1. J Solution Chem (2006) 35:1505–1514
DOI 10.1007/s10953-006-9078-1
ORIGINAL PAPER
Ion Association and Solvation Behavior of Some 1-1
Electrolytes in 2-Ethoxyethanol Probed by a
Conductometric Study
Ranjit De · Chandrani Guha · Bijan Das
Received: 27 February 2006 / Accepted: 1 May 2006 / Published online: 19 October 2006
C Springer Science+Business Media, Inc. 2006
Abstract Precise measurements of the electrical conductances of solutions of potassium
thiocyanate (KCNS), ammonium thiocyanate (NH4CNS), sodium nitrate (NaNO3) and am-
monium nitrate (NH4NO3) in 2-ethoxyethanol (EE) at temperatures 35, 40, 45 and 50 ◦
C are
reported. The conductance data have been analyzed by the 1978 Fuoss conductance equation.
A thermodynamic analysis of the ionic association processes has also been made and the
Coulombic forces are found to play a major role in the association processes. The ionic con-
tributions to the limiting equivalent conductances have been determined using the reference
electrolyte method. Strong association was found for all these electrolytes in this solvent
medium. The cations are found to be substantially solvated in 2-ethoxyethanol, whereas the
anions appear to have only weak interaction with the solvent molecules.
Keywords Electrolytic conductance · Electrolytes · 2-Ethoxyethanol · Ion association ·
Solvation
1. Introduction
Knowledge of the state of association of electrolytes in solution and of their interaction
with the solvent molecules is essential for a proper understanding of their behavior in
solution. The conductometric method is well suited to investigate the ion-ion and ion-
solvent interactions in electrolyte solutions. We have initiated a comprehensive program
to study the solvation and association behavior of 1-1 electrolytes in different nonaquous
solvents by using measurements of various transport, thermodynamic and spectroscopic
properties [1–8]. In this paper, an attempt has been made to reveal the nature of various
types of interactions prevailing in solutions of potassium thiocyanate (KCNS), ammonium
thiocyanate (NH4CNS), sodium nitrate (NaNO3) and ammonium nitrate (NH4NO3) in 2-
ethoxyethanol by using precise conductivity measurements. The solvent 2-ethoxyethanol
R. De . C. Guha . B. Das ( )
Department of Chemistry, North Bengal University, Darjeeling 734 013, India
e-mail: bijan dasus@yahoo.com
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2. 1506 J Solution Chem (2006) 35:1505–1514
Table 1 Physical properties of
2-ethoxyethanol t (◦C) ρ0 (g·cm−3) η0 (mPa·s) D
35 0.91735 1.518 12.81
40 0.91370 1.359 12.52
45 0.90994 1.189 12.25
50 0.90602 1.087 11.99
is an amphiprotic dipolar solvent with a low relative permittivity (D = 13.38 at 25 ◦
C). It
has unique solvating properties associated with its “quasi-aprotic” character and is a good
industrial solvent [9, 10].
2. Experimental
2-Ethoxyethanol (EE, G.R.E. Merck) was dried with potassium carbonate, distilled twice in
an all-glass distillation set immediately before use and the middle fraction was collected for
solution preparations. The purified solvent had a density of 0.92497 g·cm−3
and a coefficient
of viscosity of 1.8277 mPa·s at 25 ◦
C. These values are in good agreement with the literature
data [10–12]. The properties of the solvent are recorded in Table 1.
The salts (all A.R., B.D. H.) were purified by recrystallization twice from conductivity
water. The samples were dried in vacuum and stored over P2O5 under vacuum.
Conductance measurements were carried out on a Pye-Unicam PW 9509 conductivity
meter at a frequency of 2000 Hz using a dip-type cell with a cell constant of 1.14 cm−1
. Mea-
surements were made in an oil bath maintained within ±0.005 ◦
C of the desired temperature.
The details of the experimental procedure have been described elsewhere [13, 14]. Solutions
were prepared by mass for the conductance runs, the molalities being converted to molari-
ties by the use of densities measured with an Ostwald-Sprenger type pycnometer of about
25 cm3
capacity. Several independent solutions were prepared and runs were performed to
ensure the reproducibility of the results. Appropriate corrections were made for the specific
conductance of the solvent at all temperatures. The uncertainties in the experimental molar
conductivity values were found to be always within ±0.02 to ±0.04 S·cm2
·mol−1
.
