(1) + Water

Nov 27, 2012 - Department of Chemistry, Sikkim Government College, Tadong, Gangtok, East Sikkim 737 102, India. ABSTRACT: Electrical conductances of ...
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Conductance Studies of Tetrabutylammonium Bromide, Sodium Bromide, and Sodium Tetraphenylborate in 2‑Butoxyethanol (1) + Water (2) Mixtures at (298.15, 303.15, 308.15, and 313.15) K Binod Sharma, Ramesh Sharma, and Chanchal Das* Department of Chemistry, Sikkim Government College, Tadong, Gangtok, East Sikkim 737 102, India ABSTRACT: Electrical conductances of solutions of tetrabutylammonium bromide (Bu4NBr), sodium bromide (NaBr), and sodium tetraphenylborate (NaBPh4) in 2-butoxyethanol (1) + water (2) mixture with 0.017, 0.037, 0.061, 0.092, and 0.132 mole fraction of 2-butoxyethanol have been 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 the 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, tetrabutylammonium bromide, sodium bromide, and sodium tetraphenylborate, suggests a weak electrostatic ion−solvent interaction and that they exist as free ions in all the solvent compositions and the temperature range covered in this study. The Walden products of these salts deviate from ideal behavior with varying temperature and solvent composition. conductance studies24,25 in 2-butoxyethanol and its aqueous mixtures, are insufficient. Studies on the fundamental physicochemical properties like density and dielectric constant along with isentropic compressibilities and heat capacities have been reported for 2-butoxyethanol.1,26−28 Dielectric constants and density measurements on the 2-butoxyethanol−water mixtures have been performed at 298.15 K by Douheret and Pal.28 Later Reddy et al.29 reported densities, viscosities, and isentropic compressibilities for this mixed solvent media at 308.15 K. Very recently, Chiou et al.30 reported densities, viscosities, and refractive indexes of 2-butoxyethanol−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.27 Dielectric spectroscopy of 2-butoxyethanol−water mixtures in the complete composition range have been measured by Kaatze et al.31 and their findings point at a substantial effect of the hydrogen bonding of the ether oxygen atoms in the 2-butoxyethanol−water system. The present paper reports the equivalent conductivities of tetrabutylammonium bromide (Bu4NBr), sodium bromide (NaBr), and sodium tetraphenylborate (NaBPh4) in 2-butoxyethanol (1) + water (2) mixtures containing 0.017, 0.037, 0.061, 0.092, and 0.132 mole fraction of 2-butoxyethanol at (298.15, 303.15, 308.15, and 313.15) K to obtain accurate single-ion conductivities at the temperatures mentioned above.

1. INTRODUCTION A proper understanding of ion−solvent interactions would form the basis of quantitatively explaining the influence of the solvent and the extent of interactions of ions in solvents, thus paving the way for the real understanding of the different phenomena associated with solution chemistry. 2-Butoxyethanol (BE) belongs to a class of compounds commercially known as cellosolves. It is, in fact, the monobutyl ether of ethylene glycol. Hence, it is very likely that its physicochemical properties are between dipolar aprotic and protic solvents. It is well-known that, at low BE content in BE-water mixtures, BE exists as a molecular dispersion in water, but at higher BE content, micelle-like aggregation is occurs due to a radical change in the BE-water mixture structure.1−6 Hence, it would be interesting to study the behavior of electrolytes in such an uncharacteristic solvent medium. In spite of the extensive use of cellosolves as solvents and solubilizing agents in many commercial industries,7,8 the studies on the electrical properties of electrolytes in these media and their mixtures with water have not stimulated much interest so far. However, knowledge of the electrical properties of different electrolytes in these solvents would be helpful in indicating the potential usefulness of cellosolves in various technologies like high-energy nonaqueous batteries, ion exchangers, and so forth. The situation is somewhat better with the first and second homologue of this class of solvents, namely, 2-methoxyethanol and 2-ethoxyethanol. Extensive studies on the transport properties of various electrolytes in these two homologues both in pure as well as in its binary mixtures with water have already been reported.9−23 Unfortunately, such investigations, particularly © XXXX American Chemical Society

Received: April 15, 2012 Accepted: November 12, 2012

A

dx.doi.org/10.1021/je300737t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

Article

From the experimentally obtained concentration−conductance data three very important parameters, namely, equivalent conductance of an electrolyte at infinite dilution (Λ0), ionic association constant (KA), and the association diameter (R), as a function of concentration can be obtained by the use of appropriate equations. Several models and their mathematical formulations are available, and their choice for the calculations of Λ0, KA, and R depends on the precision desired and their appropriateness.32,33 We have used the Fuoss 78 conductance−concentration equation34,35 for our analysis as this equation is based on a more realistic model as compared to the others.

