J. Chem. Thermodynamics 37 (2005) 1177–1185 www.elsevier.com/locate/jct
Correlation of the osmotic coefficients of the solutions of 1:1 salts in methanol by modified local composition models at 298.15 K Jaber Jahanbin Sardroodi a,*, Moayad Hossaini Sadr a, Mohammed Taghi Zafarani-Moattar b a
Department of Chemistry, Faculty of Basic Sciences, Azerbaijan University of Tarbiat Moallem Tabriz, 35th km of Tabriz-Maraghe road, Tabriz, East Azerbaijan 5375171379, Iran b Physical Chemistry Department, Faculty of Chemistry, University of Tabriz, Tabriz, Iran Received 16 October 2004; received in revised form 16 February 2005; accepted 16 February 2005 Available online 5 April 2005
Abstract Published osmotic coefficient data for the solutions of some 1:1 electrolytes in methanol along with new experimental data for tetramethylguanidinium perchlorate were correlated using local composition models. The studied models are electrolyte non-random two liquid (e-NRTL), non-random factor (NRF), modified NRTL (MNRTL), mean spherical approximation NRTL (MSA-NRTL) and extended Wilson models. In the e-NRTL, NRF, MNRTL and EW models the MSA term was used as the long-range contribution. Results were compared with Pitzers ion interaction model. All of the models give reliable results. 2005 Elsevier Ltd. All rights reserved.
1. Introduction Thermodynamic properties of binary electrolyte solutions are of essential needs in design and control of industrial processes containing multi component electrolyte solutions ranging from protein precipitation to fertilizer production to gas hydrate suppression [1–3]. The electrolyte solutions were modeled in detail by Debye– Hu¨ckel in small salt concentrations [4]. Up to the present, this theory keeps its importance as the correct limiting low at infinite dilution. From the 1970s pioneering work of Pitzer [5] creates a new generation of electrolyte solutions theories using multi parameter regression for express or predict of thermodynamic properties of electrolyte solutions. After the Pitzers work various models were developed in both fields of physical chemistry and chemical engineering such as *
Corresponding author. Tel.: +98 412 4325146/914 3162584; fax: +98 412 4524991. E-mail address:
[email protected] (J.J. Sardroodi). 0021-9614/$ - see front matter 2005 Elsevier Ltd. All rights reserved. doi:10.1016/j.jct.2005.02.009
MSA, HNC, local composition (LC) models and so on. Recently, excellent reviews have been published containing recent progresses in the thermodynamics of the electrolyte solutions [6,7]. The LC theory developed by Renon and Prausnitz [8] for non electrolyte mixtures have been extended to electrolyte solutions by Chen and Evans [9]. These models use the non-random two liquid theory [10] and two additional assumptions about the structure of electrolyte solutions; say electroneutrality and like-ion repulsion [9]. The unique aspect of these models, in comparison to other models such as Pitzer and Mayorge [11] or Clegg–Pitzer [12] models, is that the excess Gibbs energy equation for multi-component solutions provided by LC models contains no ternary or higher order parameters. Therefore, prediction of thermodynamic properties of multi-component systems is possible if only binary parameters of involved species are known [13]. Besides, because of non-linear dependency of excess Gibbs energy to the model parameters, expression for excess volume or excess enthalpy of the electrolyte solutions
J.J. Sardroodi et al. / J. Chem. Thermodynamics 37 (2005) 1177–1185
