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Fluid Phase Equilibria 250 (2006) 66–71

Vapor pressures and osmotic coefficients of the acetone solutions of three bis(tetraalkylammonium)tetrathiomolybdates at 298.15 K measured by head-space gas chromatography Moayad Hossaini Sadr, Jaber Jahanbin Sardroodi ∗ Department of Chemistry, Faculty of Sciences, Azarbaijan University of Tarbiat Moallem, Tabriz, Iran Received 31 May 2006; received in revised form 13 September 2006; accepted 18 September 2006

Abstract The vapor pressures and osmotic coefficients of solutions of (R4 N)2 [MoS4 ] (R = ethyl, n-propyl and n-butyl) in acetone have been measured by head space-gas chromatography (HS-GC). Experimental data for the osmotic coefficients have been expressed by three thermodynamic models including the ionic interaction model of Pitzer, the electrolyte non-random two liquid (e-NRTL) model and the non-random factor (NRF) model. The ability of the models to fit the osmotic coefficient was compared on the basis of the standard deviation of the fittings. The results show that the considered models provide reliable results, but the Pitzer’s model gives better results than the NRTL and the NRF methods, especially in the dilute region. © 2006 Published by Elsevier B.V. Keywords: Vapor pressure; Osmotic coefficient; Tetrathiomolybdate; Local composition models; Gas chromatography

1. Introduction The chemistry of [MS4 ]2− (M = Mo, W) anions and their related compounds has been extensively investigated because of their relevance for biological systems, rich structural chemistry, industrial applications and special reaction properties as well as their applications as starting reagents in preparation of novel optical (NLO) materials [1–15]. Currently, tetrathiomolybdates have received a great deal of attention due to their possible role in the treatment of some diseases such as metastatic cancer and Wilson’s disease [16–19]. In this regard, investigation on the solution chemistry of these compounds in various solvents may play a key role in the understanding the unique properties of [MS4 ]2− multifunctional anion. Additionally, these compounds, due to the sizes and structures of their anion and cation, could be used as suitable candidates for physicochemical investigations of electrolyte solutions, similar to other tetraalkylammonium salts [20]. Continuing our interest in heterothiometallic cluster chemistry [21–26], in this paper we focus on the thermodynamic properties of the acetone solutions of different salts of tetrathiomolybdate dianion, (Et4 N)2 [MoS4 ], ∗

Corresponding author. Tel.: +98 412 4524991; fax: +98 412 4524991. E-mail address: [email protected] (J.J. Sardroodi).

(n-Pr4 N)2 [MoS4 ] and (n-Bu4 N)2 [MoS4 ]. The vapor pressures and osmotic coefficients of the solutions of the aforementioned solutions are reported. The activity coefficient of the solvent has been evaluated from the osmotic coefficients. The osmotic coefficients have been correlated using the Pitzer ion interaction model [27] and two local composition models. The local composition models used here for data correlation are the electrolyte non-random two liquid (e-NRTL) model [28] and the non-random factor (NRF) model [29]. 2. Experimental 2.1. Materials Acetone was purchased from Merck Company (maximum 0.01% H2 O, SeccoSolv® ) and used without further purification. The different tetrathiomolybdate salts were prepared and purified by published procedures [30–32]. 2.2. Method and apparatus Head space-gas chromatography has been used to determine activity coefficients in various mixtures [33,34] including nonaqueous electrolyte solutions [35]. Following the standard rela-

0378-3812/$ – see front matter © 2006 Published by Elsevier B.V. doi:10.1016/j.fluid.2006.09.015 FLUID-7390; No. of Pages 6

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tions, the vapor pressure of the solvent over the studied solutions (p) is evaluated with the help of the equation: D p = p0 D0

(1)

in which p and D are, respectively, vapor pressure and response of detector; subscript 0 refers to the pure solvent. Since for the studied solutions 1 < p/p0 < 1.2, the detector response will be linear and consequently we can use Eq. (1). A Shimadzu model GC-16A gas chromatograph equipped with FID detector was used. Solutions of (R4 N)2 [MoS4 ] in acetone were prepared gravimetrically and thermostatted (25 ± 0.005 ◦ C) with a Heto temperature controller (Hetotherm PF, Heto Lab Equipment, Denmark). Samples (0.3 ml) of the head-space above the solution were taken using a 1 ml gas-tight syringe (Hamilton) and injected into the gas chromatograph and the value of peak area as detector response (D) was measured. Then the same volume of the vapor above the pure solvent (thermostatted at 25 ± 0.005 ◦ C) was injected and the value of peak area as detector response (D0 ) was also measured. Usually samples at time intervals of 2 h of interval time (time necessary for equilibrium to be established between the gas phase and liquid phase) were injected. All measurements were repeated four to six times and the standard deviation of activity was calculated and found to be in the range of 0.0002–0.001, which assured us of the reproducibility of the measurements. After the vapor pressures were measured, the activity of acetone (a1 ), activity coefficient of acetone (γ 1 ) and osmotic coefficient (Φ) of the investigated solutions were calculated using the following equations [36]:   (B1 − V¯ 1 )(p − p0 ) p ln a1 = ln + (2) p0 RT Φ=−