Table 1. Physical Properties (Density, Viscosity, and Dielectric Constant) of 2-Butoxyethanol (1) + Water (2) Mixtures Containing 0.017, 0.037, 0.061, 0.092, and 0.132 Mole Fractions of 2-Butoxyethanol at Different Temperaturesa ρ0/g·cm−3

2. EXPERIMENTAL SECTION 2.1. Chemicals. 2-Butoxyethanol (purchased from G. R. E. Merck with a mass fraction purity >0.995) was first dried with potassium carbonate, and the dry BE was distilled twice just prior to use in a Borosil distillation set. The measured density (ρ0) and the coefficient of viscosity (η0) of the purified BE were found to be 0.89616 g·cm−3 and 2.7820 mPa·s, respectively, at 298.15 K. A comparison of these values with the literature values26,36 shows a good agreement with the published values. The mixed solvents containing 0.017, 0.037, 0.061, 0.092, and 0.132 mole fraction of 2-butoxyethanol 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, which are given in Table 1. These density values along with the density and relative permittivity values of the pure solvents at the experimental temperatures (obtained from the literature) have been used to calculate the relative permittivities of the mixed solvents with the help of the equations as described in the literature37 and are also given in Table 1. The salts used were obtained from Fluka and were of puriss grade (99.9 % pure). Tetrabutylammonium bromide (Bu4NBr) was recrystallized from acetone and dried in vacuo at 333.15 K for 48 h prior to use. Sodium bromide (NaBr) was dried in vacuo for 72 h at room temperature before use. Sodium tetraphenylborate (NaBPh4) was purified by recrystallization thrice from acetone and then dried in vacuo for 72 h at 353.15 K. 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 of 1.15 cm−1 and an uncertainty of 0.01 %. The calibration of the cell was done using 0.01N aqueous potassium chloride solutions by the method suggested by Lind et al.39 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 of the measurements have been described earlier.40−42 For the measurement of conductance molal solutions were prepared. The densities of these molal 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 of the experimental temperatures were also measured and subtracted from those of the salt solutions. A suspended level Ubbelohde-type viscometer was used to measure the kinematic viscosities of the solvents. All solutions were prepared with utmost care in a dehumidified room.

T/K

this work

298.15 303.15 308.15 313.15

0.99326 0.99082 0.98889 0.98594

298.15 303.15 308.15 313.15

0.98646 0.98292 0.98038 0.97764

298.15 303.15 308.15 313.15

0.97633 0.97423 0.97137 0.96864

298.15 303.15 308.15 313.15

0.96710 0.96431 0.96145 0.95848

298.15 303.15 308.15 313.15

0.94810 0.94474 0.94159 0.93757

298.15 303.15 308.15 313.15

0.89616 0.89274 0.88888 0.88429

η0/mPa·s lit.

0.89624c 0.89268d 0.88891c 0.88421d

this work x1 = 0.017 1.2844 1.1307 0.9936 0.8871 x1 = 0.037 1.8493 1.6217 1.4654 1.3025 x1 = 0.061 2.4499 2.1610 1.9160 1.7543 x1 = 0.092 2.9975 2.6354 2.3342 2.0545 x1 = 0.132 3.9178 3.3944 2.9205 2.5386 x1 = 1.00 2.7817 2.4993 2.2064 1.9459

lit.

εb 71.56 69.94 68.49 66.89 64.31 62.82 61.43 60.03 57.23 55.87 54.57 53.22 50.21 48.93 47.70 46.49 36.49 35.47 34.46 33.43

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 and u(X) = 0.0002, and combined expanded uncertainties Uc are uc(ρ0) = 0.0005 g·cm−3, and uc(η0) = 0.01 mPa·s (0.95 level of confidence). bCalculated with the equations as described in ref 37. cFrom ref 38. dFrom ref 30.