The dielectric constants of 2-ethoxyethanol at different temperatures were taken from the
literature [7].
3. Results
The measured molar conductances ( ) of the studied electrolyte solutions as a function of
the molar concentration (c) at 35, 40, 45 and 50 ◦
C are given in Table 2.
The conductance data have been analyzed with the 1978 Fuoss conductance-concentration
equation [15, 16]. For a given set of conductivity values (cj , j ; j = 1, . . . , n), three ad-
justable parameters, the limiting molar conductivity ( ◦
), the association constant (KA), and
the cosphere diameter (R), are derived from the following set of equations:
= p[ ◦
(1 + RX) + EL] (1)
p = 1 − α(1 − γ ) (2)
γ = 1 − KAcγ 2
f 2
(3)
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4. 1508 J Solution Chem (2006) 35:1505–1514
constant evaluated from the association constants of the contact pairs, KS, and of the solvent-
separated pairs, KR, ε is the relative permittivity of the solvent, e is the electronic charge, kB
is the Boltzmann constant, k−1
is the radius of the ion atmosphere, c is the molarity of the
solution, f is the activity coefficient, T is the temperature on the absolute scale, and β is twice
the Bjerrum distance. The computations were performed on a computer using the program
suggested by Fuoss [15, 16]. The initial ◦
values for the iteration procedure were obtained
from a Shedlovsky-type extrapolation [17] of the data. Input information for this program
is the set of information (cj , j ; j = 1, . . . , n), n, D, η, T, an initial estimated value of ◦
,
and an instruction to cover a pre-selected range of R values.
In practice, calculations are made by finding the values of ◦
and α that minimize the
standard deviation, σ, where
σ2
= [ j (calculated) − j (observed)]2
/(n − 2) (7)
for a sequence of R values. The resulting σ values are plotted against R; the best-fit value of R
corresponds to the minimum in the σ versus R curve. However, as the relative permittivity of
the medium is very low, no significant minima in the σ (%) versus R curves were observed.
This insensitivity of the goodness of fit to the parameter R was also observed previously
[13, 36] for other solvent systems with low relative permittivity. The explanation for the
relative insensitivity of KA to R at low relative permittivities is found in the mass action
expression, Eq. (3), where the product f γ appears; if R is increased, we are counting more
ions as being paired, thereby decreasing γ at a given concentration. But, more ion pairs
means fewer free ions are present in the space charge and therefore have a larger activity
coefficient. This point has been amply discussed by Fuoss [16]. In order to treat the present
data, therefore, the R value was arbitrarily preset [16] at the center-to-center distance of the
solvent-separated pair.
R = a + d (8)
where a is the sum of the crystallographic radii of the ions and d is the average distance
corresponding to the side of a cell occupied by a solvent molecule. The distance d is given
by
d = 1.183(M/ρ0) (9)
where M is the molar mass of the solvent and ρ0 its density.
A representative plot (Fig. 1) shows some selected experimental data along with the fit
according to the Fuoss equation. The quality of the fit is found to be excellent.
The values of ◦
, KA, and R obtained by this procedure are reported in Table 3.
4. Discussion
Table 3 shows that for all of the studied salts, the limiting molar conductances ( ◦
) increase
as the temperature increases. The ◦
values have been fitted to the following polynomial
expression:
◦
= a0 + a1(308.15 − T ) + a2(308.15 − T )2
(10)
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5. J Solution Chem (2006) 35:1505–1514 1509
Fig. 1 Experimental equivalent conductivity as a function of the square root of the concentration for KSCN
( ), NH4SCN ( ), NH4NO3 ( ), and NaNO3 (◦) in 2-ethoxyethanol at 35 ◦C along with the fitted values
(lines) following the Fuoss conductivity equation
and the coefficients of these fits are given in Table 4 together with the standard deviations
(σ). Polynomials truncated after the second term always yielded higher standard deviations
(i.e., poorer fits).
