Conductance of Some Higher Homologues of Quaternary Ammonium Bromide Salts in 2-Butoxyethanol (1) + Water (2) Mixtures at 298.15, 303.15, 308.15, and 313.15 K

Abstract

Conductance data of some higher homologues of quaternary ammonium salts, namely, tetrapentylammonium bromide (Pen₄NBr), tetrahexylammonium bromide (Hex₄NBr), and tetraheptylammonium bromide (Hep₄NBr) 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 1978 Fuoss conductance-concentration equation was used to analyze the measured experimental conductance data. The values of limiting molar conductance ($\Lambda^{0}$), ionic association constant (K_A) and the association diameter (R) were obtained from the analysis. The ionic contributions to the limiting molar conductances were estimated using tetrabutylammonium tetraphenylborate (Bu₄NBPh₄) as the “reference electrolyte”. A weak electrostatic ion solvent interaction was observed for these three salts from their calculated K_A and R values. The study also revealed that in all solvent compositions and experimental temperatures, these salts exist as free ions. The association constants of the electrolytes do not vary significantly as a function of temperature. However, as the temperature was increased or solvent compositions were changed, a noticeable variation in the single-ion conductivity values as well as Walden product for the ions were seen.

1 Introduction

Transport properties of electrolytes are frequently used to understand the ion behavior of electrolytes in different solvent media. Quaternary ammonium salts show numerous interesting properties in solution. Owing to low surface charge density, these salts demonstrate very little solvation [1, 2] in solution. As such, quaternary ammonium salts are often selected as desired electrolytes in conductance studies. The solvent, 2-butoxyethanol (BE) is the third homologue of the class of compounds commercially known as cellosolves. Like the other members of this class, BE is also used extensively in industry and modern technologies. It is well-known that, in water-rich mixtures, BE exists as a molecular dispersion in water, but as the mixture enrich with BE, a radical change of the mixture structure occurs and a micelle-like aggregation [3,4,5,6] of BE in the mixture takes place. Thus, studies of electrolyte in such an uncharacteristic solvent media may provide interesting information on solution properties of the system.

Transport properties of electrolytes in the lower members of cellosolves and their aqueous mixtures have been studied by many researchers [7,8,9,10,11,12,13,14]. However, less attention is being drawn on these studies, particularly in the case of quaternary ammonium salts, in BE and their mixtures with water. The situation is somewhat better with the lower homologues [15, 16] of quaternary ammonium salts in BE. But, conductance studies of higher homologues of quaternary ammonium salts in 2-butoxyethanol are absent.

Conductance method [1, 17,18,19] is considered as one of the best method for the investigation of the ion–solvent and ion–ion interactions in electrolyte solutions. One can obtain the values of limiting conductance of an electrolyte at infinite dilution ($\Lambda^{0}$), ionic association constant (K_A), and the association diameter (R) from conductance data as a function of concentration, by using an appropriate conductance equation. However, it is important to select an appropriate conductance equation to analyze conductance data in order to attain a highly precise result [20, 21]. Many conductance equations are available in the literature for analyzing conductance data of electrolytes in solutions. Owing to its capability of accommodating more variables than the primitive models, we rely on the Fuoss 78 conductance-concentration equation [22, 23] for analyzing our conductance data.

In this paper we report the equivalent conductivities of tetrapentylammonium bromide (Pen₄NBr), tetrahexylammonium bromide (Hex₄NBr) and tetraheptylammonium bromide (Hep₄NBr), 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 obtain precise temperature-dependent single-ion conductivities, since such data are relatively scarce in mixed solvent media [1, 24]. The values of Walden product for the ions at variable temperature and solvent compositions are also shown.

2 Experimental

2.1 Chemicals

2-Butoxyethanol (E. Merck India with a purity > 99%) was dried with potassium carbonate and fractionally distilled before the use. The middle fraction was collected and redistilled. The density (ρ₀) and the coefficient of viscosity (η₀) of the distilled BE at 298.15 K were 0.89616 g·cm⁻¹ and 2.7820 mPa·s respectively. These values agree well with the reported literature values [25, 26] of pure BE. The mixed solvents were prepared in a dehumidified room with triply-distilled water of specific conductance value ~ 10^–6 S·cm⁻¹. The measured values of density and viscosity of the mixed solvents at (298.15, 308.15, 313.15, and 318.15) K are shown in Table 1. With the help of density and relative permittivity values of the pure solvents [25, 26] at experimental temperatures and following the method of literature [27], the relative permittivities of the solvent mixtures were evaluated and are also included in Table 1.

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 MPa) and at different temperatures

Quaternary ammonium bromide salts were of Fluka’s purum or puriss grade (Switzerland, 99.8% pure).