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 mole fractions of 0.017, 0.037, 0.061, 0.092, and 0.132 of 2-butoxyethanol at (298.15, 303.15, 308.15, and 313.15) K are shown in Table 2. The 1978 Fuoss conductance concentration equation34,35 has been 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, namely, 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:

B

Λ = p[Λ0(1 + RX) + EL]

(1)

p = 1 − α(1 − γ )

(2)

γ = 1 − KAcγ 2f 2

(3)

dx.doi.org/10.1021/je300737t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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Table 2. Equivalent Conductances (Λ) and Corresponding Molalities (m) of Electrolytes in 2-Butoxyethanol (1) + Water (2) Mixtures at (298.15, 303.15, 308.15, and 313.15) Ka T = 298.15 K

mol·kg

T = 303.15 K Λ

m −1

−1

S·cm ·mol 2

mol·kg

T = 308.15 K Λ

m −1

S·cm ·mol 2

−1

T = 313.15 K Λ

m

Λ

m

−1

S·cm ·mol

0.00710 0.01481 0.02075 0.02967 0.03860 0.04755 0.05352 0.05950

77.465 75.564 74.257 72.066 69.742 67.756 66.415 64.990

0.00710 0.01481 0.02075 0.02967 0.03860 0.04755 0.05352 0.05950

85.425 83.524 81.980 79.841 77.465 75.445 73.901 72.356

0.00623 0.01248 0.01872 0.02497 0.03122 0.03748 0.04374 0.05313

115.050 112.871 110.693 108.515 106.337 104.221 101.980 99.009

0.00623 0.01248 0.01872 0.02497 0.03122 0.03748 0.04374 0.05313

125.941 123.942 121.584 119.406 116.832 114.851 112.091 109.307

0.00710 0.01480 0.02074 0.02964 0.03855 0.04747 0.05343 0.05939

63.633 62.207 61.178 59.277 57.791 55.950 54.762 53.574

0.00710 0.01480 0.02074 0.02964 0.03855 0.04747 0.05343 0.05939

69.475 68.049 67.019 65.118 63.348 61.475 60.128 59.019

0.00611 0.01019 0.01427 0.02040 0.02653 0.03063 0.03472 0.04087

66.475 65.524 64.455 63.267 61.722 60.597 59.703 58.396

0.00611 0.01019 0.01427 0.02040 0.02653 0.03063 0.03472 0.04087

73.597 72.712 71.762 70.099 68.673 67.722 66.653 65.108

0.00611 0.01019 0.01427 0.02039 0.02652 0.03061 0.03470 0.04012

99.405 98.019 96.633 94.653 92.475 91.236 89.834 87.920

0.00611 0.01019 0.01427 0.02039 0.02652 0.03061 0.03470 0.04012

110.139 108.614 107.089 104.911 102.515 101.426 100.119 98.158

0.00615 0.01026 0.01436 0.02053 0.02670 0.03081 0.03493 0.04111

54.128 53.138 52.445 51.356 50.465 49.772 48.980 47.792

0.00615 0.01026 0.01436 0.02053 0.02670 0.03081 0.03493 0.04111

59.297 58.505 57.811 56.722 55.534 54.643 53.851 52.452

mol·kg

2

−1

mol·kg

−1

S·cm ·mol−1 2

x1 = 0.017 Bu4NBr 0.00710 0.01481 0.02075 0.02967 0.03860 0.04755 0.05352 0.05950

63.168 61.518 60.313 58.048 56.097 54.237 53.049 51.980

0.00710 0.01481 0.02075 0.02967 0.03860 0.04755 0.05352 0.05950

70.514 68.732 67.515 65.287 63.148 61.247 60.031 58.752

0.00623 0.01248 0.01872 0.02497 0.03122 0.03748 0.04374 0.05313

94.257 92.079 89.901 87.822 86.138 84.158 82.178 79.009

0.00623 0.01248 0.01872 0.02497 0.03122 0.03748 0.04374 0.05313

104.554 102.178 100.000 97.753 95.841 93.861 91.871 89.108

0.00710 0.01480 0.02074 0.02964 0.03855 0.04747 0.05343 0.05939

52.227 50.960 50.089 48.505 46.920 45.336 44.307 43.356

0.00710 0.01480 0.02074 0.02964 0.03855 0.04747 0.05343 0.05939

58.009 56.663 55.554 54.049 52.324 50.564 49.376 48.188

NaBr

NaBPh4

x1 = 0.037 Bu4NBr 0.00611 0.01019 0.01427 0.02040 0.02653 0.03063 0.03472 0.04087