Limiting ionic equivalent conductivities at the experimental temperatures were obtained
from the ionic conductances of the Na+
ion taken from the literature [7], using ◦
values
of sodium bromide (NaBr), sodium tetraphenylborate (NaBPh4) and tetrabutylammonium
Table 3 Conductance parameters of electrolytes in 2-ethoxyethanol at 35, 40, 45 and 50 ◦C
Electrolyte t (◦C) ◦ (S·cm2·mol−1) KA (dm3·mol−1) R (Å) σ (%)
KSCN 35 36.70 ± 0.03 855 ± 7 8.92 0.04
40 40.30 ± 0.08 1014 ± 20 8.93 0.11
45 45.31 ± 0.09 1218 ± 21 8.93 0.10
50 49.92 ± 0.11 1480 ± 27 8.94 0.11
NH4SCN 35 36.31 ± 0.03 1053 ± 7 9.07 0.02
40 39.10 ± 0.05 1242 ± 12 9.08 0.03
45 42.50 ± 0.03 1416 ± 8 9.08 0.02
50 46.02 ± 0.05 1596 ± 11 9.09 0.02
NaNO3 35 30.32 ± 0.08 1811 ± 35 8.30 0.14
40 33.51 ± 0.10 1970 ± 42 8.31 0.15
45 36.95 ± 0.12 2127 ± 44 8.31 0.15
50 40.10 ± 0.13 2390 ± 47 8.32 0.15
NH4NO3 35 31.14 ± 0.11 1556 ± 37 8.83 0.09
40 34.10 ± 0.03 1590 ± 10 8.84 0.02
45 38.15 ± 0.04 1628 ± 10 8.84 0.02
50 41.58 ± 0.06 1691 ± 15 8.85 0.03
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6. 1510 J Solution Chem (2006) 35:1505–1514
Table 4 Coefficients of the
polynomial Eq. (10) Electrolyte a0 a1 a2 σ
KSCN 36.61 −0.7419 0.0101 0.40
NH4SCN 36.29 −0.5411 0.0073 0.11
NaNO3 30.29 −0.6616 −0.0004 0.12
NH4NO3 31.05 −0.6369 0.0047 0.38
bromide (Bu4NBr) that were reported at 35, 40, 45 and 50 ◦
C. Ionic divisions were accom-
plished through the following relationships
◦
(Bu4NBPh4) = λ◦
(Bu4N+
) + λ◦
(Ph4B−
) (11)
λ◦
(Bu4N+
)
λ◦(Ph4B−)
=
r(Ph4B−
)
r(Bu4N+)
=
5.35
5.00
(12)
using the salt tetrabutylammonium tetraphenylborate (Bu4NBPh4) as the “reference elec-
trolyte” and with the ionic radii (r) values taken from the literature. The ◦
values of
Bu4NBPh4 have been obtained by combining those of NaBr, NaBPh4 and Bu4NBr using the
Kohlrausch additivity rule
◦
(Bu4NBPh4) = ◦
(Bu4NBr) + ◦
(NaBPh4) − ◦
(NaBr) (13)
The single-ion conductivities (λ◦
±) along with the Walden products (λ◦
±η0) are reported in
Table 5. These single-ion conductivity values were then fitted by the following polynomial
equation in T:
λ◦
± = b0 + b1(308.15 − T ) + b2(308.15 − T )2
(14)
and the coefficients of these fits along with the standard deviations (σ) are listed in Table 6.
Polynomials truncated after the second term always yielded higher standard deviations.
Table 5 shows that the Stokes radii of the cations Na+
, K+
and NH+
4 are significantly
higher than their crystallographic radii [18]. This indicates that these ions are substantially
solvated in 2-ethoxyethanol. The Stokes radii of the anions SCN−
and NO−
3 are found to be in
agreement with their crystallographic radii. These ions are, therefore, only slightly solvated
in 2-ethoxyethanol. This observation is quite expected since alkoxyethanol molecules lack
a well-developed center of positive charge; spectroscopic investigations [19, 20] indicate
Table 5 Limiting ionic conductances,a ionic Walden productsb and ionic Stokes radiic (rS, Å) in 2-
ethoxyethanol at 35, 40, 45 and 50 ◦C
35 ◦C 40 ◦C 45 ◦C 50 ◦C
Ion λ◦
± λ◦
±η0 rS λ◦
± λ◦
±η0 rS λ◦
± λ◦
±η0 rS λ◦
± λ◦
±η0 rS
Na+
11.46 0.017 4.71 11.95 0.016 5.06 12.27 0.015 5.61 12.68 0.014 5.94
K+ 12.67 0.019 4.27 13.74 0.019 4.39 16.28 0.019 4.23 18.06 0.020 4.18
NH+
4 12.28 0.019 4.41 12.54 0.017 4.82 13.47 0.016 5.12 14.16 0.015 5.32
SCN− 24.03 0.036 2.25 26.56 0.036 2.27 29.03 0.035 2.38 31.86 0.035 2.37
NO−
3 18.86 0.029 2.87 21.56 0.029 2.80 24.68 0.029 2.80 27.46 0.030 2.75
Note. Units: aλ◦
±, S·cm2·mol−1; bλ◦
±η0, S·cm2·mol−1·Pa·s; crS, Å.
