Apparent molal volumes of symmetrical and asymmetrical isomers of tetrabutylammonium bromide in water at several temperatures

J. Chem. Thermodynamics 68 (2014) 117–121

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Apparent molal volumes of symmetrical and asymmetrical isomers of tetrabutylammonium bromide in water at several temperatures Nicolás Moreno a, Andrés Malagón a, Richard Buchner b, Edgar F. Vargas a,⇑ a b

Laboratorio de Termodinámica de Soluciones, Departamento de Química, Universidad de Los Andes, Cr. 1 No. 18 A-10, Bogotá, Colombia Institut für Physikalische und Theoretische Chemie, Universität Regensburg, D-93040 Regensburg, Germany

a r t i c l e

i n f o

Article history: Received 27 June 2013 Received in revised form 26 August 2013 Accepted 31 August 2013 Available online 8 September 2013 Keywords: Apparent molal volumes Asymmetrical cations Partial molar volumes Aqueous solutions Quaternary ammonium cations

a b s t r a c t Apparent molal volumes of a series of differently substituted quaternary ammonium bromides, namely tetra-iso-butyl-, tetra-sec-butyl-, tetra-n-butyl-, di-n-butyl-di-sec-butyl- and di-n-butyl-di-iso-butylammonium bromide have been determined as a function of molal concentration at (298.15, 303.15 and 308.15) K. Partial molar volumes at infinite dilution and ionic molar volumes of these quaternary ammonium cations were determined. Structural volume contributions to the ionic molar volume were also calculated. The symmetric and asymmetric quaternary ammonium cations are ‘‘structure making’’ ions. The contribution of the branched butyl chains predominates over the linear butyl chains in the asymmetric cations. Ó 2013 Elsevier Ltd. All rights reserved.

1. Introduction Quaternary ammonium cations are widely used in several areas of chemistry [1]. Since their hydrophobicity is easily tuned by changing the length and/or the three-dimensional structure of the non-polar moieties these cations are often used as model systems for the investigation of ion–ion, ion–solvent and solvent–solvent interactions in electrolyte solutions [1–3]. Studies of the volumetric properties of symmetrical quaternary n-alkylammonium cations in aqueous solution are abundant in the literature and various reviews have summarized and commented the results [1–3]. However, corresponding investigations of symmetrical and asymmetrical quaternary ammonium cations having branched alkyl chains are still scarce [4–6]. These cations are of special interest because they provide a way of establishing the influence of the geometry of the non polar groups on the structural properties of water. This contribution intends to widen the available data base on the effect of the geometry of the non-polar alkyl side chain on the solvent by a systematic study of the volumetric behavior of aqueous solutions of five isomers of tetrabutylammonium bromide as a function of concentration (0.01 to 0.1 mol  kg1) at three temperatures (298.15, 303.15 and 308.15 K). Three symmetrical cations, namely tetra-n-butylammonium (Bu4N+), tetra-iso-butylammonium (isoBu4N+) and tetra sec-butylammonium (secBu4N+) ⇑ Corresponding author. Tel.: +57 1 3394949x2786; fax: +57 1 3324366. E-mail address: [email protected] (E.F. Vargas). 0021-9614/$ - see front matter Ó 2013 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jct.2013.08.031

were selected in addition to the asymmetric ions di-n-butyl-diiso-butylammonium (Bu2isoBu2N+) and di-n-butyl-di-sec-butylammonium (Bu2secBu2N+), figure 1. Apparent molal volumes were determined by density measurements to an uncertainty of ±5  106 g  cm3. Limiting partial molar ionic volumes of the cations were calculated from the limiting partial molar volumes at infinite dilution of the solutes. The concentration dependence of these apparent molal volumes was also examined. 2. Experimental 2.1. Materials The salt Bu4NBr was obtained from Sigma and used without further purification, whereas isoBu4NBr, secBu4NBr, Bu2isoBu2NBr and Bu2secBu2NBr were synthesized and purified according to established methods in literature [7,8]. The purity of all salts was better than 0.99 in mass. The water used was doubly distilled from an alkaline KMnO4 solution and degassed before use. The conductivity of the water employed always was less than 2 lS  cm1. The detailed specifications of chemical samples are given in table 1. 2.2. Apparatus and procedures Solution densities, q, were measured using an Anton Paar density meter, model DSA 5000 M, with a reproducibility of ±1  106 g  cm3. This instrument is equipped with a Peltier type thermostating unit, which permitted a temperature control of

