Electrical Conductance of Some Tetraalkylammonium Bromide Salts

Jan 7, 2014 - 308.15, and 313.15) K. Chanchal Das*. Department of Chemistry, Sikkim Government College, Tadong, Gangtok, East Sikkim 737 102, India...
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Electrical Conductance of Some Tetraalkylammonium Bromide Salts in 2‑Butoxyethanol (1) + Water (2) mixtures at (298.15, 303.15, 308.15, and 313.15) K Chanchal Das* Department of Chemistry, Sikkim Government College, Tadong, Gangtok, East Sikkim 737 102, India ABSTRACT: Conductance measurements of tetramethylammonium bromide (Me4NBr), tetraethylammonium bromide (Et4NBr), and tetrapropylammonium bromide (Pr4NBr) solutions in 2-butoxyethanol (1) + water (2) mixture with 0.20, 0.40, and 0.60 mass fraction of 2-butoxyethanol were reported at (298.15, 303.15, 308.15, and 313.15) K. The experimental values of electrical conductances are analyzed using the 1978 Fuoss conductance−concentration equation to obtain values of limiting molar conductance (Λ0), ionic association constant (KA) and the association diameter (R). The values of KA and R obtained for these three salts, namely, tetramethylammonium bromide, tetraethylammonium bromide, and tetrapropylammonium bromide suggest a weak electrostatic ion solvent interaction. Besides, they exist as free ions in all the solvents compositions and temperature range covered in this study. The Walden products for the ions show perceptible variations under increasing temperature and in different solvent composition. and their findings point at a substantial effect of the hydrogenbonding ether oxygen in the BE−water system. To investigate the ion−solvent and ion−ion interactions in electrolyte solutions one can use the conductance method.23,24 From conductance data as a function of concentration, by using an appropriate equation, values of equivalent or molar conductance of an electrolyte at infinite dilution (Λ°), ionic association constant (KA), and the association diameter (R) can be obtained. However, precision demands the right choice of conductance equation to analyze conductance data.25,26 Hence, this paper relies on the Fuoss 78 conductance−concentration equation,27,28 because it is capable of accommodating more variables than the primitive models. The present paper reports the equivalent conductivities of tetramethylammonium bromide (Me4NBr), tetraethylammonium bromide (Et4NBr), and tetrapropylammonium bromide (Pr4NBr), in BE (1) + water (2) mixtures containing 0.20, 0.40, and 0.60 mass fraction of BE at (298.15, 303.15, 308.15, and 313.15) K in order to attain accurate equivalent ionic conductivities at different temperatures.

1. INTRODUCTION To understand ion behavior one has to assess the transport properties of electrolytes in different solvent media. Many research centers have studied cellosolves and their aqueous mixtures. They are used in industry and modern technologies. However, these studies in cellosolves and their mixtures with water have not stimulated interest so far. The situation is somewhat better with the first and second homologue of this class, namely, 2-methoxyethanol and 2-ethoxyethanol. Reports indicating transport properties of electrolytes in these two homologues1−13 both in pure and in its binary mixtures with water already exist, but conductance studies14,15 in 2-butoxyethanol and its aqueous mixtures are infrequent. 2-Butoxyethanol (BE) belongs to a class of compounds commercially known as cellosolves. For many years the thermodynamic and transport properties of BE in pure and aqueous solutions have been a subject of interest. Studies on fundamental physicochemical properties like density and dielectric constant along with isentropic compressibilities and heat capacities have been reported for 2-butoxyethanol.16−18 Douheret and Pal19 studied dielectric constants and densities of BE−water mixtures at 298.15 K. Reddy et al.20 reported densities, viscosities, and isentropic compressibilities for this mixed solvent media at 308.15 K. Very recently Chiou et al.21 reported densities, viscosities, and refractive indexes of BE− water mixtures at various temperatures. Excess apparent molal heat capacities and volumes of 2-alkoxyethanol in the water-rich region at different temperatures have been reported by Roux et al.17 Dielectric spectroscopy of BE−water mixtures in the complete composition range have been measured by Kaatze et al.22 © 2014 American Chemical Society

2. EXPERIMENTAL SECTION 2.1. Chemicals. 2-Butoxyethanol (G. R. E. Merck with a mass fraction purity > 0.995) was dried with potassium carbonate, and then it was distilled twice immediately before use. Thereafter, the middle fraction was collected. The measured density (ρ0) and the coefficient of viscosity (η0) of the purified Received: November 19, 2012 Accepted: December 26, 2013 Published: January 7, 2014 168