Tetrapentylammonium bromide (Pen₄NBr) was recrystallised from a mixture of acetone and ether and dried in vacuum at 333 K for 48 h. Tetrahexylammonium bromide (Hex₄NBr) and Tetraheptylammonium bromide (Hep₄NBr) were washed with ether and dried in vacuum at room temperature for 48 h.

2.2 Experimental

A Systronics (India) μ-Controller Based Conductivity-TDS Meter having an accuracy of 0.15% was used for the measurements of specific conductance. A dip-type conductance cell with platinum black coated electrode was used. The cell constant (1.11 cm⁻¹) of the conductance cell was accurately determined by measuring the specific conductance of standard aqueous KCl solutions according to the method of Lind and co-workers [30]. To prevent the admission of air into the cell, a dry and pure nitrogen gas was passed through the solutions before each conductance measurement. All experiments were carried out in a thermostatic water bath operating with an accuracy of ± 0.05 K. The detailed experimental procedure has been described earlier [31,32,33]. Molar solutions were prepared for conductance measurement. The densities of these molar solutions were measured with an Ostwald-Sprengel type pycnometer of about 25 ml capacity and 1 mm internal capillary diameter. The pycnometer was calibrated at experimental temperatures with doubly distilled water. The precision of the density measurements was ± 5 × 10⁻⁵ g·cm⁻¹. Molar solutions were converted to molal solutions with the help of measured density data. Several solutions of the same concentration were prepared and experiments were repeated in order to get a precise result. Due correction was made for the influence of solvent on the conductivity of the solutions by subtracting the specific conductance of the respective solvent medium from those of the salt solutions. For the measurement of kinematic viscosities of solvents a suspended level Ubbelohde-type viscometer with a flow time of about 539 s for distilled water at 298.15 K was used. The time of efflux was measured with a stop watch capable of recording ± 0.1 s. The calibration of the viscometer was done by using distilled water and methanol as the calibrating liquids at experimental temperatures. The viscometer constants C and K were found to be 1.648 × 10⁻⁵ cm¹·s⁻² and (− 0.02332) cm² respectively. All solutions were prepared with utmost care in a dehumidified room to avoid moisture pickup.

3 Results and Discussion

The variation of experimental conductances (Λ) of electrolyte solutions with molal concentration (m) in mixed solvent media with different mass fractions of 2-butoxyethanol at 298.15, 303.15, 308.15 and 313.15 K are shown in Table 2.

Table 2 Conductances ($\Lambda$) and corresponding molalities (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) K ^a

The 1978 Fuoss conductance concentration equation [22, 23] was used to study the conductance data. In this analysis, the three parameters namely, the limiting conductances ($\Lambda^{0}$), association constant (K_A), and the association diameter (R) were calculated for a given set of molal concentration and equivalent conductance values (c_j, Λ_j; j = 1, …, n). These three parameters are related by the following Eqs.:

$$\Lambda = p[\Lambda ^{0} \left( {1 + RX} \right) + EL]$$

(1)

$$p = 1 - \alpha \left( {1 - \gamma } \right)$$

(2)

$$\gamma = {1} - K_{{\text{A}}} m\gamma^{{2}} f^{{2}}$$

(3)

$$- {\text{1n}}f = \frac{\beta k}{{2\left( {1 + kR} \right)}}$$

(4)

$$\beta = \frac{{e^{2} }}{{\varepsilon k_{{\text{B}}} T}}$$

(5)

$$K_{{\text{A}}} = K_{{\text{R}}} \left( {1 + K_{{\text{S}}} } \right)$$

(6)

where RX is the relaxation field effect, EL is the electrophoretic countercurrent, $\gamma$ is the fraction of unpaired ions, and $\alpha$ is the fraction of contact-pairs, K_A is the overall pairing constant evaluated from the association constants of contact-pairs, K_S, and of solvent-separated pairs, K_R, $\varepsilon$ is the relative permittivity of the solvent, e is the electron charge, k_B is the Boltzmann constant, k⁻¹ is the radius of the ion atmosphere, c is the molal concentration of the solution, f is the activity coefficient, T is the temperature in absolute scale, and $\beta$ is twice the Bjerrum distance.

The three parameters ($\Lambda^{0}$_, K_A, R) were calculated by an iterative computer program as suggested by Fuoss. The input data set for the program is (c_j,Λ_j; j = 1,….., n), n, $\varepsilon$, $\eta$, T, M₁ and M₂ and an initial value of $\Lambda^{0}$. The initial values of $\Lambda^{0}$ for the iteration procedure were obtained from Shedlovsky extrapolation [34] of the experimental conductance data. The program also contains an instruction to cover a given range (4 to 20 $\Lambda^{0}$) of R values.