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N. Moreno et al. / J. Chem. Thermodynamics 68 (2014) 117–121

FIGURE 1. Structures of the investigated asymmetric (1 Bu2isoBu2N+; 2 Bu2secBu2N+) and symmetric (3 isoBu4N+; 4 secBu4N+; 5 Bu4N+) quaternary ammonium cations.

TABLE 1 Specification of chemical samples. Compounds

Source

Bu4NBr isoBu4NBr secBu4NBr Bu2isoBu2NBr Bu2secBu2NBr Water

Sigma Synthesis Synthesis Synthesis Synthesis

Purification Method Recrystallization Recrystallization Recrystallization Recrystallization Doubly distilled

±0.001 K. The density meter was calibrated using dry air and pure water and the calibration was periodically checked. The experimental uncertainty, determined using aqueous solutions of KCl, was better than ±5  106 g  cm3 at all temperatures. The solutions were prepared by mass using an Ohaus Analytical Plus balance that has an uncertainty of 1  105 g in the range of interest. 3. Results and discussion The densities, q, of the studied aqueous quaternary ammonium bromide solutions are given in tables S1 to S3 in Supporting Information. The apparent molal volumes, V/, of the solutes were calculated from q and the density of water, qo, according to

V/ ¼

M2

q



1000ðq  qo Þ ; mqqo

ð1Þ

where m is the molal concentration of the solute and M2 its molar mass. Water densities at the three studied temperatures were taken from reference [9]. Tables S1 to S3 also list the apparent molal volumes of the solutes with their uncertainties at the studied temperatures. The uncertainties were calculated according to the law of propagation of uncertainties [10]. The dependency of the apparent molal volumes on solute molality was fitted by means of a weighted linear regression of the Redlich–Meyer equation [11]

V/ ¼

V /

1=2

þ SV m

þ BV m;

ð2Þ

where V / is the apparent molal volume at infinite dilution (which is equal to the partial molal volume of the solute at infinite

Mass fraction purity

Analysis method

0.99 0.99 0.99 0.99 0.99

Potentiometric Potentiometric Potentiometric Potentiometric Potentiometric

titration titration titration titration titration

dilution,V 2 ), SV is the Debye–Hückel limiting slope for 1:1 electrolytes at the given temperature (1.8743, 1.9616 and 2.0547 cm3  kg1/2  mol3/2 at 298.15, 303.15 and 308.15 K, respectively) [12] and BV is an empirical constant. The values of V / and BV at the studied temperatures, and their uncertainties, are summarized in table 2. Values of V / for Bu4NBr in aqueous solutions reported by other authors [6,13–16] are also included in table 2. Generally, a good agreement between this study and the literature is observed.The partial molar volume at infinite dilution, V 2 , can be expressed in terms of the ionic molar volume of the quaternary ammonium cation, V°(QA+), and bromide anion, V°(Br) , as:

  V 2 ¼ V  QAþ þ V  ðBr Þ:

ð3Þ

To our knowledge, there are no systematic studies in the literature that report the ionic molar volumes of the bromide ion as a function of temperature. However, the method reported by Hefter and Marcus [17] and Hedwig and Hakin [18] can be used to calculate V  ðBr Þ for the temperature range employed in this study. This method assumes that the partial molar volume at infinite dilution of a suitably chosen electrolyte can be separated into well-defined cation and anion contributions. Hence, the ionic molar volume of  the bromide ion, V ðBr Þ, can be calculated from the following set of equations:

V  ðBr Þ ¼ V 2 ðNaBrÞ þ V 2 ðHClÞ  V 2 ðHþ Þ  V 2 ðNaClÞ;

ð4Þ

V 2 ðHþ Þ ¼ 5:1  0:008ðT= CÞ  1:7  104 ðT= CÞ;