ln(a1 ) νmM1

ln(γ1 ) = ln(a1 ) − ln(x1 )

(3) (4)

in which B1 , V¯ 1 , M1 and x1 are the second virial coefficient of the pure acetone, the molar volume of the pure acetone, molar mass of acetone (in kg mol−1 ) and mole fraction of acetone (x1 = 1 − xc − xa ; xc = mole fraction of cation and xa = mole fraction of anion), respectively; ν and m are, respectively, the number of ions in one molecule of the salt and the molality of the solution. The values of −2.13 × 10−3 m3 mol−1 , 7.4047 × 10−5 m3 mol−1 and 30,803 Pa have been taken from Ref. [37] and have been used for B1 , V¯ 1 and p0 , respectively. 3. Correlation of data Several models are available in the literature for modeling the thermodynamic properties of electrolyte solutions. Among these models, the Pitzer model has been used widely because of its simplicity and high precision. This model has three or four adjustable parameters for a binary electrolyte solution dependent on the stoichiometry of salt. Usually for 1:1, 2:1 and 1:2 salts in aqueous media the Pitzer model is used in threeparameter form; while, for 2:2 and higher stoichiometry in

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aqueous media or for 1:1, 1:2 and 2:1 salts in non-aqueous solvents its four-parameter form is applied [38]. In the present work, the Pitzer model with four adjustable parameters works better and we used it for correlation of experimental osmotic coefficient data. The four-parameter Pitzer equation has the following form for the osmotic coefficient of a binary electrolyte solution [38]: 4 21.5 2 Φ m C Φ = 1 + 2f Φ + mBΦ + 3 3

(4a)

where f

Φ

√ AΦ I √ =− 1+b I

√ √ BΦ = β(0) + β(1) exp(−α1 I) + β(2) exp(−α2 I)

(4b) (4c)

In these equations β(0) , β(1) , β(2) and CΦ are adjustable parameters of the model obtained by the fitting of the Eq. (4a) to the osmotic coefficients; α1 , α2 and b are also the constant parameters of the model. The results show that for the investigated solutions the best values of the α1 , α2 and b parameters are 0.2, 5 and 3.2 (all in kg0.5 mol−0.5 ), respectively. AΦ is the Debye–H¨uckel constant for osmotic coefficients and in the case of acetone solutions at 25.0 ◦ C it has the value of 0.080905 kg0.5 mol−0.5 (calculated by using the values given in Ref. [37]). Another category of the electrolyte solutions models are local composition (LC) theories. The electrolyte non-random two liquid model (e-NRTL) [28] and the non-random factor model (NRF) [29] used here belong to this category. In the LC models it is assumed that the non-ideal behaviour of electrolyte solutions has two contributions, namely long-range (LR) and shortrange (SR) contributions. The LR contribution is expressed by Pitzer–Debye–H¨uckel (PDH) equation, which is an extended form of the Debye–H¨uckel equation, and the SR contribution is expressed by equations obtained by the model. The PDH equation for the activity coefficient of the solvent is given by [39]:    AΦ Ix1.5 1 √ ln γ1,PDH = 2 (5) M1 1 + ρ Ix in which ρ and Ix are the closest distance parameter and the ionic strength on a mole fraction basis, respectively. It has been proven that a value of 14.9 is the best choice for the ρ parameter in aqueous solutions at 298.15 K [28,39]. However, data analysis shows that the same value for the ρ parameter gives the best results for the studied solutions; so, for the present case, we use the value of 14.9 for this parameter. The detailed forms of the model equations for the used LC models are given in Appendix A. 4. Results and discussions The D/D0 ratio, vapor pressures, osmotic coefficients and activity coefficients of acetone in the studied solutions are summarized in Tables 1–3. The vapor pressures and osmotic coef-

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Table 1 Vapor pressures, osmotic coefficients and activity coefficient of acetone in the solutions of (Et4 N)2 [MoS4 ] in acetone at 25.0 ◦ C