52.930 52.099 51.029 49.722 48.415 47.584 46.871 45.564

0.00611 0.01019 0.01427 0.02040 0.02653 0.03063 0.03472 0.04087

59.346 58.514 57.683 56.376 54.831 53.877 52.930 51.505

0.00611 0.01019 0.01427 0.02039 0.02652 0.03061 0.03470 0.04012

77.465 76.158 74.633 72.525 70.475 69.188 67.881 65.920

0.00611 0.01019 0.01427 0.02039 0.02652 0.03061 0.03470 0.04012

87.920 86.178 84.871 82.910 80.732 79.425 77.730 75.722

0.00615 0.01026 0.01436 0.02053 0.02670 0.03081 0.03493 0.04111

42.901 42.207 41.514 40.623 39.534 38.742 38.049 36.861

0.00615 0.01026 0.01436 0.02053 0.02670 0.03081 0.03493 0.04111

48.247 47.554 46.861 45.772 44.683 43.990 43.495 42.306

NaBr

NaBPh4

C

dx.doi.org/10.1021/je300737t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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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

0.00377 0.00786 0.01101 0.01574 0.02047 0.02520 0.02836 0.03152

53.663 52.816 52.188 51.089 50.216 49.004 48.415 47.722

0.00377 0.00786 0.01101 0.01574 0.02047 0.02520 0.02836 0.03152

59.802 58.811 58.020 56.831 55.841 54.752 53.960 53.267

0.00361 0.00602 0.00904 0.01205 0.01507 0.01809 0.02111 0.03017

79.688 79.009 77.821 76.831 75.643 74.834 73.663 71.089

0.00361 0.00602 0.00904 0.01205 0.01507 0.01809 0.02111 0.03017

87.547 86.534 85.544 84.356 83.366 82.257 81.188 78.303

0.00368 0.00768 0.01075 0.01537 0.01999 0.02461 0.02769 0.03077

43.772 42.940 42.465 41.752 40.920 40.326 39.706 39.138

0.00368 0.00768 0.01075 0.01537 0.01999 0.02461 0.02769 0.03077

47.673 46.841 46.247 45.415 44.821 44.109 43.463 43.039

0.00312 0.00517 0.00724 0.01035 0.01346 0.01637 0.01762 0.02073

46.108 45.574 45.039 44.326 43.613 43.079 42.722 42.009

0.00312 0.00517 0.00724 0.01035 0.01346 0.01637 0.01762 0.02073

50.831 50.386 49.940 49.185 48.425 47.891 47.534 46.821

0.00310 0.00517 0.00724 0.01035 0.01346 0.01553 0.01760 0.02071

65.722 65.057 64.238 63.435 62.544 62.029 61.402 60.594

0.00310 0.00517 0.00724 0.01035 0.01346 0.01553 0.01760 0.02071

72.376 71.544 70.802 69.772 68.742 68.222 67.455 66.683

0.00310 0.00517 0.00725 0.01035 0.01347 0.01554 0.01761 0.02073

32.346 31.990 31.633 31.039 30.445 30.089 29.732 29.120

0.00310 0.00517 0.00725 0.01035 0.01347 0.01554 0.01761 0.02073

35.673 35.316 34.960 34.366 33.817 33.415 33.059 32.518

x1 = 0.061 Bu4NBr 0.00377 0.00786 0.01101 0.01574 0.02047 0.02520 0.02836 0.03152

