Isopiestic determination of the osmotic and activity coefficients of dilute aqueous solutions of symmetrical and unsymmetrical quaternary ammonium bromides with a new isopiestic cell at 298.15 K

Fluid Phase Equilibria 233 (2005) 230–233

Short communication

Isopiestic determination of the osmotic and activity coefficients of dilute aqueous solutions of symmetrical and unsymmetrical quaternary ammonium bromides with a new isopiestic cell at 298.15 K Eliseo Amado G a,∗ , Luis H. Blanco b,1 b

a IBEAR, Universidad de Pamplona, Bogot´ a, Colombia LIB, Universidad Nacional de Colombia, A.A. 078, Bogot´a, Colombia

Received 15 February 2005; received in revised form 19 April 2005; accepted 19 April 2005

Abstract The osmotic coefficients of Bu4 NBr, sec-Bu4 NBr, iso-Bu4 NBr, Bu2 Et2 NBr and Bu3 EtNBr were determined by isopiestic method at 298.15 K in dilute aqueous solutions. A branched isopiestic cell was used. The osmotic coefficients of tetra-alkyl-ammonium solutions were analyzed comparing these with the Debye–H¨uckel limiting law. The order of the osmotic coefficient variation is Bu2 Et2 N+ > BuEt3 N+ > sec-Bu4 N+ > iso-Bu4 N+ > n-Bu4 N+ . The results were fitted to the Pitzer equation and the parameters β0 and β1 were calculated. The results are discussed. © 2005 Elsevier B.V. All rights reserved. Keywords: Activity coefficient; Osmotic coefficient; Unsymmetrical quaternary ammonium bromides; Pitzer model

1. Introduction

1.1. Theory

The tetra-alkyl-ammonium halides (TAAX, X = Cl, Br, I) were identified early as interesting models for studying hydrophobic phenomena due to their fairly large solubility in water and because of the possibility of changing the length of the alkyl chains as was proposed by Lowe and Rendall [1]. The effects due to the interaction of the apolar groups with the water are known as hydrophobic hydration, and could be the cause of the low solubility as well as of their large positive heat capacity changes upon salvation found by Franks [2]. The first objective of this work is to test the performance of the branched isopiestic cell to get accurate data of osmotic coefficients of aqueous dilute solute solutions of TTA at 298.15 K. The second is to fit the data to a modified equation of the Pitzer model.

The isopiestic method is an accurate way to determine solvent activity using an isopiestic chamber and good thermal contact with sample containers, keeping the whole apparatus at a constant temperature. The vapor space is evacuated and the volatile component is transported through the vapor phase until the solutions reach equilibrium. The quality of the attainment of isopiestic equilibrium depends on the equalization of temperature between the solutions, so that chemical potentials of the solvent in each of the solutions within the isopiestic apparatus must be identical

∗

Corresponding author. Tel.: +57 75686507; fax: +57 75686507. E-mail addresses: [email protected] (E.A. G), [email protected] (L.H. Blanco). 1 Tel.: +57 13150188. 0378-3812/$ – see front matter © 2005 Elsevier B.V. All rights reserved. doi:10.1016/j.fluid.2005.04.012

␮1w = ␮2w = . . . = ␮nw

(1)

An auxiliary function called activity (aw ) is used. The solvent activity is related to the chemical potential by ln aw =

(␮w − ␮0w ) RT

(2)

where aw is the solvent activity, R is the gas constant, ␮0w is the standard state chemical potential of the solvent, and T is

where, F, the long-range electrostatic term, is given by   √   √ 2 I ln(1 + 1.2 I) (9) F = −Aφ √ + 1.2 1 + 1.2 I The value of Aφ is 0.3915 (kg/mol)1/2 In the above equations, I, is the molality based on ionic strength; the equations also contain the following functions
Z= (10) mi |zi | i

√ 0 1 Bca = βca + βca g(αca I)

(11)

0.0911 0.1801 0.3373 0.4305 0.5681 0.6253 0.7850 0.8774 0.9576 1.0052 0.7343 0.6611 0.5851 0.5536 0.5167 0.5032 0.4724 0.4567 0.4448 0.4382 0.9023 0.8719 0.8402 0.8274 0.8071 0.7985 0.7821 0.7723 0.7674 0.7632 0.0908 0.1785 0.3313 0.4214 0.5545 0.6121 0.7646 0.8551 0.9308 0.9752 0.7232 0.6424 0.5561 0.5196 0.4771 0.4617 0.4249 0.4066 0.3917 0.3836 0.8993 0.8614 0.8170 0.7970 0.7721 0.7630 0.7378 0.7259 0.7153 0.7084

(m) (γ ± ) (φ) (m) (φ)

(γ ± )

Bu2 Et2 NBr iso-Bu4 NBr

(m)