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BE was found to be 0.89616 g·cm−3 and 2.7820 mPa·s, respectively, at 298.15 K. Comparison of these values with reported values16,29 shows a good agreement. The mixed solvents containing 0.20, 0.40, and 0.60 mass fraction of BE by weight were prepared accurately by mixing 2-butoxyethanol with triple distilled water, and their densities and viscosities measured at (298.15, 303.15, 308.15, and 313.15) K are given in Table 1. These density values along with the density and relative permittivity values of the pure solvent published in the literature at the experimental temperatures were used to calculate the relative permittivities of the mixed solvents with the help of the equations as shown in the literature30 and are also provided in Table 1. Tetraalkylammonium bromides were of purum or puriss grade (Fluka, Switzerland, 99.8 %). Tetramethylammonium bromide (Me4NBr) was recrystallized from a mixture of methanol and ethanol (1:1) and dried at 363 K for 24 h. Tetraethylammonium bromide (Et4NBr) was recrystallized from methanol and dried at 363 K for 24 h. Tetrapropylammonium bromide (Pr4NBr) was taken in a minimum volume of methanol, reprecipitated from dry ether, and dried at 363 K for 48 h. 2.2. Experimental Process. The conductivity meter used for the measurements of specific conductance was a Pye-Unicam PW 9509 conductivity meter operating at a frequency of 2000 Hz using a dip-type cell having a cell constant 1.15 cm−1 and an uncertainty of 0.01 %. The calibration of the cell was done using 0.01 N aqueous potassium chloride solutions by the method suggested by Lind et al.32 The water bath, where all measurements were made, was maintained within ± 0.005 K of the desired experimental temperature. The experimental procedures followed for all the measurements have been described earlier.33−35 For the measurement of conductance

Table 1. Physical Properties (Density, Viscosity, and Dielectric Constant) of 2-Butoxyethanol (1) + Water (2) Mixtures Containing 0.20, 0.40, and 0.60 Mass Fractions of 2-Butoxyethanol at Pressure (p = 0.1 M Pa) and at Different Temperaturesa ρ0/g·cm−3 T/K

this work

298.15 303.15 308.15 313.15

0.98646 0.98292 0.98038 0.97764

298.15 303.15 308.15 313.15

0.96710 0.96431 0.96145 0.95848

298.15 303.15 308.15 313.15 298.15 303.15 308.15 313.15

η0/mPa·s lit.

this work

εb

lit.

w1 = 0.20 1.8493 1.6217 1.4654 1.3025

64.31 62.82 61.43 60.03

2.9975 2.6354 2.3342 2.0545

50.21 48.93 47.70 46.49

0.94810 0.94474 0.94159 0.93757

3.9178 3.3944 2.9205 2.5386

36.49 35.47 34.46 33.43

0.89616 0.89274 0.88888 0.88429

w1 = 1.00 0.89624c 2.7817 0.89268d 2.4993 0.88891c 2.2064 0.88421d 1.9459

w1 = 0.40

w1 = 0.60

2.7820c 2.4995d 2.2060c 1.9459d

9.45 8.88 8.35 7.79

a Standard uncertainties u are u(T) = 0.01 K, u(w) = 0.0002 and combined expanded uncertainties Uc are uc(ρ0) = 0.0005 g·cm−3, and uc(η0) = 0.015 mPa·s (0.95 level of confidence). bCalculated with the equations as described in the ref 30. cFrom ref 31. dFrom ref 21.

Table 2. Equivalent Conductances (Λ) and Corresponding Molalitiesa (m) of Electrolytes in 2-Butoxyethanol (1) + Water (2) Mixtures at Pressure (p = 0.1 M Pa) and at (298.15, 303.15, 308.15 and 313.15) Kb T = 298.15 K