provided by LC models contains the excess Gibbs energy parameters [14,15]. These parameters are determined by fitting the experimental activity or osmotic coefficient data. Therefore, our knowledge about the correct numerical values of the excess Gibbs energy parameters of the LC models is very important in application of these models to the multi-component systems or other thermodynamic properties. Purposes of this work are obtaining the binary interaction parameters of various LC models for the solutions of some 1:1 salts in methanol at 298.15 K and investigation on their capability with the MSA equation instead of PDH or DH equation. The considered LC models are the electrolyte non-random two liquid (eNRTL) [9], non-random factor (NRF) [16], Modified NRTL (MNRTL) [17], mean spherical approximation NRTL (MSA-NRTL) [18] and Extended Wilson (EW) [19] models. Systems which osmotic coefficients used for correlations, have been listed in table 1. This Table have been also included the molality range and data source for each salt. Osmotic coefficient data for tetramethylguanidinium perchlorate (TMGP) solutions were evaluated from isopiestic equilibrium molalities of NaI and TMGP in methanol reported by Bonner [26]. However, the obtained osmotic coefficients are very scattered (figure 1) so that their standard deviation obtained by the Pitzer model is near 0.03. Furthermore the molalities are not so precise because they have three meaningful figures. For obtaining reliable parameters, we have to use more precise data; therefore, the isopiestic experiments for TMGP were repeated. The new isopiestic molalities and osmotic coefficients have been given in table 2. Figure 1 is also a comparison of the Bonners osmotic TABLE 1 Systems which osmotic coefficients used in this work Salt
m/(mol Æ kg1)
Data source
LiCl LiBr LiClO4 LiOAc NaCl NaBr NaI NaSCN NaClO4 KBr KI KOAc NaOAc RbI CsI Et4NBr Bu4NBr Bu4NI Bu4NClO4 Am4NBr TMGP
0.2–0.4 0.2–3.9 0.04–5.0 0.2–3.0 0.04–0.2 0.2–1.6 0.2–4.3 0.2–3.4 0.06–1.3 0.04–0.1 0.03–0.8 0.2–2.5 0.2–1.8 0.03–0.4 0.03–0.1 0.05–1.9 0.05–2.5 0.04–0.9 0.05–2.5 0.05–1.5 0.2–7.6
[20] [20] [21] [20] [22] [22,23] [22] [23] [22] [22] [22] [24] [24] [22] [22] [25] [25] [25] [25] [25] This work
0.75 0.7 0.65 0.6 0.55
Φ
1178
0.5 0.45 0.4 0.35 0.3 0
1
2
3
4
5
6
7
8
9
m / mol•kg-1
FIGURE 1. Osmotic coefficients for methanol solution of TMGP at 298.15 K: }, obtained in this work; ·, reported by Bonner [26].
coefficients [26] and those obtained in this work. We calculated the osmotic coefficients for other considered solutions according to the reported isopiestic equilibrium molalities and Pitzer parameters for reference solution given from reference [20]. We recalculate the all osmotic coefficient data used in this paper according to the reported isopiestic equilibrium molalities. We observed slightly differences between recalculated and reported osmotic coefficients of the methanol solutions of KOAc and NaOAc reported by Neueder co-workers [22] and NaBr and NaSCN reported by Nasirzadeh and Salabat [23], while for other solutions the results were the same as those reported in the source papers. Table 3 have been contained the molalities and recalculated osmotic coefficients for KOAc, NaOAc, NaBr and NaSCN solutions in methanol. The recalculated osmotic coefficients have been used for correlations.
2. Experimental 2.1. Materials The methanol was obtained from Merck (methanol GR. 99.8%) and was dried by the method described by Vogel [29]. TMGP was prepared by direct titration of the stoichiometric amounts of 1,1,3,3-tetramethylguanidine by perchloric acid (both supplied from Merck). Cooling the solution by a dry ice–acetone bath causes the precipitation of TMGP from the solution [30]. The precipitated TMGP was then recrystallized three times from acetone–ether. 2.2. Methods and apparatus The isopiestic apparatus employed is essentially the same as the one used previously [15,20,31,32]. This
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TABLE 2 Isopiestic equilibrium molalities for tetramethylguanidinium perchlorate (TMGP) in methanol at 298.15 Ka mr/(mol Æ kg1)
mTMGP/(mol Æ kg1)
UTMGP/(mol Æ kg1)
mr/(mol Æ kg1)
mTMGP/(mol Æ kg1)
UTMGP/(mol Æ kg1)
0.1821 0.1852 0.1765 0.1909 0.1902 0.2501 0.3298 0.4170 0.5015 0.5832 0.6666
0.2193 0.2194 0.2390 0.2707 0.2953 0.4073 0.6040 0.8031 1.0248 1.2203 1.4282
0.6921 0.7037 0.6155 0.5881 0.5371 0.5153 0.4644 0.4496 0.4320 0.4304 0.4293
0.7522 0.8298 0.9159 1.0175 1.0820 1.3218 1.5799 1.5863 1.7988 2.1530 2.3976
1.6502 1.8591 2.0993 2.3942 2.5878 3.3515 4.2505 4.2738 5.0757 6.5326 7.6266
0.4287 0.4284 0.4283 0.4284 0.4287 0.4299 0.4317 0.4317 0.4332 0.4352 0.4363
a
mr is the molality of reference NaI solution in methanol.