0.0911 0.1806 0.3407 0.4375 0.5796 0.6406 0.8105 0.9086 0.9098 1.0505 0.7242 0.6445 0.5601 0.5249 0.4835 0.4682 0.4329 0.4153 0.4010 0.3937 0.8983 0.8622 0.8204 0.8038 0.7721 0.7690 0.7462 0.7351 0.7251 0.7208 0.0912 0.1805 0.3393 0.4338 0.5744 0.6356 0.8014 0.8984 0.9851 1.0325

(8)

a

Units: m (mol kg−1 ). a φ: Osmotic coefficient. b Activity coefficients of the TTA (aq) were calculated from the parameters of the Pitzer equation.

c

0.7212 0.6391 0.5511 0.5136 0.4699 0.4539 0.4163 0.3971 0.3818 0.3738

Aφ I 3/2 2 φ−1 =  2 − √ 1 + 1.2 I i mi

Tφ + mc ma (Bca + ZCca )

0.8979 0.8598 0.8136 0.7922 0.7654 0.7548 0.7294 0.7155 0.7044 0.6987

(7)

c

0.0912 0.1810 0.3421 0.4401 0.5847 0.6475 0.8198 0.9229 0.1014 1.0660

T mc (2Bca + ZCca )

(γ ± )




0.0876 0.1682 0.3023 0.3788 0.4856 0.5299 0.6464 0.7124 0.7691 0.8004

ln(γa ) = z2X F +

(m)

(6)

a

(γ ± )b

T ma (2Bca + ZCca )

(φ)a




(m)

(5)

a

(m)

c

sec-Bu4 NBr

√ 4Aφ I Gex =− ln(1 + 1.2 I) nw RT 1.2

T + mc ma (2Bca + ZCca )

Bu4 NBr

The osmotic coefficient of NaCl was determined as a function of molality and temperature from the extended Bradley–Pitzer correlation proposed by Archer [3]. Osmotic coefficients φ are listed in Table 1. Eq. (1) assumes complete dissociation of both the reference and the studied compounds. Our experimental osmotic coefficients were represented with Pitzer’s equation [4] for an ion-interaction model and modified by Clegg and Whitfield [5] who have been successful to fit osmotic data over a wide range of temperatures. The equations to the activity coefficient and osmotic coefficient of an electrolyte of the 1:1 charge type (the present case) in a solution containing an indefinite number of cations, c, and anions, a, are given by

ln (γc ) = z2c F +

BuEt3 NBr

(4)

NaCl

mNaCl φNaCl m

Table 1 Isopiestic molalities, osmotic and activity coefficients of aqueous solutions of tetra-alkyl-ammomium salts at 298.15 K

φ=

(φ)

Here, νs is the salt stoichiometric coefficient; ms is the salt molality; Mw is the solvent molecular weight, and φr is the practical osmotic coefficient. The osmotic coefficient was calculated form the isopiestic molalities by means of the relationship

0.8989 0.8642 0.8253 0.8100 0.7878 0.7817 0.7618 0.7526 0.7459 0.7404

(3)

(φ)

ln aw = −0.00 1νs ms Mw φ

(γ ± )

the absolute temperature. The water activity can be calculated from

231

0.7250 0.6467 0.5650 0.5314 0.4924 0.4787 0.4461 0.4301 0.4174 0.4104

E.A. G, L.H. Blanco / Fluid Phase Equilibria 233 (2005) 230–233

232

 Bca φ Bca

E.A. G, L.H. Blanco / Fluid Phase Equilibria 233 (2005) 230–233

=

1  αca βca g

=

0 βca

√

I

I

1 + βca exp (−αca

(12) √

I)

T 0 Cca = Cca Tφ

0 |zc za |1/2 Cca = 3Cca

(13) (14) (15)

where g(x) = 2

1 − (1 + x) exp (−x) x2

g (x) = exp (−x) − g(x)

(16) (17)

2. Experimental Details of the apparatus (the isopiestic cell) and general techniques were the same as previously described by Amado and Blanco [6]. The cell has 12 legs. The volume of the cell is approximately 2400-cc. The cell has an evacuation valve on the body. It is attached to an electric motor with an axis inclined at 90◦ , so every sample cup is rotated around the central axis as shown; therefore stirring was provided during the whole equilibrium process. Glass spheres provide additional agitation inside the sample cups. (Fig. 1.)

The 12 cups of the apparatus were set as follows: two cups contained the standard NaCl solutions, nine cups containing the solution of the salts and the remaining cup was used as a water reservoir. Other processes were sometimes used. Fresh, doubly distilled deionized water was used to prepare the solutions. The sample sizes were used in the range 1.2–1.5 g. All the weighings were done around room temperature at 20 ± 2 ◦ C. The analytical balance Metler AT261, used to weigh the sample cups and solution samples has a precision of 1 × 10−5 g. Each isopiestic sample cup was closed at the equilibrium temperature. All apparent sample masses were converted to masses using buoyancy corrections. Both NaCl(aq) isopiestic reference standard stock solutions were prepared by mass from oven-dried analytical reagent grade NaCl (analytical) and purified water. Molar masses used for molality calculations or gravimetric analysis of solutions are 58.443 g mol−1 for NaCl. The average relative uncertainty in the observed water activity was less than 0.005%. Equilibrium isopiestic molalities of the references electrolyte NaCl(aq) and aqueous solutions of the five TTA bromides are listed in Table 1 along with the corresponding osmotic coefficients. The molalities m listed in Table 1 are accurate to ±0.002 m. For some of those equilibrations with shorter times, the air was removed form the branched cell with a vacuum pump until the pressure was ≈4.5 kPa. It was found that with this procedure isopiestic equilibrium was achieved in 5 or 6 days with good consistency between the replicate samples. At low molalities the rate of approach to isopiestic equilibrium is controlled mainly by mass transport through the vapor phase. Isopiestic times of equilibration used in experiments at molalities of m > 0.3 mol kg−1 were typically 6–12 days and good agreement between molalities of replicate samples was achieved with any of these times.