mol·kg

T = 303.15 K Λ

m −1

S·cm ·mol 2

−1

mol·kg

T = 308.15 K Λ

m −1

−1

S·cm ·mol 2

mol·kg

T = 313.15 K Λ

m −1

−1

S·cm ·mol 2

Λ

m mol·kg

−1

S·cm ·mol−1 2

w1 = 0.20 Me4NBr 0.00552 0.01105 0.01659 0.02213 0.02990 0.03323 0.03879 0.04435

69.908 68.158 66.198 64.475 61.742 60.435 59.009 57.108

0.00552 0.01105 0.01659 0.02213 0.02990 0.03323 0.03879 0.04435

77.825 76.000 74.217 72.554 70.059 68.752 67.089 65.188

0.00509 0.01018 0.01528 0.02039 0.02550 0.03062 0.03574 0.04087

64.752 63.366 62.269 60.124 58.811 57.227 55.841 54.059

0.00509 0.01018 0.01528 0.02039 0.02550 0.03062 0.03574 0.04087

72.475 70.693 68.910 67.326 66.138 64.819 63.168 61.584

0.00537 0.01074 0.01612 0.02151 0.02906

58.316 57.128 55.940 54.586 53.010

0.00537 0.01074 0.01612 0.02151 0.02906

65.297 64.108 62.772 61.435 59.802

0.00552 0.01105 0.01659 0.02213 0.02990 0.03323 0.03879 0.04435

85.663 83.910 82.336 80.792 78.415 77.346 75.683 73.782

0.00552 0.01105 0.01659 0.02213 0.02990 0.03323 0.03879 0.04435

93.861 92.079 90.415 88.871 86.495 85.307 83.762 82.099

0.00509 0.01018 0.01528 0.02039 0.02550 0.03062 0.03574 0.04087

80.396 79.010 78.019 76.435 75.247 73.244 71.919 71.302

0.00509 0.01018 0.01528 0.02039 0.02550 0.03062 0.03574 0.04087

88.036 87.128 85.742 84.158 82.772 81.188 79.406 78.510

0.00537 0.01074 0.01612 0.02151 0.02906

72.574 71.237 69.901 68.712 66.930

0.00537 0.01074 0.01612 0.02151 0.02906

80.742 79.405 78.069 76.881 75.099

Et4NBr

Pr4NBr

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Table 2. continued T = 298.15 K

T = 303.15 K

T = 308.15 K

T = 313.15 K

m

Λ

m

Λ

m

Λ

m

Λ

mol·kg−1

S·cm2·mol−1

mol·kg−1

S·cm2·mol−1

mol·kg−1

S·cm2·mol−1

mol·kg−1

S·cm2·mol−1

0.03229 0.03769 0.04310

52.227 50.891 49.554

0.03229 0.03769 0.04310

58.870 57.477 56.089

0.03229 0.03769 0.04310

66.188 64.993 63.811

0.03229 0.03769 0.04310

74.532 73.168 71.831

0.00266 0.00554 0.00832 0.01110 0.01500 0.01667 0.01945 0.02224

63.049 62.099 61.148 60.316 58.891 58.178 57.222 56.514

0.00266 0.00554 0.00832 0.01110 0.01500 0.01667 0.01945 0.02224

68.990 67.920 67.089 66.257 64.950 64.356 63.524 62.574

0.00311 0.00649 0.00975 0.01300 0.01626 0.01952 0.02278 0.02604 0.00273 0.00546 0.00820 0.01093 0.01367 0.01641 0.01915 0.02189

56.826 55.836 54.846 53.658 52.440 52.146 50.407 49.697 50.752 50.156 49.436 48.821 48.079 47.336 46.742 46.148

0.00311 0.00649 0.00975 0.01300 0.01626 0.01952 0.02278 0.02604 0.00273 0.00546 0.00820 0.01093 0.01367 0.01641 0.01915 0.02189

61.980 60.990 60.120 59.130 58.019 57.029 56.039 55.247 55.858 55.285 54.814 54.158 53.564 52.970 52.376 51.633