42.970 42.173 41.627 40.594 39.604 38.712 38.118 37.524

0.00377 0.00786 0.01101 0.01574 0.02047 0.02520 0.02836 0.03152

48.316 47.333 46.633 45.643 44.653 43.762 42.871 42.277

0.00361 0.00602 0.00904 0.01205 0.01507 0.01809 0.02111 0.03017

65.346 64.356 63.366 62.090 61.563 60.554 59.604 56.831

0.00361 0.00602 0.00904 0.01205 0.01507 0.01809 0.02111 0.03017

71.683 70.891 69.901 69.108 68.020 67.016 66.138 63.564

0.00368 0.00768 0.01075 0.01537 0.01999 0.02461 0.02769 0.03077

35.198 34.604 34.247 33.415 32.821 32.227 31.649 31.039

0.00368 0.00768 0.01075 0.01537 0.01999 0.02461 0.02769 0.03077

39.475 38.762 38.287 37.455 36.742 35.992 35.554 35.079

NaBr

NaBPh4

x1 = 0.092 Bu4NBr 0.00312 0.00517 0.00724 0.01035 0.01346 0.01637 0.01762 0.02073

35.683 35.307 34.683 34.130 33.722 33.188 32.972 32.475

0.00312 0.00517 0.00724 0.01035 0.01346 0.01637 0.01762 0.02073

40.495 40.138 39.693 39.069 38.534 38.000 37.617 37.019

0.00310 0.00517 0.00724 0.01035 0.01346 0.01553 0.01760 0.02071

52.673 52.051 51.485 50.633 50.118 49.429 49.186 48.316

0.00310 0.00517 0.00724 0.01035 0.01346 0.01553 0.01760 0.02071

58.950 58.514 57.920 57.148 56.376 55.603 55.089 54.316

0.00310 0.00517 0.00725 0.01035 0.01347 0.01554 0.01761 0.02073

25.580 25.217 24.861 24.386 23.792 23.435 23.108 22.538

0.00310 0.00517 0.00725 0.01035 0.01347 0.01554 0.01761 0.02073

28.970 28.663 28.306 27.766 27.227 26.910 26.530 25.925

NaBr

NaBPh4

D

dx.doi.org/10.1021/je300737t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

Journal of Chemical & Engineering Data

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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

0.00105 0.00211 0.00316 0.00422 0.00475 0.00527 0.00633 0.00739

29.970 29.732 29.439 29.141 28.963 28.782 28.465 28.240

0.00105 0.00211 0.00316 0.00422 0.00475 0.00527 0.00633 0.00739

33.217 33.021 32.742 32.505 32.282 32.188 31.950 31.712

0.00107 0.00214 0.00321 0.00429 0.00482 0.00536 0.00643 0.00751

44.297 43.940 43.485 42.990 42.752 42.574 42.217 41.802

0.00107 0.00214 0.00321 0.00429 0.00482 0.00536 0.00643 0.00751

48.059 47.623 47.207 46.851 46.673 46.495 46.079 45.722

0.00108 0.00217 0.00325 0.00434 0.00488 0.00543 0.00651 0.00760

23.924 23.718 23.538 23.358 23.255 23.142 22.936 22.762

0.00108 0.00217 0.00325 0.00434 0.00488 0.00543 0.00651 0.00760

25.914 25.714 25.485 25.247 25.152 25.057 24.819 24.582

x1 = 0.132 Bu4NBr 0.00105 0.00211 0.00316 0.00422 0.00475 0.00527 0.00633 0.00739

23.475 23.296 23.079 22.762 22.60 22.524 22.366 22.128

0.00105 0.00211 0.00316 0.00422 0.00475 0.00527 0.00633 0.00739

26.722 26.485 26.247 26.009 25.851 25.693 25.455 25.217

0.00107 0.00214 0.00321 0.00429 0.00482 0.00536 0.00643 0.00751

36.930 36.574 36.178 35.80 35.623 35.386 35.029 34.673

0.00107 0.00214 0.00321 0.00429 0.00482 0.00536 0.00643 0.00751

40.613 40.257 39.901 39.425 39.247 39.009 38.653 38.297

0.00108 0.00217 0.00325 0.00434 0.00488 0.00543 0.00651 0.00760

20.015 19.861 19.679 19.501 19.398 19.324 19.150 18.986

0.00108 0.00217 0.00325 0.00434 0.00488 0.00543 0.00651 0.00760

21.906 21.716 21.536 21.330 21.225 21.124 20.918 20.734

NaBr

NaBPh4

a

Conductivity was measured with a relative uncertainty ur(Λ) of 0.01. The uncertainty of the strength of the solution in molality was ± 2·10−5 mol·kg−1.