3. Results and discussion

Fig. 1. Isopiestic apparatus. Height with samples cups: 31 cm. Diameter 23 cm. Total volume: 2400 ml. Sample cups (12 cups) are 25 ml flasks equipped with standard taper male ground-glass fittings.

One of the problems in designing the isopiestic apparatus was the choice of the material used to build it. Even glass has a lower thermal conductivity than any metal, to overcome this problem, the isopiestic cell was attached to a motor so it was stirred gently all the time and a glass sphere within the cup provided an additional agitation. Equilibration times were determinate by trial and error. At 298.15 K an equilibration time between 7 and 10 days were required. However, longer equilibrium times were used to reach equilibrium at the lowest molalities. Table 1 contains the osmotic and activity coefficients of aqueous solutions of tetra-alkyl-ammonium salts at 298.15 K. From the osmotic coefficients data shown in Fig. 2, it was noticed that larger deviations from the limiting law to small cations as Bu2 Et2 N+ was found. The order of the osmotic coefficient variation is Bu2 Et2 N+ > BuEt3 N+ > secBu4 N+ > iso-Bu4 N+ > n-Bu4 N+ .

E.A. G, L.H. Blanco / Fluid Phase Equilibria 233 (2005) 230–233

233

Table 2 Coefficients β0 and β1 of ion-interaction parameters obtained by fitting Eq. (8) to experimental data of aqueous solutions of the TTA Br salts Parameter

Bu4 NBr

sec-Bu4 NBr

iso-Bu4 NBr

Bu2 Et2 NBr

BuEt3 NBr

β0 β1 σ(φ)

−0.0898 −0.1963 −0.0004

−0.0735 −0.1855 −0.0002

−0.0828 −0.1846 0.0004

−0.0465 −0.1106 0.0004

0.0525 0.2112 0.0001

σ(φ) Standard error.

The residual values of the data suggest an excellent fit of the data to the Pitzer model with two parameters with a maximum variation around 0.003 (see Fig. 3). Table 2 contains the least-squares coefficient values and their standard errors for fits of the parameters of Eq. (8) to molality data. From the present results and those obtained from the calibration of the cell by Amado and Blanco, 2004, it can be

concluded that the multiple isopiestic cell used here is an appropriate equipment for collecting data of osmotic coefficients at 298.15 K of aqueous solutions of TTA. List of symbols m molality (mol kg−1 ) M molecular weight (g mol−1 ) R gas constant (J mol−1 K−1 ) T absolute temperature (K) Greek letters a activity µ chemical potential (J mol−1 ) ν stoichiometric coefficient φ osmotic coefficient Subscripts o standard state r reference s solute w water or solvent

Fig. 2. Concentration dependence of the osmotic coefficients for aqueous solutions of TTA salts at 298.15 K compared to limiting law.

Acknowledgements The authors are grateful to Professor Simon Clegg for his helpful suggestions. To Dr. D. Archer, N.I.S.T., for his kind collaboration with his computer programs. To Professor Luis F. Hernandez for his critical observations. To Colciencias and Universidad de Pamplona for its financial support.

References

Fig. 3. Differences (residuals) between experimental osmotic coefficients φ and least-squares fit values φ (calc) of TTA salts as a function of m at T = 298.15 K, for fits with the molality region (0–1.00) mol kg−1 using Eq. (8). The parameter C(0) was set equal to zero since it was not significant.

[1] B.M. Lowe, H.M. Rendall, Trans. Faraday Soc. (1971) 2318–2327. [2] F. Franks (Ed.), Water: A Comprenhensive Treatise, vol. 2, Plenum Press, New York, 1973, p. 353. [3] D.G. Archer, J. Phys. Chem. Ref. Data 28 (1999) 1–17. [4] K.S. Pitzer, J. Phys. Chem. 77 (1973) 268–277. [5] S.L. Clegg, M. Whitfield, in: K.S. Pitzer (Ed.), Activity Coefficients in Electrolyte Solutions, 2nd ed., CRC Press, Boca Raton, FL, 1991, pp. 279–434. [6] E. Amado, L.H. Blanco, Fluid Phase Equilibr. 226 (2004) 261– 265.