To ensure convergence, the values of $\Lambda^{0}$ and r are computed which minimize the standard deviation,$\sigma$,

$$\sigma = \left[ {{{\sum {\left[ {\Lambda_{j} \left( {{\text{calcd}}} \right) - \Lambda_{j} \left( {{\text{obsd}}} \right)} \right]}^{2} } \mathord{\left/ {\vphantom {{\sum {\left[ {\Lambda_{j} \left( {{\text{calcd}}} \right) - \Lambda_{j} \left( {{\text{obsd}}} \right)} \right]}^{2} } {\left( {n - 2} \right)}}} \right. \kern-\nulldelimiterspace} {\left( {n - 2} \right)}}} \right]^{1/2}$$

(7)

When $\sigma$(%) 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 $\sigma$(%) 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 ion-pair 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 by [23]

$$d = {1}.{183}\left( {M/\rho_{0} } \right)^{{{1 \mathord{\left/ {\vphantom {1 3}} \right. \kern-\nulldelimiterspace} 3}}}$$

(8)

where M and $\rho_{0}$ are the mole fraction average molecular weight and the density of the mixed solvent respectively.

The computed values of $\Lambda^{0}$, K_A, and R are shown in Table 3. The variation of the experimental equivalent conductivity as a function of molal concentration of Pen₄NBr, Hex₄NBr and Hep₄NBr along with the corresponding fitted profiles according to Eqs. 1 through 6 in BE (1) + water (2) mixtures with mass fraction 0.20 at 298.15, 303.15, 308.15, and 313.15 K are shown in Fig. 1.

Table 3 Derived conductance parameters (limiting conductance, 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

Fig. 1

Variation of conductance as a function of concentration for: a Pen₄NBr; b Hex₄NBr; and c Hep₄NBr in 2-butoxyethanol (1) + water (2) with w₁ = 0.02. Experimental: ●, 298.15 K; ■, 303.15 K; ▲, 308.15 K; and, ▼, 313.15 K. The fitted lines represent the calculations according to Eqs. 1 through 6

The ionic conductivities of Br⁻ ion were calculated from the known [15] $\Lambda^{0}$ values of sodium bromide (NaBr), sodium tetraphenylborate (NaBPh₄) and tetrabutylammonium bromide (Bu₄NBr) at 298.15, 303.15, 308.15, and 313.15 K. The limiting ionic conductivities of other ions were computed using the calculated ionic conductivities of Br⁻ ions at the experimental temperatures. From the literature, values of ionic radii (r_ion), using the reference electrolyte salt, tetrabutylammonium tetraphenylborate (Bu₄NBPh₄), the following quotients were computed:

$$\Lambda^{0} \left( {{\text{Bu}}_{{4}} {\text{NBPh}}_{{4}} } \right) = \lambda^{{0}} \left( {{\text{Bu}}_{{4}} {\text{N}}^{ + } } \right) + {\lambda }^{{0}} \left( {{\text{Ph}}_{{4}} {\text{B}}^{ - } } \right)$$

(9)

$$\frac{{\lambda^{{0}} \left( {{\text{Bu}}_{{4}} {\text{N}}^{ + } } \right)}}{{\lambda^{{0}} \left( {{\text{Ph}}_{{4}} {\text{B}}^{ - } } \right)}} = \frac{{{{r}}\left( {{\text{Ph}}_{{4}} {\text{B}}^{ - } } \right)}}{{{r\text{(Bu}}_{{4}} {\text{N}}^{ + } {)}}} = \frac{5.35}{{5.00}}$$

(10)

$$\lambda^{0} ({\text{Bu}}_{{4}} {\text{N}}^{ + } ) = 0.517\Lambda^{0} ({\text{Bu}}_{{4}} {\text{NBPh}}_{{4}} )$$

(11)

Kohlrausch law of independent migration of ions was employed (Eq. 12) to derive the $\Lambda^{0}$ values of Bu₄NBPh₄ by combining $\Lambda^{0}$ values of NaBr, NaBPh₄ and Bu₄NBr.

$$\Lambda^{0} \left( {{\text{Bu}}_{{4}} {\text{NBPh}}_{{4}} } \right) \, = \Lambda^{0} \left( {{\text{Bu}}_{{4}} {\text{NBr}}} \right) \, + \Lambda^{0} \left( {{\text{NaBPh}}_{{4}} } \right) - \Lambda^{0} \left( {{\text{NaBr}}} \right)$$

(12)

The single-ion conductivities ($\lambda^{0}$) calculated from the above equations as well as ionic Walden products ($\lambda^{0} \eta_{0}$) are shown in Table 4.