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7. J Solution Chem (2006) 35:1505–1514 1511
Table 6 Coefficients of the
polynomial Eq. (14) Electrolyte b0 b1 b2 σ
Na+ 11.47 −0.0916 −0.0008 0.06
K+ 12.56 −0.2677 0.0071 0.50
NH+
4 12.23 −0.0669 0.0043 2.19
SCN− 24.05 −0.4742 0.0030 0.09
NO−
3 18.82 −0.5700 0.0004 0.18
that the anions appear to weakly interact with the solvent molecules. The Stokes radii of
these ions are available in the literature [6] at 35 ◦
C for a similar solvent, 2-methoxyethanol
(the values are 4.90, 3.22, 3.66, 1.54 and 1.56 Å for Na+
, K+
, NH+
4 , SCN−
and NO−
3 ,
respectively); these values show a similar solvation behavior for these ions in that medium.
All of these electrolytes are found to be strongly associated (cf., the KA values from
Table 3) in 2-ethoxyethanol at all the temperatures investigated. This is expected owing to
the low relative permittivity of that solvent. These electrolyte solutions, in general, show an
increase in the association constant values with an increase in temperature.
The standard Gibbs energy changes for the ion association process, Go
, can be calculated
from the association constants using the equation:
Go
= −RT ln KA (15)
In order to evaluate the standard enthalpy change, Ho
, and the standard entropy change,
So
, of the ion-association process, we have fitted the Go
values by a polynomial function
of temperature, T , of the type:
Go
= c0 + c1(308.15 − T ) + c2(308.15 − T )2
(16)
The coefficients of the fits are compiled in Table 7, together with the σ values of the fits.
Polynomials truncated after the second term always yielded higher standard deviations.
The Ho
and So
values of the ion-association process can then be evaluated from the
temperature dependence of Go
using the following equations:
Ho
= −T 2 ∂( Go
/T )
∂T p
(17)
So
= −
∂ Go
∂T p
(18)
It is observed from Table 7 that the So
values for ion association of all these electrolytes
are positive. These positive So
values may be attributed to the increasing number of degrees
of freedom occurring upon association, mainly due to the release of solvent molecules as
shown below:
M+
· n(EE) + X−
· m(EE) →← MX · z(EE) + (n + m − z)EE (19)
In other words, solvation of the individual ions is weakened as soon as these ion pairs are
formed.
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8. 1512 J Solution Chem (2006) 35:1505–1514
Table 7 Coefficients of the polynomial, Eq. (16), and thermodynamic standard data of the association
c0 Go
35 c1 So
35 102 × c2 c0 + 308.15c1
Electrolyte (J·mol−1) (J·K−1·mol−1) (J·K−2·mol−1) σ Ho
35 (J·mol−1)
KSCN −17297 ± 1 140.3 ± 0.1 −0.94 ± 0.01 0.38 11129.6
NH4SCN −17833 ± 9 146.4 ± 2.0 0.96 ± 0.17 12.58 23807.9
NaNO3 −19226 ± 19 96.1 ± 6.2 −1.01 ± 0.40 28.26 10313.1
NH4NO3 −18832 ± 5 68.7 ± 1.6 −0.48 ± 0.11 7.48 11262.2
The So
values of the electrolytes are found to decrease in the following order:
NH4SCN > KSCN > NaNO3 > NH4NO3
This trend indicates that the degree of weakening of ion solvation due to the formation of an
ion pair also decreases in the same order.
Table 7 shows that the Ho
values for all the electrolytes are large and positive. It is
obvious, therefore, that for these electrolytes the enthalpic term is counterbalanced by a
favorable entropy change which results from the short- and long-range desolvation of ions.
The attribution of the So
values to desolvation is also supported by the positive enthalpies,
implying a lack of covalent bonds.
The association constant of a pure electrolyte is largely influenced by the radius of the
electrolyte under investigation and the dielectric constant of the solvent. There is, however,
considerable evidence that some ions are solvated [18], i.e., each ion is surrounded on the
average by a number of solvent molecules that accompany the ions in solution. Consequently,
the value of the association constant will also depend on the non-electrostatic interaction
between the solvent medium and the electrolyte.