TABLE 3 Molalities and recalculated osmotic coefficients for the solutions of NaBr, NaOAc, KOAc, NaOAca mNaBr/(mol Æ kg1)
UNaBr
mNaSCN/(mol Æ kg1)
UNaSCN
mKOAc/(mol Æ kg1)
UKOAc
mNaOAc/(mol Æ kg1)
UNaOAc
0.1703 0.2571 0.3439 0.4090 0.5066 0.5826 0.7012 0.7476 0.8634 0.9291 1.0387 1.1097 1.2470 1.3053 1.4190 1.4668 1.5547 1.5679
0.841 0.835 0.833 0.833 0.835 0.836 0.840 0.850 0.856 0.866 0.885 0.897 0.922 0.933 0.955 0.964 0.981 0.983
0.1572 0.3332 0.4724 0.6442 0.7182 0.8436 1.2318 1.345 1.461 1.5608 1.6283 1.717 1.7675 1.8623 2.019 2.2982 2.4364 2.5054 2.6436 2.852 2.9926 3.1348 3.2064 3.426
0.798 0.821 0.856 0.885 0.898 0.919 0.987 1.007 1.028 1.046 1.058 1.074 1.083 1.1 1.128 1.177 1.201 1.212 1.235 1.266 1.285 1.302 1.311 1.333
0.1783 0.2915 0.4044 0.5171 0.6295 0.7416 0.8534 0.9649 1.0761 1.2976 1.4630 1.6281 1.7380 1.7929 1.7819 1.9577 2.0676 2.1778 2.2329 2.399 2.3435 2.4545 2.5102
0.804 0.798 0.798 0.800 0.803 0.807 0.811 0.815 0.819 0.827 0.833 0.838 0.842 0.844 0.843 0.849 0.853 0.856 0.858 0.862 0.861 0.864 0.866
0.2558 0.2822 0.2943 0.3319 0.3878 0.4154 0.4436 0.4948 0.5554 0.5789 0.6799 0.7385 0.7601 0.8676 0.8863 0.9084 0.9424 1.0246 1.0441 1.0964 1.2215 1.2877 1.4175 1.4997 1.5384 1.7631
0.776 0.769 0.77 0.776 0.773 0.771 0.776 0.775 0.779 0.78 0.783 0.784 0.79 0.79 0.794 0.791 0.792 0.793 0.796 0.798 0.802 0.804 0.814 0.807 0.813 0.813
a
OAc stands for acetate.
apparatus consisted of a five-leg manifold attached to round-bottom flasks. Five flasks were typically used as follows. Two flasks contained the standard NaI solutions, two flasks contained TMGP solutions, and the central flask was used as a methanol reservoir. The isopiestic apparatus was held in a constant-temperature bath for equilibrium at (298.15 ± 0.005) K at least 120 h. After equilibrium has been reached, the manifold assembly was removed from the bath and each flask was weighted with a high precision analytical balance (Shimadzu, 321-34553, Shimadzu co., Japan). It was assumed that the equilibrium condition was reached when the dif-
ferences between the mass fractions of each duplicates are less than 1%. In all cases, averages of the duplicates are reported as the final isopiestic molality. The uncertainty in the solvent activity was estimated to be ±0.0002.