Table 4 Limiting ionic conductivities, Walden Product and Stokes radii (r_s) 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

Table 3 shows that the limiting molar conductivities of the tetraalkylammonium bromides decrease with increasing length of the alkyl chain. Similar observations were noticed with earlier findings in several pure and mixed solvents [1]. A careful observation of the Fig. 1 reveals that the fitted limiting molar conductivities for all electrolytes are always greater than that obtains from Shedlovsky extrapolation. Such deviation is due to the fact that the fitted results are derived using Fuoss’ 78 model which is based upon the characteristic of real physical systems and eliminates a number of artifacts that are properties of the primitive model. A direct comparison of our result with those derived from the primitive model is beyond the scope as such results are not available in the literature for this system.

Very low values (Table 3) of the association constants (K_A), ranging from 3 to 19, were obtained for all the three electrolytes under the experimental conditions. This indicates that there is little association of the ions [35] and that they move as free ions in the solutions throughout the experimental range of mixed solvent media and the temperature range studied. As the relative permittivities of the solvent mixtures (33.43 ≤ $\varepsilon$ ≥ 71.56) were reasonably high (Table 1), the dissociation of electrolytes became favorable. The most outstanding feature of the association constant given in Table 3 is the fact that the salt containing larger ions shows comparatively more association. Furthermore, the process of ionic association in 2-BE does not exhibit the simple dependence upon ionic size predicted by electrostatic theory. This type of behavior has also been reported for tetraalkylammonium salts in other solvents [11, 12]. However, an increase in the temperature results in a negligible decrease in association constant.

The association diameter (R) values for the salts under study in BE (1) + water (2) mixtures are also reported in Table 3. No systematic trend in the R values for the salts has been observed. Because the best-fit conductivity parameters were found to be reproduced almost equally over a wide range of arbitrarily chosen R values, a comprehensive correlation of association diameter of the investigated system could not be made in the present situation. This type of behavior has also been reported earlier [35, 36]. The R values, deviates considerably from the sum of radii of the ions [1] constituting the electrolytes, thus indicating ionic solvation.

From Table 4 it is clear that limiting ionic conductivities values of tetrapentylammonium ion (Pen₄N⁺) were always higher as compared to tetrahexylammonium (Hex₄N⁺) or tetraheptylammonium ion (Hep₄N⁺) ion. This indicates that in all of the mixed solvent media over the entire temperature range investigated, the tetrapentylammonium ion has a greater ionic mobility than the tetrahexylammonium or tetraheptylammonium ion. Generally, the lower the crystallographic sizes of the bare ions, the lower are the ionic mobilities, as the smaller ions associate with more solvent molecules due to their greater surface charge density. Though the crystallographic sizes of the investigated ions follow the order [36] Pen₄N⁺  < Hex₄N⁺  < Hep₄N⁺, a reverse order of ionic mobilities was seen for these ions. This is probably due to very weak electrostatic ion–solvent interaction of these ions in aqueous 2-butoxyethanol solutions. Otherwise, the limiting ionic conductivities values of these ions should have been following the order: Pen₄N⁺  < Hex₄N⁺  < Hep₄N⁺, which is obviously not the case here. A similar conclusion might be ascribed for the trend of the Walden product values ($\lambda^{0} \eta_{0}$) in Table 4.

From Table 4 it is clear that the values of Walden product ($\lambda^{0} \eta_{0}$) for the ions become irregular when the temperature of the system is varied. However, Stokes law does not “allow” such variations in the Walden product [37] with temperature. Thus, in the studied solvent mixtures Stokes law does not hold good. Similar temperature driven irregularities for Walden product values have also been observed in other solvent media [13, 38].

4 Conclusions

The present investigation indicates that for all three quaternary ammonium salts, namely, tetrapentylammonium bromide, tetrahexylammonium bromide and tetraheptylammonium bromide, the association constants values are very low and they exist as free ions in all solvent compositions and the temperature range covered in the investigation. This is probably due to very weak electrostatic ion–solvent interaction of these ions in aqueous 2-butoxyethanol solutions. For these salts, deviation of association diameter values from the sum of radii of the ions indicates ionic solvation. The Walden product values of these quaternary ammonium ions do not remain constant, when the temperatures of the mixed solvent system undergo a change. Both the limiting equivalent conductances of the electrolytes and the single-ion conductivity values of ions amplify with the increase in temperature, but a reverse trend is observed for these two parameters with increase of 2-butoxyethanol in the mixed solvent media in all the experimental temperatures.