0.00105 0.00202 0.00304 0.00405 0.00547 0.00608 0.00710 0.00811

46.455 46.138 45.772 45.346 44.871 44.623 44.237 43.792

0.00105 0.00202 0.00304 0.00405 0.00547 0.00608 0.00710 0.00811

50.128 49.782 49.336 49.019 48.505 48.267 47.990 47.475

0.00118 0.00236 0.00354 0.00472 0.00637 0.00708 0.00826 0.00944

38.811 38.415 38.019 37.821 37.425 37.227 37.029 36.831

0.00118 0.00236 0.00354 0.00472 0.00637 0.00708 0.00826 0.00944

42.178 41.782 41.782 41.188 40.990 40.594 40.396 40.000

0.00107 0.00206 0.00309 0.00413 0.00557 0.00619 0.00723 0.00826

30.683 30.435 30.237 30.039 29.792 29.643 29.396 29.198

0.00107 0.00206 0.00309 0.00413 0.00557 0.00619 0.00723 0.00826

34.237 33.891 33.658 33.514 33.108 32.732 32.732 32.356

Pr4NBr

w1 = 0.40 Me4NBr 0.00266 0.00554 0.00832 0.01110 0.01500 0.01667 0.01945 0.02224

52.198 51.247 50.178 49.346 47.802 46.970 46.159 45.188

0.00266 0.00554 0.00832 0.01110 0.01500 0.01667 0.01945 0.02224

57.940 56.990 56.158 55.445 54.138 53.544 52.504 51.405

0.00311 0.00649 0.00975 0.01300 0.01626 0.01952 0.02278 0.02604 0.00273 0.00546 0.00820 0.01093 0.01367 0.01641 0.01915 0.02189

45.742 44.950 43.960 42.772 41.584 40.594 39.667 38.613 39.712 39.197 38.564 37.930 37.336 36.742 36.297 35.851

0.00311 0.00649 0.00975 0.01300 0.01626 0.01952 0.02278 0.02604 0.00273 0.00546 0.00820 0.01093 0.01367 0.01641 0.01915 0.02189

51.479 50.291 49.301 48.113 47.047 46.266 45.539 44.747 45.217 44.786 43.978 43.435 42.693 42.247 41.801 41.059

Et4NBr

w1 = 0.60 Me4NBr 0.00105 0.00202 0.00304 0.00405 0.00547 0.00608 0.00710 0.00811

38.128 37.811 37.336 37.019 36.544 36.227 35.980 35.633

0.00105 0.00202 0.00304 0.00405 0.00547 0.00608 0.00710 0.00811

42.128 41.861 41.495 41.099 40.534 40.237 39.990 39.544

0.00118 0.00236 0.00354 0.00472 0.00637 0.00708 0.00826 0.00944

31.683 31.485 31.089 30.693 30.297 30.297 29.995 29.703

0.00118 0.00236 0.00354 0.00472 0.00637 0.00708 0.00826 0.00944

35.445 35.049 34.653 34.257 33.861 33.663 33.465 33.267

0.00107 0.00206 0.00309 0.00413 0.00557 0.00619 0.00723 0.00826

24.009 23.811 23.564 23.465 23.168 23.069 22.871 22.722

0.00107 0.00206 0.00309 0.00413 0.00557 0.00619 0.00723 0.00826

27.386 27.188 26.940 26.742 26.445 26.346 26.148 26.000

Et4NBr

Pr4NBr

a Molalities are expressed in moles per kilogram of solvent (2-butoxyethanol(1) + water (2) mixtures). bStandard uncertainties u are u(T) = 0.01 K, u(w) = 0.0002, and conductivity was measured with a relative uncertainty ur(Λ) of 0.30. The uncertainty of the strength of solutions in molality was ± 2·10−5 mol·kg−1.

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molar solutions were prepared. The densities of these molar solutions were measured with an Ostwald-Sprengel type pycnometer of about 25 mL capacity. With the help of the density values, the strength of the solutions was converted from molarity to molality. To ensure the precision of the results, the experiments were repeated with at least five sets of independently prepared solutions, and the results were averaged. The specific conductance of the solvents at all the experimental temperatures were also measured and subtracted from those of the salt solutions. A suspended level Ubbelohdetype viscometer was used to measure the kinematic viscosities of the solvents. All solutions were prepared with utmost care in a dehumidified room.

Table 3. Derived Conductivity Parameters (Limiting Equivalent Conductivity, Association Constant, and Association Diameter) of Electrolytes in 2-Butoxyethanol (1) + Water (2) Mixtures at (298.15, 303.15, 308.15 and 313.15) K

3. RESULTS AND DISCUSSION The experimental equivalent conductances (Λ) of electrolyte solutions as functions of molal concentration (m) in 2-butoxyethanol (1) + water (2) mixtures with mass fractions of 0.20, 0.40, and 0.60 of 2-butoxyethanol at (298.15, 303.15, 308.15 and 313.15) K are shown in Table 2. The 1978 Fuoss conductance concentration equation27,28 was used to analyze the conductance data. In this treatment, for a given set of molar concentration−equivalent conductance values, (cj, Λj; j = 1, ..., n), the three parameters viz the limiting molar conductivity (Λ0), association constant (KA), and the association diameter (R) appearing in the expression for Λ(c, Λ0, KA, R), are related by the following equations: Λ = p[Λ0(1 + RX) + EL]