3. Theoretical framework 3.1. Pitzer model The Pitzers equation for a binary solution of a 1:1 electrolyte in a solvent has the following form:
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U ¼ 1 þ f U þ mBU þ m2 CU :
ð1Þ
In which f U ¼ AU ðIÞ
1=2
=1 þ bðIÞ
1=2
ð2Þ
and BU ¼ bð0Þ þ bð1Þ expða1 ðIÞ
1=2
Þ þ bð2Þ expða2 ðIÞ
1=2
Þ: ð3Þ
In this equation b(0), b(1), b(2) and CU are adjustable parameters of the model, and a1, a2 and b are also the constant parameters of model. 3.2. LC models In the LC models it is assumed that the excess Gibbs energy of electrolyte solutions and consequently activity coefficients has been composed from two long-range (LR) and short-range (SR) contributions [8,14–17]: ln ci ¼ ln ci;LR þ ln ci;SR :
ð5Þ
in which a1, c1, M1 and x1 are activity, activity coefficient, molar mass (kg Æ mol1) and mole fraction of the solvent; m and m are total number of ions in a molecule of the salt and molality of the solution, respectively. 3.2.1. Long-range contribution Usually the Pitzer–Debye–Hu¨ckel (PDH) [27] or Debye–Hu¨ckel (DH) [28] equations are used for the LR contribution in the LC models [9,16–19]. Recently, Papaiconomou et al. [18] used a primitive version of MSA equation for the LR term in the excess Gibbs energy equation. This equation has the following form [18]: ln c1;MSA ¼ ðC=3pÞðM 1 =N A d 1 Þ;
3.2.2. Short-range contribution The SR contributions for the solvent activity coefficient used in this work are as the following: 1. The e-NRTL model [9] gives the solvent activity coefficient as h ln c1;NRTL ¼ 2X 2c 2sca;m expð2asca;m Þ= 2
ðX 1 þ 2X c expðasca;m ÞÞ þ sm;ca expðasm;ca Þ=ðX 1 expðasm;ca Þ þ X c Þ2
ð6Þ
where NA and d1 are the Avogadros number and density of solvent; C is the screening parameter of MSA defined as C ¼ ð1 þ 2jrÞ1=2 1 =2r; ð7Þ jis the screening parameter of the Debye–Hu¨ckel theory !1=2 X 2 qi zi ð8Þ j ¼ 4pk
i
ð10Þ
ð4Þ
Therefore the osmotic coefficient of the solution, U, can be also obtained as U ¼ lnða1 Þ=mmM 1 ¼ lnðc1;LR Þ þ lnðc1;SR Þþ lnðx1 Þ=mmM 1
and r, zi and qi are, respectively, the mean ionic size of the electrolyte (r = (r+ + r)/2), the charge number and the number density of ionic species i. We have used this version of MSA equation as the long-range term in the activity coefficient of solvent. Following Papiconomou et al. [18] the mean ionic size parameter of electrolyte, r, of MSA model regarded as an adjustable parameter and its value fitted to the data.
in which Xi and a are the effective mole fraction of i (Xi = jixi; ji = zi for an ion and ji = 1 for solvent) and non randomness factor (set to 0.2); sca,m, sm,ca are the adjustable parameters of the e-NRTL model. 2. In the NRF model [14], activity coefficient of solvent is represented as ( " # expðkE =ZÞ ln c1;NRF ¼ X c ½mX c kE =zc mc 1 þ ðX c expðkE =ZÞ þ X 1 Þ2 X 1 kS ðm=zc mc 2 expðkS =ZÞÞ 2X c expðkS =ZÞ þ X 1 ) 1 2 X1 1 þ ; 2X c expðkS =ZÞ þ X 1 ð11Þ
where m and mc are, respectively, total number of ions produced in solution by a molecule of salt and number of cations in one mole of the salt. Z is the coordination number and was set to 8 [14]; kE and kS are the adjustable parameters of the model. 3. The modified NRTL (MNRTL) model has been developed by Jaretum and Aly [17]. According to this model the activity coefficient of the solvent could be written as h 2 ln c1;MNRTL ¼ 4X 2c sca;m W ca;m =ðX 1 þ 2W ca;m X c Þ þ i 2 sm;ca ðW ca;m 1Þ=ðX c þ X 1 W ca;m Þ ð12Þ in which sca,m and sm,ca are the model parameters, and the following definition have been carried out:
i¼ions
W i ¼ exp ðasi þ xi Þ;
in which k ¼ be2 =4pe0 D
ð9Þ
ð13Þ
where the xca,m and xm,ca are also adjustable parameters.