−ln f =

β=

βk 2(1 + kR )

e2 εkBT

KA = KR (1 + K s)

To ensure convergence, the values of Λ0 and R are computed which minimize the standard deviation, σ,

(4)

σ = [∑ [Λj(calcd) − Λj(obsd)]2 /(n − 2)]1/2 (5)

(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 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 solvent separated ion-pair. 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 by35

(6)

where RX is the relaxation field effect, EL is the electrophoretic countercurrent, γ is the fraction of unpaired ions, 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 Shedlovsky extrapolation43 of the conductance data. The program also contains an instruction to cover a given range of R values.

d = 1.183(M /ρ0 )1/3

(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 Bu4NBr, NaBr, and NaBPh4 in 2-butoxyethanol (1) + water (2) mixtures with x1 = 0.30 at (298.15, 303.15, 308.15, and 313.15) K depicts the variation of the experimental equivalent conductivity as a function of molal concentration of the salts. The figure also contains the corresponding fitted profiles according to eqs 1 to 6. E

dx.doi.org/10.1021/je300737t | J. Chem. Eng. Data XXXX, XXX, XXX−XXX

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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 Λ0

T K

a

KA

S·cm ·mol 2

−1

298.15 303.15 308.15 313.15

69.54 77.31 84.81 93.30

± ± ± ±

0.55 0.55 0.59 0.60

298.15 303.15 308.15 313.15

102.13 112.82 124.22 136.03

± ± ± ±

0.81 0.64 0.85 0.97

298.15 303.15 308.15 313.15

57.79 64.19 70.21 76.65

± ± ± ±

0.53 0.61 0.56 0.61

298.15 303.15 308.15 313.15

57.59 64.59 71.96 79.56

± ± ± ±

0.26 0.44 0.36 0.39

298.15 303.15 308.15 313.15

84.50 95.30 106.99 118.17

± ± ± ±

0.56 0.65 0.54 0.44

298.15 303.15 308.15 313.15

47.06 52.58 58.64 64.52

± ± ± ±

0.36 0.26 0.25 0.40

± ± ± ±

298.15 303.15 308.15 313.15

46.14 51.74 57.38 63.80

0.26 0.27 0.30 0.27

298.15 303.15

69.60 ± 0.36 76.24 ± 0.38

R −1

L·mol x1 = 0.017 Bu4NBr 5.82 ± 5.09 ± 4.64 ± 4.15 ± NaBr 5.62 ± 4.95 ± 4.45 ± 4.14 ± NaBPh4 4.91 ± 4.71 ± 4.06 ± 3.70 ± x1 = 0.037 Bu4NBr 6.36 ± 5.78 ± 5.06 ± 4.60 ± NaBr 7.74 ± 6.67 ± 5.07 ± 4.64 ± NaBPh4 5.80 ± 4.64 ± 3.99 ± 4.00 ± x1 = 0.061 Bu4NBr 7.09 ± 6.73 ± 5.58 ± 5.50 ± NaBr 7.64 ± 6.24 ±