ð5Þ

V 2 ðHClÞ ¼16:22 þ 0:108ðT=K  273:15Þ  1:99  103 ðT=K  273:15Þ2 þ 9:7  106 ðT=K  273:15Þ3 ;

ð6Þ

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N. Moreno et al. / J. Chem. Thermodynamics 68 (2014) 117–121 TABLE 2 Partial molar volumes at infinite dilution,V / , and parameter BV of equation (2) for quaternary ammonium bromides at (298.15, 303.15 and 308.15) K. Also given are the uncertainties rV and rBV. T

V /

rV

BV

rB

K

cm3  mol1

cm3  mol1

cm3  kg  mol2

cm3  kg  mol2

298.15

300.21 300.35a 300.38b 301.0c 301.77 302.57d 303.86 304.8e

0.20

Bu4NBr 5.1

2.6

0.15

8.9

2.0

0.20

15.6

2.5

298.15 303.15 308.15

271.14 272.18 273.87

0.16 0.12 0.22

isoBu4NBr 9.2 11.7 18.4

2.0 1.5 2.8

298.15 303.15 308.15

277.46 278.47 280.34

0.19 0.20 0.24

secBu4NBr 57.9 53.5 61.4

2.4 2.5 3.3

272.51 272.80 273.22

Bu2isoBu2NBr 0.19 22.7 0.21 21.2 0.24 21.3

2.3 2.5 3.0

272.38 272.98 273.50

Bu2secBu2NBr 0.17 37.0 0.18 36.1 0.19 36.5

2.1 2.1 2.3

303.15 308.15

298.15 303.15 308.15 298.15 303.15 308.15 a b c d e

ð7Þ 6

TABLE 3 Ionic molar volumes for the bromide anion, V 2 (Br), and the quaternary ammonium cations, V 2 (QA+), together with the structural contribution of the cations, Vstruct(QA+), for aqueous solutions at (298.15, 303.15 and 308.15) K. T K

4

¼1:1372  10  2:3647  10 =ðT=KÞ  2:1468  10 lnðT=KÞ þ 65:4671  ðT=KÞ  3:3521  102  ðT=KÞ2 :

V ðiÞ ¼ V intr ðiÞ þ V elec ðiÞ þ V struct ðiÞ;

3 1 Vþ intr: /cm  mol 298.15 30.2 30.12a 303.15 30.4 308.15 30.7

3 1 Vþ intr: /cm  mol 298.15 30.2 303.15 30.4 308.15 30.7

3 1 Vþ intr: /cm  mol 298.15 30.2 303.15 30.4 308.15 30.7

3 1 Vþ intr: /cm  mol 298.15 30.2 303.15 30.4 308.15 30.7

ð9Þ

where V intr ðiÞ describes the intrinsic volume of the ions, Velec(i) is the contribution due to electrostriction of the solvent in the surroundings of the ion caused by its electrical field and Vstruct(i) describes any further effects the ion may have on the solvent in its surroundings, particularly if the solvent is structured [21]. For the intrinsic ionic volume (in cm3  mol1) of spherical ions of radius r(i) (in nm), such as the symmetrical quaternary ammonium cations Marcus [19] gives

V 2 (Br) cm3  mol1

V 2 (QA+) cm3  mol1

Vstruct(i) cm3  mol1

Bu4NBr

ð8Þ

For the analysis equation (5) was taken from reference [19], equations (6) and (7) are from reference [18] and equation (8) is from reference [20]. The values of V 2 ðBr Þ obtained according to the above set of equations are shown in table 3, together with data reported by Marcus [19] for this ion at 298.15 K. Good agreement between the result reported here and that of Marcus is observed. Thus, the obtained molar volume of Br, V 2 ðBr Þ was subtracted from the V 2 values of the five quaternary ammonium bromides Bu4NBr, isoBu4NBr, secBu4NBr, Bu2isoBu2NBr and Bu2secBu2NBr to obtain the ionic molar volumes for the quaternary ammonium cations, V  ðQAþ Þ, listed in table 3. According to Marcus [21] the ionic molar volume can be described as the sum of three contributions 

ð11Þ

In this approach A is a ‘‘constant covolume’’ term, Bi is the contribution of the ith functional group, which appears ni times in the solute molecule. According to the data reported by these authors, reproducibility within ±0.9 cm3  mol1 can be obtained in the values predicted by equation (11). However, this relationship does not apply when branched aliphatic chains are considered [24,25]. Then the predicted values are usually higher than the experimental values, as is illustrated in table 4. Data of asymmetrical quaternary ammonium cations obtained by Blanco and Vargas [6] are also shown in this table.