Table 3 Vapor pressures, osmotic coefficients and activity coefficient of acetone in the solutions of (n-Bu4 N)2 [MoS4 ] in acetone at 25.0 ◦ C

m (mol kg−1 )

D/D0

p (kPa)

Φ

ln(γ 1 )

m (mol kg−1 )

D/D0

p (kPa)

Φ

ln(γ 1 )

0.0000 0.0235 0.0524 0.0963 0.1321 0.1921 0.2558 0.3231 0.3760 0.4051 0.437 0.4705 0.5011 0.5070 0.5281 0.5543 0.5765 0.5930 0.6437 0.6656 0.7156 0.7922 0.8561 0.9022 0.9178 1.0079 1.0935

1.00000 0.99828 0.99695 0.99497 0.99321 0.98971 0.98539 0.98052 0.97549 0.97263 0.96880 0.96491 0.96085 0.96013 0.95715 0.95358 0.95030 0.94757 0.93887 0.93462 0.92494 0.90722 0.89128 0.87761 0.87352 0.84557 0.81833

30.803 30.750 30.709 30.648 30.594 30.486 30.353 30.203 30.048 29.960 29.842 29.722 29.597 29.575 29.483 29.373 29.272 29.188 28.920 28.789 28.491 27.945 27.454 27.033 26.907 26.046 25.207

1.000 0.407 0.324 0.292 0.288 0.300 0.321 0.340 0.368 0.382 0.405 0.424 0.445 0.448 0.463 0.479 0.494 0.507 0.5478 0.568 0.609 0.687 0.752 0.809 0.824 0.931 1.026

0.0000 0.0024 0.0061 0.0117 0.0161 0.0229 0.0293 0.0356 0.0393 0.0412 0.0425 0.0440 0.0448 0.0451 0.0454 0.0459 0.0461 0.0459 0.0449 0.0439 0.0415 0.0345 0.0269 0.0188 0.0166 −0.0017 −0.0211

0.0000 0.0211 0.0471 0.0866 0.1188 0.1727 0.2531 0.2905 0.3380 0.3642 0.3929 0.4230 0.4505 0.4558 0.4748 0.4983 0.5183 0.5331 0.5787 0.5984 0.6433 0.6763 0.7122 0.7436 0.7741 0.8111 0.8251

1.00000 0.99834 0.99718 0.99536 0.99412 0.99166 0.98461 0.98107 0.97653 0.97335 0.96439 0.95332 0.93958 0.93059 0.90618 0.89284 0.88680 0.87829 0.87478 0.86287 0.85888 0.85222 1.00000 0.99834 0.99718 0.99536 0.99412

30.803 30.743 30.704 30.650 30.598 30.506 30.340 30.235 30.107 30.021 29.918 29.810 29.692 29.659 29.583 29.465 29.354 29.274 29.010 28.892 28.583 28.343 28.048 27.773 27.505 27.180 27.035

1.000 0.513 0.381 0.322 0.314 0.313 0.334 0.358 0.377 0.394 0.414 0.432 0.456 0.464 0.475 0.498 0.519 0.533 0.579 0.598 0.650 0.688 0.735 0.778 0.818 0.863 0.884

0.0000 0.0018 0.0050 0.0101 0.0140 0.0202 0.0284 0.0313 0.0350 0.0365 0.0379 0.0392 0.0398 0.0396 0.0402 0.0400 0.0396 0.0393 0.0377 0.0368 0.0334 0.0303 0.0257 0.0210 0.0162 0.0103 0.0072

ficients of the studied solutions versus molality show that the vapor pressure for the solutions of (Et4 N)2 [MoS4 ] is the highest and for the solutions of (n-Bu4 N)2 [MoS4 ] is the lowest (Figs. 1 and 2). This trend is probably caused by the higher surTable 2 Vapor pressures, osmotic coefficients and activity coefficient of acetone in the solutions of (n-Pr4 N)2 [MoS4 ] in acetone at 25.0 ◦ C m (mol kg−1 )

D/D0

p (kPa)

Φ

ln(γ 1 )

0.0000 0.0190 0.0425 0.0780 0.1070 0.1557 0.2618 0.3047 0.3521 0.3805 0.4557 0.5281 0.6037 0.6483 0.7505 0.8011 0.8247 0.8544 0.8699 0.9111 0.9234 0.9481

1.00000 0.99834 0.99718 0.99536 0.99412 0.99166 0.98461 0.98107 0.97653 0.97335 0.96439 0.95332 0.93958 0.93059 0.90618 0.89284 0.88680 0.87829 0.87478 0.86287 0.85888 0.85222

