the Kirkwood model. According to the comparisons, this
computational procedure can be used for predicting the dielectric constant of fluids from
the Kirkwood model using a constant g-factor, molecular weight, density, molecular polarizability and dipole moment as the necessary input data.
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