(1)

p = 1 − α(1 − γ )

(2)

2 2

γ = 1 − KAcγ f

βk 2(1 + kR )

−ln f =

(3)

(4)

2

β=

e εkBT

KA = KR (1 + K s)

(5)

T

Λ0

KA

R

σ

K

S·cm2·mol−1

dm3·mol−1

Å

%a

11.10 11.11 11.11 11.12

0.85 0.82 0.71 0.58

11.63 11.64 11.64 11.65

0.96 0.54 0.66 0.69

12.15 12.16 12.16 12.17

0.75 0.74 0.47 0.46

11.14 11.15 11.15 11.16

0.64 0.67 0.52 0.45

11.67 11.67 11.68 11.69

0.91 0.31 0.69 0.53

12.19 12.19 12.20 12.21

0.36 0.41 0.45 0.49

11.18 11.18 11.19 11.20

0.32 0.37 0.43 0.41

11.71 11.71 11.72 11.73

0.41 0.23 0.27 0.57

12.23 12.23 12.24 12.25

0.34 0.34 0.41 0.49

298.15 303.15 308.15 313.15

76.66 ± 0.74 84.59 ± 0.75 92.27 ± 0.67 100.43 ± 0.58

298.15 303.15 308.15 313.15

70.69 78.11 86.18 94.44

± ± ± ±

0.75 0.44 0.57 0.63

298.15 303.15 308.15 313.15

63.21 70.59 77.81 86.24

± ± ± ±

0.50 0.54 0.36 0.38

298.15 303.15 308.15 313.15

56.11 61.70 67.03 72.87

± ± ± ±

0.38 0.42 0.34 0.31

298.15 303.15 308.15 313.15

49.88 55.26 61.06 66.86

± ± ± ±

0.51 0.18 0.44 0.36

298.15 303.15 308.15 313.15

42.32 48.03 53.95 59.14

± ± ± ±

0.15 0.19 0.24 0.27

298.15 303.15 308.15 313.15

40.14 44.37 48.64 52.53

± ± ± ±

0.13 0.16 0.18 0.19

298.15 303.15 308.15 313.15

33.29 37.28 40.62 44.32

± ± ± ±

0.12 0.08 0.09 0.22

298.15 303.15 308.15 313.15

25.23 28.78 32.28 36.03

± ± ± ±

0.08 0.08 0.12 0.16

(6)

where RX is the relaxation field effect, EL is the electrophoretic countercurrent, γ is the fraction of unpaired ions, and α is the fraction of contact-pairs, KA is the overall pairing constant evaluated from the association constant of contact-pairs, KS, of 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 molar concentration of the solution, f is the activity coefficient, T is the temperature in absolute scale, and β is twice the Bjerrum distance. An iterative computer program to evaluate the three parameters Λ0, KA, and R which was suggested by Fuoss was used for computations. The input data set for the program is (cj, Λj; j = 1, ..., n), n, ε, η, T, M1, and M2 and an initial value of Λ0. The initial value of Λ0 can be obtained either by Walden’s rule or extrapolation of Kohlrausch’s plot, but we have obtained it from the Shedlovsky extrapolation36 of the conductance data. The program also contains instructions to cover a given range of R values. To ensure convergence, the values of Λ0 and R are computed which minimize the standard deviation, σ,

a

w1 = 0.20 Me4NBr 9.23 ± 0.84 7.42 ± 0.72 5.62 ± 0.55 4.75 ± 0.42 Et4NBr 8.34 ± 0.94 6.86 ± 0.48 4.76 ± 0.51 4.36 ± 0.51 Pr4NBr 6.39 ± 0.63 5.74 ± 0.59 4.46 ± 0.34 3.72 ± 0.31 w1 = 0.40 Me4NBr 12.55 ± 1.07 8.83 ± 0.98 8.20 ± 0.73 6.27 ± 0.59 Et4NBr 13.71 ± 1.49 10.43 ± 0.45 9.48 ± 0.97 8.89 ± 0.72 Pr4NBr 7.40 ± 0.50 6.34 ± 0.55 6.36 ± 0.61 4.34 ± 0.61 w1 = 0.60 Me4NBr 10.45 ± 1.08 8.92 ± 1.23 6.04 ± 1.30 4.67 ± 1.24 Et4NBr 7.02 ± 1.14 7.23 ± 0.67 3.41 ± 0.70 2.95 ± 1.50 Pr4NBr 4.44 ± 1.03 3.71 ± 1.00 2.61 ± 1.22 3.73 ± 1.48

σ/% = 100σ/Λ0.