30.803 30.752 30.716 30.660 30.622 30.546 30.329 30.220 30.080 29.982 29.706 29.365 28.942 28.665 27.913 27.502 27.316 27.054 26.946 26.579 26.456 26.251

1.000 0.487 0.372 0.332 0.307 0.300 0.331 0.350 0.377 0.397 0.444 0.506 0.577 0.620 0.734 0.791 0.815 0.849 0.860 0.906 0.9226 0.944

0.0000 0.0017 0.0046 0.0090 0.0127 0.0186 0.0295 0.0331 0.0364 0.0379 0.0411 0.0415 0.0393 0.0370 0.0269 0.0203 0.0172 0.0123 0.0108 0.0036 0.0009 −0.0030

face charge density of Et4 N+ (or its larger charge-to-size ratio) as well as by the lower surface charge density of n-Bu4 N+ . Higher surface charge density leads to stronger ionic association and higher vapor pressure. On the other hand, the lower vapor pressure of the solutions of (n-Bu4 N)2 [MoS4 ] is probably due to the

Fig. 1. Vapor pressures of the solutions of (R4 N)2 [MoS4 ] in acetone at 298.15 K vs. molality of the salt.

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Fig. 3. Experimental and predicted osmotic coefficients of the solutions of (Et4 N)2 [MoS4 ] in acetone at 298.15 K.

Fig. 2. Osmotic coefficients of the solutions of (R4 N)2 [MoS4 ] in acetone at 298.15 K vs. molality of the salt. Table 4 Pitzer model parameters for the studied solutions (α1 = 0.2, α2 = 5 and b = 3.2) Salt

β(0)

β(1)

β(2)

CΦ

σ(Φ)

(Et4 N)2 [MoS4 ] (n-Pr4 N)2 [MoS4 ] (n-Bu4 N)2 [MoS4 ]

9.1441 12.2585 11.0980

−12.1608 −15.7575 −14.4974

−53.3820 −48.3110 −46.3219

−0.3986 −0.7480 −0.4792

0.013 0.015 0.005

Table 5 e-NRTL model parameters for the studied systems (ρ = 14.9 and α = 0.2) Salt

τ ca,m

τ m,ca

σ(Φ)

(Et4 N)2 [MoS4 ] (n-Pr4 N)2 [MoS4 ] (n-Bu4 N)2 [MoS4 ]

−4.7383 −4.8179 −4.8879

11.2376 11.4292 11.5258

0.126 0.132 0.106

greater non-electrostatic solute–solvent interactions, caused by its larger size and mass. The model parameters and standard deviation in osmotic coefficient have been collected as Tables 4–6. Standard deviation in osmotic coefficient, σ(Φ), is defined as:   2 i (Φcal − Φexp ) (6) σ(Φ) = N where cal, exp and N stand for calculated value, experimental data and the number of data points, respectively. It is clear from these tables that the Pitzer model correlates the data with Table 6 NRF model parameters for the studied systems (ρ = 14.9 and Z = 8) Salt

λS

λE

σ(Φ)

(Et4 N)2 [MoS4 ] (n-Pr4 N)2 [MoS4 ] (n-Bu4 N)2 [MoS4 ]

−13.8076 −14.3203 −14.5685

18.2796 20.2051 22.2130

0.163 0.169 0.138

an excellent precision, but the e-NRTL or the NRF models do not work satisfactory. This probably results from the large sizes of anions and cation, complex ion–ion or ion–solvent interactions such as ion association or ion solvation processes, which are not considered by these models. The large sizes of ions in the studied solutions perhaps affect the local cells defined in the LC theory; therefore, the basic assumptions of e-NRTL and NRF models, possibly, are not valid. Fig. 3 includes the experimental osmotic coefficients and those calculated from the considered models for (Et4 N)2 [MoS4 ]. This figure shows that the Pitzer model describes excellently osmotic coefficients in the entire concentration range. However, calculated osmotic coefficients produced by e-NRTL and NRF models have considerable deviations from experimental values, especially in the dilute region (m < 0.4 mol kg−1 ). In the concentrated region, e-NRTL and NRF models give better fittings compared to their fittings in the dilute region. The parameters of the studied models can be used for qualitative molecular interpretation of the experimental results. The numerical value of the β(2) parameter of the Pitzer’s model is a measure of the extent of the ion-association that occurs in the solution. Table 4 shows that the numerical value of this parameter for (Et4 N)2 [MoS4 ] is the greatest, so the extent of ion association for this salt is higher. This is consistent with the experimental observation that the highest vapor pressure is found for the solutions of the (Et4 N)2 [MoS4 ] salt. Furthermore, model parameters of e-NRTL and NRF models are related to the ion–solvent, solvent–solvent and ion–ion interactions in the solution via the following equations:     gam − gmm gcm − gmm = exp (7a) τca,m = exp RT RT     gmc − gac gma − gca = exp (7b) τm,ca = exp RT RT λE =

ge − ges RT

(8a)