The non-Coulombic contribution to the Gibbs energy, G∗
, has been calculated from the
following equation [21]:
G∗
= NAW∗
± (20)
KA = (4π NA/1000)
R
a
r2
exp
2q
r
−
W∗
±
kT
dr (21)
where the symbols have their usual meaning. The quantity 2q/r is the Coulombic part of
the interionic mean force potential and W∗
± is its non-Coulombic part. In Eq. (21), the
association constants (KA) count all oppositely charged pairs of ions at distances a ≤ r ≤ R
as ion pairs; the lower distance for association (a) is generally identified with the sum of the
ionic crystallographic radii.
The procedure for the evaluation of the non-Coulombic contribution to the entropy and
enthalpy ( S∗
and H∗
, respectively) is similar to that used for obtaining S◦
and H◦
.
The G∗
values at different temperatures were fitted to the polynomial expression:
G∗
= c∗
0 + c∗
1(308.15 − T ) + c∗
2(308.15 − T )2
(22)
and the coefficients of the fits along with their σ values, are given in Table 8. Polynomials
truncated after the second term always yielded higher standard deviations.
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9. J Solution Chem (2006) 35:1505–1514 1513
Table 8 Coefficients of the polynomial, Eq. (21), for the non-coulombic contribution to the association
process
c∗
0 G∗
35 c∗
1 S∗
35 102×c∗
2 c∗
0 + 308.15c∗
1
Electrolyte (J·mol−1) (J·K−1·mol−1) (J·K−2·mol−1) σ H∗
305 (J·mol−1)
KSCN −4048 ± 7 86.7 ± 2.1 −0.98 ± 0.14 1.65 8104.9
NH4SCN −4586 ± 8 92.7 ± 2.5 0.92 ± 0.16 11.31 20781.0
NaNO3 −5973 ± 19 42.4 ± 6.0 −1.05 ± 0.38 26.98 7298.1
NH4NO3 −5583 ± 0.4 15.0 ± 1.4 −0.52 ± 0.09 6.20 8237.9
The non-Coulombic parts of the Gibbs energy, G∗
35, of all of the salts are found to be
small (Table 8): 23% (KSCN), 26% (NH4SCN), 31% (NaNO3), 30% (NH4NO3) of their
corresponding total Gibbs energy values in 2-ethoxyethanol. These values indicate that the
Coulombic forces play a major role in the association processes. This is further supported
by the higher values of the Coulombic parts of So
and Ho
in comparison with their
non-Coulombic counterparts.
It may thus be concluded that these electrolytes remain strongly associated in 2-
ethoxyethanol to form ion pairs and that solvation of the ions is weakened as soon as
the ion pair is formed. The cations are found to be substantially solvated in 2-ethoxyethanol
whereas the anions appear to have weak interactions with the solvent molecules. The results
further indicate that the Coulombic forces play a major role in the ion association processes.
Acknowledgments
The authors are thankful to the University of North Bengal for financial assistance. They
also gratefully acknowledge the research support given by the Special Assistance Program
of the University Grants’ Commission, New Delhi, India.
References
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phenomena of alkali-metal ions and ion-pairs in 2-methoxyethanol. J. Phys. Chem. 99, 269–273 (1995)
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methoxymethanol at 25 ◦C. J. Chem. Soc., Faraday Trans. 84, 1057–1063 (1988)
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![J Solution Chem (2006) 35:1505–1514
DOI 10.1007/s10953-006-9078-1
ORIGINAL PAPER
Ion Association and Solvation Behavior of Some 1-1
Electrolytes in 2-Ethoxyethanol Probed by a
Conductometric Study
Ranjit De · Chandrani Guha · Bijan Das
Received: 27 February 2006 / Accepted: 1 May 2006 / Published online: 19 October 2006
C Springer Science+Business Media, Inc. 2006
Abstract Precise measurements of the electrical conductances of solutions of potassium
thiocyanate (KCNS), ammonium thiocyanate (NH4CNS), sodium nitrate (NaNO3) and am-
monium nitrate (NH4NO3) in 2-ethoxyethanol (EE) at temperatures 35, 40, 45 and 50 ◦
C are
reported. The conductance data have been analyzed by the 1978 Fuoss conductance equation.