σ = [∑ [Λj(calcd) − Λj(obsd)]2 /(n − 2)]1/2

(7)

When σ (%) is plotted against R, the corresponding value of R in the minima corresponds to the best fit R value. In our investigation however, a coarse scan using R values from 4 to 20 171

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Figure 1. Variation of molar conductivity as a function of concentration for (a) Me4NBr; (b) Et4Br; and (c) Pr4NBr in 2-butoxyethanol (1) + water (2) with w1 = 0.04. Experimental data: ○, 298.15 K; □, 303.15 K; ●, 308.15 K; and, ■, 313.15 K. The lines represent the calculations according to eqs 1 through 6.

yielded very shallow minima in the σ (%) vs R curves for all the three salts investigated. In such cases, it is a standard practice to preselect R as the distance between the two centers of the ionpair separated in the solvent. Mathematically, this R value is given by R = a + d, where a is the sum of the ionic crystallographic radii of the ions and d is given by28 d = 1.183(M /ρ0 )1/3

the three electrolytes, which were studied exist as free ions in the experimental range of 2-butoxyethanol (1) + water (2) mixed solvent media and the temperature range covered in this investigation. This conclusion is expected as the relatively high values of the relative permittivity of the solvent mixtures (33.43 ≤ ε ≥ 71.56) provide a conducive environment for the dissociation of electrolytes. With the use of the Λ0 values of sodium bromide (NaBr), sodium tetraphenylborate (NaBPh4), and tetrabutylammonium bromide (Bu4NBr) that were reported in the literature38 at 298.15, 303.15, 308.15, and 313.15 K the ionic conductances of Br− ion was derived. Then from the derived ionic conductances of Br− ion value limiting ionic equivalent conductivities at the experimental temperatures were obtained. From the salt tetrabutylammonium tetraphenylborate (Bu4NBPh4) as the “reference electrolyte” and with the ionic radii (r) values taken from the literature the ionic divisions were extracted through the use of the following equations:

(8)

where M and ρ0 are the mole fraction average molecular weight and the density of the mixed solvent, respectively. The values of Λ0, KA, and R computed as described above are contained in Table 3. A representative plot (Figure 1) for Me4NBr, Et4NBr, and Pr4NBr in BE (1) + water (2) mixtures with w1 = 0.40 at (298.15, 303.15, 308.15, and 313.15) K reflects the difference of the experimental equivalent conductivity as a function of molal concentration of the salts. Figure 1 also contains the results obtained after supplying the experimental data to eqs 1 to 6. The values of the association constants (KA) obtained for the systems under investigations are all less than 15 (Table 3). This means that there is no significant association of the ions,37 and

Λ0(Bu4NBPh4) = λ 0(Bu4N+) + λ 0(Ph4B−) 172

(9)

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Table 4. Limiting Ionic Conductances, Walden Product, and Stokes Radii in BE (1) + Water (2) Mixtures Containing 0.20, 0.40, and 0.60 Mass Fractions of BE at (298.15, 303.15, 308.15, and 313.15) K λ0±

T

S·cm ·mol 2

K

λ0±η0 × 103 −1

−1

S·cm ·mol 2

rs

Pa s

T K

Å

29.49 31.31 32.52 34.26

0.523 0.489 0.454 0.433

1.57 1.68 1.81 1.88

0.419 0.388 0.369 0.357

1.96 2.11 2.22 2.30

0.285 0.270 0.252 0.253

2.87 3.04 3.25 3.24

298.15 303.15 308.15 313.15

Et4N 23.62 24.83 26.43 28.27

S·cm ·mol

16.04 17.31 18.06 20.07

298.15 303.15 308.15 313.15

47.17 53.28 59.75 66.17

298.15 303.15 308.15 313.15

0.98 0.98 0.98 0.98

298.15 303.15 308.15 313.15

0.681 0.626 0.581 0.537

17.12 18.27 19.45 20.97

λ 0(Bu4N+) 0

−

λ (Ph4B )