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4. The MSA-NRTL [18] provides the following equation for activity coefficient of solvent. ln c1;MSA-NRTL ¼ A=B2 þ mc ma ðC c þ Ca Þ þ ms2mc;ac x2s xis ðDc þ Da Þ;
1181
where Ee1 and E1e are the model parameters; C, R and T are the coordination number (set to 10 [19]), the gas constant and the absolute temperature, respectively.
ð14Þ where the following definitions have been carried out: A ¼ ðmc pcm scm þ ma pam sam Þðmc pcm þ ma pam Þ;
ð15Þ
B ¼ mc pcm þ ma pam þ x1s ;
ð16Þ
2 C c ¼ pmc;ac smc;ac = ma þ xis pmc;ac ;
ð17Þ
2 C a ¼ pma;ca sma;ca = mc þ xis pma;ca ;
ð18Þ
2
Dc ¼ mc pmc;ac = ma þ xis pmc;ac 1 ma asmc;ac = ma þ xis pmc;ac ; ð19Þ 2
Da ¼ ma pma;ca = mc þ xis pma;ca 1 mc asma;ca = mc þ xis pma;ca ; ð20Þ
and pi ¼ exp ðasi Þ;
ð21Þ
sma;ca ¼ smc;ac þ sam scm ;
ð22Þ
smc;ac ¼ s1mc;ac þ s2mc;ac X 1 :
ð23Þ
In these equations we have use the following notation: pi ¼ expðasi Þ
ð24Þ
and xi ¼ x1 =xs ¼ 1=xs m
ð25Þ
in which x1 and xs are the mole fraction of solvent and salt, respectively (xs = xc/mc; x1 + mxs = 1). 5. Zhao et al. [19] have presented an extended version of Wilson equation for electrolyte solutions that enables us to writing the solvent activity coefficient as X 1 þ 2X c expðEe1 =CRT Þ ln c1;EW ¼ C ln þ X 1 þ 2X c ð1 expðEe1 =CRT ÞÞX 1 2X c þ ðX 1 þ 2X c expðEe1 =CRT ÞÞðX 1 þ 2X c Þ X c ðexpðE1e =CRT Þ 1Þ ; ð26Þ ðX 1 expðE1e =CRT Þ þ X c ÞðX 1 þ X c Þ
4. Results and discussion The Pitzer parameters for the methanol solutions of TMGP, NaBr, NaSCN, NaOAc and KOAc are presented in table 4. The Pitzer parameters for the solutions of NaBr, NaSCN, NaOAc and KOAc reported by Nasirzadeh and coworkers [23,24] are different with those obtained in this work. For the remaining systems, the Pitzer parameters have not been reported, since parameters obtained here are identical with those reported by Zafarani-Moattar and Nasirzadeh [20] (for LiCl, LiBr and LiNO3), and by Barthel et al. [21,22,25] (for other systems). As mentioned above, for correlation of considered osmotic coefficient data and new data for TMGP with LC models the MSA equation [18] have been used as the LR contribution. When the r parameter in MSA equation is regarded as an adjustable parameter, the LC models fit the osmotic coefficient data with one additional adjustable parameter. This causes that we obtain better results than the case in which the PDH equation is as the LR contribution. The results of fitting of the studied LC models to the osmotic coefficients of 1:1 salts in methanol have been provided in tables 4–9. These Tables also contain the standard deviations of the fit in the osmotic coefficients defined as exp : 2 !1=2 P Ucal: i i¼data points Ui dðUÞ ¼ ; ð27Þ N where U, exp., calc. and N stand for the osmotic coefficients, experimental data, calculated value and the number of data, respectively. Fitting the models to data has been carried out using genfit function of Mathcad 11 package. 4.1. The e-NRTL model Table 5 contains the parameters of the e-NRTL model. It is observed that the general relation between NRTL parameters (sm,ca 2sca,m) is valid for the studied salts. This relation is a very interesting aspect of this