Å

σa

T

%

0.49 0.43 0.41 0.37

12.62 12.62 12.62 12.63

0.73 0.68 0.67 0.63

0.54 0.38 0.44 0.46

08.57 08.57 08.58 08.58

0.75 0.55 0.67 0.72

0.56 0.57 0.46 0.45

12.12 12.12 12.12 12.13

0.87 0.47 0.43 0.79

0.38 0.55 0.39 0.38

12.63 12.64 12.64 12.65

0.42 0.65 0.49 0.49

0.58 0.58 0.34 0.29

08.59 08.59 08.59 08.60

0.59 0.62 0.48 0.36

0.63 0.38 0.33 0.47

12.13 12.14 12.14 12.15

0.72 0.47 0.43 0.61

0.59 0.54 0.52 0.41

12.65 12.66 12.66 12.67

0.58 0.54 0.55 0.44

0.65 0.59

08.60 08.61

0.54 0.52

K

Λ0

R

σa

Å

%

0.52 0.50

08.61 08.62

0.47 0.46

0.66 0.43 0.43 0.31

12.15 12.15 12.16 12.17

0.68 0.45 0.47 0.35

0.34 0..58 0.43 0.49

12.67 12.67 12.68 12.69

0.24 0.42 0.30 0.36

0.44 0.67 0.39 0.38

08.62 08.63 08.63 08.64

0.31 0.47 0.28 0.26

0.93 0.85 0.73 0.62

12.17 12.18 12.18 12.19

0.57 0.56 0.49 0.43

0.59 0.54 0.52 0.41

12.71 12.71 12.72 12.73

0.38 0.40 0.44 0.38

1.43 1.44 1.33 1.19

08.66 08.66 08.67 08.68

0.37 0.38 0.35 0.32

1.33 1.48 1.34 1.52

12.21 12.21 12.22 12.23

0.38 0.41 0.41 0.43

KA −1

S·cm ·mol 2

308.15 313.15

84.73 ± 0.37 92.88 ± 0.40

298.15 303.15 308.15 313.15

37.85 42.34 46.83 50.87

± ± ± ±

0.25 0.18 0.21 0.16

298.15 303.15 308.15 313.15

37.95 43.16 49.10 54.11

± ± ± ±

0.09 0.18 0.15 0.19

298.15 303.15 308.15 313.15

55.70 62.58 69.55 76.66

± ± ± ±

0.17 0.29 0.19 0.19

298.15 303.15 308.15 313.15

27.78 31.36 34.97 38.46

± ± ± ±

0.16 0.18 0.17 0.16

298.15 303.15 308.15 313.15

24.76 28.19 31.69 35.03

± ± ± ±

0.09 0.11 0.14 0.13

298.15 303.15 308.15 313.15

38.78 42.67 46.57 50.42

± ± ± ±

0.15 0.16 0.17 0.16

298.15 303.15 308.15 313.15

21.14 23.20 25.35 27.54

± ± ± ±

0.07 0.09 0.10 0.11

−1

L·mol NaBr 5.88 ± 5.55 ± NaBPh4 5.63 ± 5.33 ± 4.58 ± 4.02 ± x1 = 0.092 Bu4NBr 6.63 ± 6.80 ± 6.45 ± 5.34 ± NaBr 5.67 ± 5.50 ± 5.22 ± 5.40 ± NaBPh4 9.41 ± 7.47 ± 6.85 ± 5.48 ± x1 = 0.132 Bu4NBr 7.44 ± 6.62 ± 7.31 ± 3.16 ± NaBr 7.81 ± 6.40 ± 5.85 ± 2.59 ± NaBPh4 3.92 ± 4.02 ± 2.00 ± 2.26 ±

σ/% = 100σ/Λ0.

λ 0(Bu4N+) = 0.517Λ0(Bu4NBPh4)

For a proper understanding of the behavior of the individual ions making up the salts, the limiting molar electrolyte conductances (Λ0) values obtained above needs to be split-up and attributed to the constituent ions of the electrolyte. This can be easily achieved by the “reference electrolyte method” using tetrabutylammonium tetraphenylborate (Bu4NBPh4) as the “reference electrolyte”.44,45 In this method, the Λ0 values of Bu4NBPh4 can be divided into the ionic components using eqs 9 to 12.46 Λ0(Bu4NBPh4) = λ 0(Bu4N+) + λ 0(Ph4B−) r(Ph4B−) 5.35 = + = 0 − r(Bu4N ) 5.00 λ (Ph4B )

(11)

The ionic radii (r) values of the two ions, Bu4N+ and Ph4B−, have been taken from the literature.47,48 The value of Λ0 (Bu4NBPh4) can easily be calculated using Kohlrausch law of the independent migration of ions. Using the Λ0 values of Bu4NBr, NaBr, and NaBPh4 from Table 3, the Λ0 value of Bu4NBPh4 can easily be obtained through a proper combination of the equivalent conductances through eq 12. Λ0(Bu4NBPh4) = Λ0(Bu4NBr) + Λ0(NaBPh4) − Λ0(NaBr)

(9)

(12)

λ 0(Bu4N+)

The limiting ion conductances of the individual ions calculated using eqs 9 to 12 is given in Table 4.