A thermodynamic analysis of the ionic association processes has also been made and the
Coulombic forces are found to play a major role in the association processes. The ionic con-
tributions to the limiting equivalent conductances have been determined using the reference
electrolyte method. Strong association was found for all these electrolytes in this solvent
medium. The cations are found to be substantially solvated in 2-ethoxyethanol, whereas the
anions appear to have only weak interaction with the solvent molecules.
Keywords Electrolytic conductance · Electrolytes · 2-Ethoxyethanol · Ion association ·
Solvation
1. Introduction
Knowledge of the state of association of electrolytes in solution and of their interaction
with the solvent molecules is essential for a proper understanding of their behavior in
solution. The conductometric method is well suited to investigate the ion-ion and ion-
solvent interactions in electrolyte solutions. We have initiated a comprehensive program
to study the solvation and association behavior of 1-1 electrolytes in different nonaquous
solvents by using measurements of various transport, thermodynamic and spectroscopic
properties [1–8]. In this paper, an attempt has been made to reveal the nature of various
types of interactions prevailing in solutions of potassium thiocyanate (KCNS), ammonium
thiocyanate (NH4CNS), sodium nitrate (NaNO3) and ammonium nitrate (NH4NO3) in 2-
ethoxyethanol by using precise conductivity measurements. The solvent 2-ethoxyethanol
R. De . C. Guha . B. Das ( )
Department of Chemistry, North Bengal University, Darjeeling 734 013, India
e-mail: bijan dasus@yahoo.com
Springer](https://image.slidesharecdn.com/2f8dae9e-9029-4a6b-bfad-4bac135d304d-160219061901/85/2006jsc-1-320.jpg)
![1506 J Solution Chem (2006) 35:1505–1514
Table 1 Physical properties of
2-ethoxyethanol t (◦C) ρ0 (g·cm−3) η0 (mPa·s) D
35 0.91735 1.518 12.81
40 0.91370 1.359 12.52
45 0.90994 1.189 12.25
50 0.90602 1.087 11.99
is an amphiprotic dipolar solvent with a low relative permittivity (D = 13.38 at 25 ◦
C). It
has unique solvating properties associated with its “quasi-aprotic” character and is a good
industrial solvent [9, 10].
2. Experimental
2-Ethoxyethanol (EE, G.R.E. Merck) was dried with potassium carbonate, distilled twice in
an all-glass distillation set immediately before use and the middle fraction was collected for
solution preparations. The purified solvent had a density of 0.92497 g·cm−3
and a coefficient
of viscosity of 1.8277 mPa·s at 25 ◦
C. These values are in good agreement with the literature
data [10–12]. The properties of the solvent are recorded in Table 1.
The salts (all A.R., B.D. H.) were purified by recrystallization twice from conductivity
water. The samples were dried in vacuum and stored over P2O5 under vacuum.
Conductance measurements were carried out on a Pye-Unicam PW 9509 conductivity
meter at a frequency of 2000 Hz using a dip-type cell with a cell constant of 1.14 cm−1
. Mea-
surements were made in an oil bath maintained within ±0.005 ◦
C of the desired temperature.
The details of the experimental procedure have been described elsewhere [13, 14]. Solutions
were prepared by mass for the conductance runs, the molalities being converted to molari-
ties by the use of densities measured with an Ostwald-Sprenger type pycnometer of about
25 cm3
capacity. Several independent solutions were prepared and runs were performed to
ensure the reproducibility of the results. Appropriate corrections were made for the specific
conductance of the solvent at all temperatures. The uncertainties in the experimental molar
conductivity values were found to be always within ±0.02 to ±0.04 S·cm2
·mol−1
.
The dielectric constants of 2-ethoxyethanol at different temperatures were taken from the
literature [7].
3. Results
The measured molar conductances ( ) of the studied electrolyte solutions as a function of
the molar concentration (c) at 35, 40, 45 and 50 ◦
C are given in Table 2.
The conductance data have been analyzed with the 1978 Fuoss conductance-concentration
equation [15, 16]. For a given set of conductivity values (cj , j ; j = 1, . . . , n), three ad-
justable parameters, the limiting molar conductivity ( ◦
), the association constant (KA), and
the cosphere diameter (R), are derived from the following set of equations:
= p[ ◦
(1 + RX) + EL] (1)
p = 1 − α(1 − γ ) (2)
γ = 1 − KAcγ 2
f 2
(3)
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