¼ 24:39 þ 0:0607ðT=K  308:15Þ

5

X ni Bi : i

 1:59ðT=K  308:15Þ2 ; V 2 ðNaClÞ

ð10Þ

For the present asymmetrical cations equation (10) appears to be a too rough approximation as their shape is more oblate than spherical. Therefore, the intrinsic volumes were assumed to be identical to the van der Waals volumes of these quaternary ammonium cations. The latter were obtained with Winmostar [22] after optimizing the geometry of the ions with MOPAC2012 using the semiempirical PM3 method [23]. The volumes, V intr ðiÞ, calculated according to these procedure are shown in table 3. The thus obtained van der Waals volume of Bu4N+ (177.4 cm3  mol1) compares very well to that reported by Marcus (177.43 cm3  mol1) [1]. For large univalent cations of radius r(i) > 0.25 nm the electrostriction term, Velec(i), is negligible [21]. As a consequence, for the present cations Vstruct(i) (¼ V  ðiÞ  V intr ðiÞ) becomes the dominating term in equation (9). As can be seen from table 3, the obtained values depend markedly on the structure of the cation. Gianni and Lepori [24,25] used additive schemes to predict the partial molar volumes of organic ions as a sum of group contributions, proposing the following equation:

V 2 ¼ A þ

Ref. [13]. Ref. [6]. Ref. [14]. Ref. [15]. Ref. [16].

V 2 ðNaBrÞ

V intr ðiÞ ¼ 2522r 3 ðiÞ:

3 1 Vþ intr: /cm  mol 298.15 30.2 303.15 30.4 308.15 30.7 a

Ref. [19].

177.4 270.0

92.6

271.3 273.2

93.9 95.8

isoBu4NBr 174.3 241.0 241.7 243.2

66.7 67.5 68.9

secBu4NBr 173.5 247.3 248.0 249.7

73.8 74.5 76.2

Bu2isoBu2NBr 176.5 242.3 242.4 242.5

65.8 65.9 66.1

Bu2secBu2NBr 175.2 242.2 242.5 242.8

67.0 67.4 67.7

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N. Moreno et al. / J. Chem. Thermodynamics 68 (2014) 117–121

On the other hand, one can also consider an additivity scheme based on alkyl-chain contributions instead of functional group contributions. For symmetrical ions the volume of the chains can be calculated as

V chain ¼ ðV  ðQAþ Þ  V  ðNþ Þ  AÞ=4;

ð12Þ

from the partial molar volume of the cation and the parameters V Nþ = 9.20 cm3  mol1 and A = 14.94 cm3 reported by Gianni and Lepori for 298.15 K [24]. Table 4 shows the molar volumes for the methyl, ethyl, butyl, isobutyl and secbutyl aliphatic chains calculated according to equation (12). Based on these data, V°(QA+) can be calculated for asymmetric quaternary ammonium cations. It turns out that the volumes obtained with this additivity scheme do not agree with the experimental data (table 4).Considering the results of V°(QA+) and Vstruct(i), table 3, the following general tendency can be seen: þ





þ

þ



V ðBu4 N Þ > V ðsecBu4 N Þ > V ðBu2 secBu2 N Þ  V  ðBu2 isoBu2 Nþ Þ > V  ðisoBu4 Nþ Þ and