(10) F

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Table 4. Limiting Ionic Conductances in 2-Butoxyethanol (1) + Water (2) Mixtures Containing 0.017, 0.037, 0.061, 0.092, and 0.132 Mole Fractions of 2-Butoxyethanol at (298.15, 303.15, 308.15, and 313.15) K λ0±/S·cm2·mol−1 T/K

Na+

298.15 303.15 308.15 313.15

45.62 50.34 55.33 60.27

298.15 303.15 308.15 313.15

37.53 42.26 47.59 52.44

298.15 303.15 308.15 313.15

31.21 34.12 37.90 40.94

298.15 303.15 308.15 313.15

22.94 25.59 27.94 30.77

298.15 303.15 308.15 313.15

17.70 18.99 20.29 21.67

Bu4N+ x1 13.03 14.83 15.92 17.54 x1 10.42 11.31 12.21 13.39 x1 7.44 9.22 10.07 11.26 x1 5.19 6.17 7.49 8.22 x1 3.68 4.51 5.41 6.28

Br− = 0.017 56.51 62.48 68.89 75.76 = 0.037 47.17 53.28 59.75 66.17 = 0.061 38.70 42.52 47.31 52.54 = 0.092 32.76 36.99 41.61 45.89 = 0.132 21.08 23.68 26.28 28.75

Ph4B− 12.17 13.85 14.88 16.38 9.53 10.32 11.05 12.08 6.64 8.22 8.93 9.93 4.84 5.77 7.03 7.69 3.44 4.21 5.06 5.90

This means that there is no significant association of the ions,49 and the three electrolytes studied exist as free ions in the entire range of 2-butoxyethanol (1) + water (2) mixed solvent media and the temperature range covered in this investigation. This conclusion is on expected lines as the relatively high values of the relative permittivity of the solvent mixtures (33.43 ≤ ε ≥ 71.56) provides a conducive environment for the dissociation of electrolytes. The variation of the Walden products as function of the solvent composition at (298.15, 303.15, 308.15, and 313.15) K is shown in Figure 2. The plot shows deviation from ideality which can be attributed to charged ion−solvent interactions which may be due to changing solvodynamic radii of the ions at different solvent compositions. The limiting ionic equivalent conductances (λ0) decreases in the order λ0Br− > λ0Na+ > λ0Bu4N+ > λ0Ph4B−, and the trend remains the same for all of the temperatures and the solvent composition studied. This order also implies that the sizes of these ions in solutions follow the reverse trend, that is, Br− < Na+ < Bu4N+ < Ph4B−. Since at a fixed solvent composition the influence of viscosity and hydrogen bonding of the solution has little effect on the conductivity, this order can be rationalized as resulting from increased solvation due to higher surface charge densities for the smaller ions. It is also observed that, as the amount of 2-butoxyethanol in the solvent medium increases, the limiting ionic equivalent conductances of all of the ions decreases which is expected as the relative permittivity of the medium is decreasing. The trend remains the same for all of the four temperatures studied.

Figure 1. Variation of molar conductivity as a function of concentration for: a, Bu4NBr; b, NaBr; and c, NaBPh4 in 2-butoxyethanol (1) + water (2) with x1 = 0.061. Experimental: ○, 298.15 K; □, 303.15 K; ●, 308.15 K; and, ■, 313.15 K. The lines represent the calculations according to eqs 1 through 6.

The values of the association constants (KA) obtained for the systems under investigations are all less than 10 (Table 3). G

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Figure 2. Walden products as a function of mole fraction 2-butoxyethanol of ○, sodium tetraphenylborate; □, sodium tetrabutylammonium bromide; and ▽, sodium bromide in 2-butoxyethanol (1) + water (2) at a, 298.15 K; b, 303.15 K; c, 308.15 K; and d, 313.15 K.

Funding

Although the limiting equivalent conductances of the electrolytes and the single-ions increases with temperature, the effect is more pronounced on the smaller ions, Br− and Na+, than on the larger ions Bu4N+ and Ph4B− in the 2-butoxyethanol−water mixed solvent.

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

4. CONCLUSION In conclusion, the solution of these three salts, namely, tetrabutylammonium bromide, sodium bromide, and sodium tetraphenlyborate, in 2-butoxyethanol−water mixed solvent contain the constituent ions in the free form in the entire temperature range investigated which is evident 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 of these salts deviate from ideality over the entire range of temperature and solvent composition studied. With 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 decreased with an increasing amount of 2-butoxyethanol in the mixed solvent media in the temperature range studied.

■

The authors declare no competing financial interest.

■

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. H

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