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ges − gss RT

(8b)

in which gij , c, a and m are the interaction energy between i and j pair, cation, anion and solvent, respectively. According to these equations, as the ion–solvent interactions get stronger (larger gcm , gam , gma , gmc and ges values), the absolute value of the model parameters get larger. Data of Tables 5 and 6 show that the absolute values of these parameters and consequently the ion–solvent interactions in the studied solutions exhibit the following order which is the reverse of the order of vapor pressures: (Et4 N)2 [MoS4 ] < (n-Pr4 N)2 [MoS4 ] < (n-Bu4 N)2 [MoS4 ] 5. Conclusions The vapor pressures and osmotic coefficients for the acetone solutions of three homologues of bis(tetraalkylammonium)tetrathiomolybdate with ethyl, n-propyl and n-butyl as the alkyl groups have been measured at 298.15 K by head spacegas chromatography. The data have also been correlated by the Pitzer, e-NRTL and NRF models. The Pitzer model correlates the data very well, while the standard deviations of e-NRTL and NRF models are relatively large. Vapor pressures of the solutions as well as the parameters of the considered models have been used for qualitative predictions of inter-particle interactions.

exp i m PDH S

experimental data point solvent Pitzer–Debye–H¨uckel solvent

Greek letters α1 , α2 constants in the Pitzer equation β(0) , β(1) , β(2) ionic interaction Pitzer parameters activity coefficient of solvent γ1 λE electrolyte parameter in NRF model λS solvent parameter in NRF model ν total number of ions in a mole of salt ρ closest distance parameter in the PDH equation σ standard deviation τ ca,m salt–solvent parameter in e-NRTL model τ m,ca solvent–salt parameter in e-NRTL model Φ osmotic coefficient Acknowledgement We thank the Research Office of Azarbaijan University of Tarbiat Moallem for financial support. Appendix A The e-NRTL model [28] gives the solvent activity coefficient as:

List of symbols a1 activity of the solvent AΦ Debye–H¨uckel constant for osmotic coefficient b closest distance parameter B second virial coefficient of solvent (m3 mol−1 ) Φ coefficient in Eq. (4a) B CΦ coefficient in Eq. (4a) D peak area of chromatogram of solution D0 peak area of chromatogram of pure solvent fΦ coefficient in Eq. (4a) g interaction energy I ionic strength in molality scale Ix ionic strength in a mole fraction scale m molality (mol kg−1 ) M1 molar mass of solvent (kg mol−1 ) N number of data points p vapor pressure of solution p0 vapor pressure of pure solvent R universal gas constant (J mol−1 K−1 ) T absolute temperature V¯ 1 molar volume of pure solvent (m3 mol−1 ) x1 mole fraction of solvent Subscripts 0 solvent 1 solvent ca salt cal calculated E electrolyte

ln γ1,NRTL  2 = 2Xc

2τca,m exp(−2ατca,m ) τm,ca exp(ατm,ca ) + (X1 +2Xc exp(−ατca,m ))2 (X1 exp(ατm,ca )+Xc )2 (A.1)

in which Xi and α are the effective mole fraction of i (Xi = ji xi ; ji = zi for an ion and ji = 1 for solvent) and non-randomness factor (set to 0.2); τ ca,m and τ m,ca are the adjustable parameters of the eNRTL model called, respectively, salt–solvent and solvent–salt parameters. In the NRF model [29], activity coefficient of solvent is represented as the following equation:

 νXc λE exp(−λE /Z) 1+ ln γ1,NRF = Xc zc ν c (Xc exp(−λE /Z) + X1 )2 X1 λS ((ν/zc νc ) − 2 exp(−λS /Z)) 2Xc exp(−λS /Z) + X1     1 × 2 − X1 1 + 2Xc exp(−λS /Z) + X1 (A.2) −

where ν and νc are, respectively, total number of ions produced in solution by a molecule of salt and number of cations in 1 mol of the salt. Z is the coordination number. The adjustable parameters of the NRF model are λE and λS . For aqueous solutions the best value of Z is 8 and data analysis reveals that this value gives the best results for the studied solutions [29].

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