V struct ðBu4 Nþ Þ > V struct ðsecBu4 Nþ Þ > V struct ðisoBu4 Nþ Þ  V struct ðBu2 secBu2 Nþ Þ > V struct ðBu4 isoBu2 Nþ Þ: Obviously, for the cations studied no simple correlation between V intr ðiÞ and Vstruct(i) exists. For example, the V°(QA+) and Vstruct(i) values for Bu4N+ are quite high compared to the other cations. The behavior of secBu4N+ and isoBu4N+ is of special interest due to the fact that Vstruct(secBu4N+) > Vstruct(isoBu4N+) whereas the corresponding intrinsic volumes are similar; see table 3. This suggests that secBu4N+ has a stronger effect on the water molecules in its surroundings as compared to isoBu4N+. Such an effect is also observed for the asymmetrical cations where Vstruct(Bu2secBu2N+) > Vstruct(Bu2isoBu2N+). Additionally, the values of Vstruct(i) for these cations are lower than those for secBu4N+ and isoBu4N+, respectively. This demonstrates a larger effect of the cation with branched chains as compared with the cation with linear chains. However, the Bu4N+ cation has a larger structural effect on its surrounding water than the other symmetrical cations. A plausible reason for this behavior of Vstruct(i) might be a cooperative effect of TABLE 4 Partial molar volumes of asymmetrical quaternary ammonium cations in water at 298.15 K. Aliphatic Chain

V°(chain) cm3  mol1

V°(cal)a cm3  mol1

Db cm3  mol1

Methyl Ethyl Butyl Isobutyl Secbutyl

22.40 37.07 68.94 61.68 63.26

21.44 37.37 69.23 69.14 69.14

0.96 0.30 0.29 7.46 5.88

Cation Me4N+ Et4N+ BuEt3N+ Bu2Et2N+ Bu3EtN+ Bu4N+ isoBu4N+ Bu2isoBu2N+ secBu4N+ Bu2secBu2N+ a b c d

V°(exp) 83.9 142.6 173.3 194.3 249.7 270.0 241.0 242.3 247.3 242.2

V°(calc) 83.9 142.6 174.4 206.3 238.2 270.0 241.0 255.5 247.3 258.7

c

the four linear butyl chains in the Bu4N+, which does not occur in the asymmetrical cations due to interference of the branched butyl chains. The values of BV (equation (2)) have been associated with the effect of ions on the structure of water [6,13]. Cations such as Me4N+ and Et4N+ have positive values of BV [6,13] and are considered to be ‘‘structure breaking’’ ions [26] whereas Bu4N+ has a negative value for BV and is considered as being a ‘‘structure making’’ ion [6,13,26]. The negative values obtained for the quaternary ammonium cations studied here permit their classification as structure making ions. The BV values of the ions increase (become less negative) in the sequence

BV ðsecBu4 NBrÞ < BV ðBu2 secBu2 NBrÞ < BV ðBu2 isoBu2 NBrÞ < BV ðisoBu4 NBrÞ < BV ðBu4 NBrÞ: This tendency is similar to that found for the V°(QA+), with Bu4N+ cation being an exception. According to equation (9) the V°(QA+) values depend on the contribution due to solute–solvent interactions, therefore a relationship between these parameters is completely plausible. However, to understand the behavior of Bu4N+ cation and the tendency of the structural contributions, Vstruct(i), with respect to the BV parameter it is necessary to make further studies in order to have major information. According to table 3 (and figure S1 in Supporting Information), the ionic molar volumes and the structural volumes for symmetrical cations increase when the temperature increases while the differences are not significant for asymmetrical cations. This can be attributed to the breakage of the water structure, which causes an increase in the structural molal volume of the solute. 4. Conclusions The ionic molar volumes and the structural contribution to the ionic volume for the five isomers of tetrabutylammonium cations have been calculated. The results showed that the group contribution methods of chain contribution methods for the calculation of the molar volume are not suitable for quaternary ammonium cation with branched chains. The structural effect of branched chains over linear chains is more pronounced as can be seen for the asymmetrical quaternary ammonium cations. In addition, all cations studied here are classified as ‘‘structure making’’. The dependence of ionic molar volumes with temperature is significant for symmetrical cations but is negligible for asymmetrical cations. Acknowledgement The authors wish to thank the Faculty of Science of the Universidad de los Andes for financial support. Appendix A. Supplementary data

d

D 0 0 1 12 12 0 0 13 0 16

Calculated using equation (11). Calculated according to equation (10) and data reported by Lepori [24]. Calculated according to additivity scheme of chain. D = V°(exp)  V°(calc).

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JCT 13-385