=

0.86 0.87 0.88 0.90

19.06 20.69 22.36 23.78

0.708 0.661 0.619 0.575

1.16 1.24 1.32 1.43

12.21 13.60 14.34 15.57

0.454 0.434 0.397 0.377

1.81 1.89 2.06 2.17

0.154 0.163 0.166 0.176

5.32 5.03 4.94 4.66

0.784 0.756 0.728 0.695

1.05 1.08 1.13 1.18

Pr4N+ 1.20 1.31 1.41 1.53

0.499 0.463 0.435 0.418

1.64 1.77 1.89 1.96

r(Ph4B−) 5.35 + = r(Bu4N ) 5.00

4.15 5.10 6.00 7.28

298.15 303.15 308.15 313.15

21.08 23.68 26.28 28.75

aqueous 2-butoxyethanol solutions. Had these interactions been very strong in this medium, the limiting ionic conductivity values should have been in the reverse order: Me4N+ < Et4N+ < Pr4N+, because a smaller ion with grater surface charge density is expected to associate more solvent molecules thus resulting in a bigger solvodynamic entity, which is obviously not the case here. The same conclusion is arrived at the Walden products’, λ0±η0 (Table 4) trend. Table 4 shows that Walden product values (λ0±η0) for the ions studied under varying temperature are irregular. However, Stokes law rejects such temperature and Walden product values relation.40 So, in 2-butoxyethanol (1) + water (2) mixtures Stokes law does not hold good. Observations of failure of this law have also been seen earlier in other solvent media.11,41

(10)

λ 0(Bu4N+) = 0.517Λ0(Bu4NBPh4)

298.15 303.15 308.15 313.15

Br−

Et4N+ 298.15 303.15 308.15 313.15

0.956 0.938 0.930 0.914

Et4N+ 0.837 0.832 0.834 0.835

23.35 24.71 25.42 26.98

2.94 2.93 2.97 3.11

w1 = 0.60 Me4N+

w1 = 0.40 Me4N+ 298.15 303.15 308.15 313.15

0.279 0.280 0.276 0.264

32.76 36.99 41.61 45.89

Br− 298.15 303.15 308.15 313.15

Å

9.56 11.04 12.34 13.25

Pr4N+ 298.15 303.15 308.15 313.15

rs

S·cm2·mol−1 Pa s

Br−

+

298.15 303.15 308.15 313.15

−1

Pr4N+

w1 = 0.20 Me4N+ 298.15 303.15 308.15 313.15

λ0±η0 × 103

λ0± 2

(11)

Using the Kohlrausch additivity rule (eq 12), the Λ0 values of Bu4NBPh4 were obtained by combining the Λ0 values of NaBr, NaBPh4, and Bu4NBr. Λ0(Bu4NBPh4) = Λ0(Bu4NBr) + Λ0(NaBPh4) − Λ0(NaBr) (12)

(λ0±)

Table 4 reflects the single-ion conductivities as well as Walden products (λ0±η0). Compared with tetraethylammonium (Et4N+) and tetrapropylammonium ion (Pr4N+), the limiting ionic conductivity values of tetramethylammonium ion (Me4N+) were always higher. This means that in all of the mixed solvent media over the temperature range investigated, the mobility of the tetramethylammonium ion is greater than that of tetraethylammonium and tetrapropylammonium ion. When the mobility trend was compared with that of the crystallographic sizes of these ions, which is in the order39 Me4N+ < Et4N+ < Pr4N+, an inverse relation is expected between size of the bare ions and ionic mobility. Since, this did not happen it is clear that the electrostatic ion−solvent interaction is very weak for these ions in

4. CONCLUSION The solution of these three salts, namely, tetramethylammonium bromide, tetraethylammonium bromide, and tetrapropylammonium bromide, exists essentially in the form of free ions in all solvent compositions and in all investigated temperatures which is clear from the low values of the association constants. The electrostatic ion−solvent interaction is found to be weak in the aqueous 2-butoxyethanol mixtures investigated. The Walden products for the ions studied here show distinct differences with increasing temperature over the entire range of 173

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temperature and solvent composition. With an increase in temperature, an appreciable increase in the limiting equivalent conductances of the electrolytes and also the single-ion conductivity values is observed, but the same is decreased with increasing amounts of 2-butoxyethanol in the mixed solvent media in the temperature range studied.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Funding

The author thanks the University Grants Commission, New Delhi, India for financial assistance through Minor Research Project. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS The author thanks Dr. Mukund Giri, Sikkim Government College for his valuable suggestions in the manuscript preparation.

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REFERENCES

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