TABLE 4 Model parameters of the Pitzer model for the osmotic coefficients of TMGP, NaBr, NASCN, NaOAc and KOAc in methanol at 298.15 K (a1 = 2, a2 = 10, b = 3.2) Salt
b(0)
b(1)
b(2)
CU
d(U)
TMGP NaBr NaSCN NaOAc KOAc
0.018355 0.143848 0.204223 0.143263 0.041609
1.798948 0.46943 0.61555 2.20871 0.16935
4177.084835 0.701852 0.573762 2.094875 0.428779
0.000274 0.054611 0.009143 0.029942 0.000010
0.015 0.001 0.006 0.0003 0.0003
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TABLE 5 e-NRTL model parameters for the osmotic coefficients of studied solutions at 298.15 K (a = 0.2)
TABLE 6 NRF model parameters for the osmotic coefficients of studied solutions at 298.15 K (Z = 8)
Salt
sca,m
sm,ca
r · 1010/m
d(U)
Salt
kE
kS
r · 1010/m
d(U)
LiCl LiBr LiClO4 LiOAc NaCl NaBra NaBrb NaI NaSCN NaClO4 NaOAc KBr KI KOAc RbI CsI Et4NBr Bu4NBr Bu4NI Bu4NClO4 Am4NBr TMGP
5.1877 5.3043 5.5321 4.4652 5.6660 4.8328 4.85882 5.22219 4.8050 4.4401 3.1068 3.6040 4.2340 3.8414 2.7725 4.5224 4.1360 4.3281 2.3071 2.0266 4.2010 3.5522
10.9222 11.2566 11.7113 9.2204 11.4766 9.5736 10.0420 10.6451 9.3829 8.6985 5.4806 6.7702 8.2600 7.4329 5.3202 9.1132 8.4321 8.8203 4.7750 4.6192 8.4774 7.1167
16.11 2.58 22.41 6.99 7.26 6.22 11.13 9.10 5.58 5.41 4.29 4.90 5.55 5.51 4.78 3.82 3.90 4.39 2.10 1.09 3.07 1.73
0.043 0.040 0.046 0.005 0.006 0.002 0.003 0.050 0.008 0.004 0.001 0.003 0.002 0.001 0.003 0.002 0.010 0.005 0.005 0.006 0.005 0.030
LiCl LiBr LiClO4 LiOAc NaCl NaBra NaBrb NaI NaSCN NaClO4 NaOAc KBr KI KOAc RbI CsI Et4NBr Bu4NBr Bu4NI Bu4NClO4 Am4NBr TMGP
10.3796 10.7397 11.5524 9.2999 14.6096 9.5592 11.1408 9.4485 7.22452 8.2928 3.8790 7.7441 7.7992 5.7801 5.0015 10.2639 8.7809 9.4624 4.2533 4.5375 8.8555 0.2581
15.5800 16.7700 18.4762 10.5598 36.0203 13.8010 15.5630 14.4644 10.21686 10.1036 4.4139 9.1891 8.9313 5.7980 4.2043 13.3563 9.0530 10.6551 2.2998 1.5309 9.5736 1.2397
5.98 6.27 8.56 5.62 7.20 6.00 9.34 5.50 4.67 5.31 4.70 7.90 5.54 5.55 4.81 3.81 3.77 4.25 2.12 1.09 3.66 1.63
0.023 0.017 0.006 0.004 0.004 0.003 0.002 0.007 0.006 0.003 0.004 0.003 0.003 0.001 0.002 0.002 0.010 0.005 0.005 0.006 0.005 0.030
a b
a
Data from reference [23]. Data from reference [22].
b
Data from reference [23]. Data from reference [22].
portional to the difference between anion–cation and solvent–solvent interaction, is negative. This is expectable since ion–ion interaction is more strength than the solvent–solvent interaction.
model can be useful in the correlation of other thermodynamic properties such as excess volume [14,15]. It is also observed from table 5 that for studied salts the salt–solvent interaction parameter, sca,m, that is pro-
TABLE 7 MNRTL model parameters for the osmotic coefficients of studied solutions at 298.15 K (a = 0.2) Salt
sca,m
xca,m
sm,ca
xm,ca
r · 1010/m
d(U)
LiCl LiBr LiClO4 LiOAc NaCl NaBra NaBrb NaI NaSCN NaClO4 NaOAc KBr KI KOAc RbI CsI Et4NBr Bu4NBr Bu4NI Bu4NClO4 Am4NBr TMGP
22.7460 11.2972 31.7715 2.9917 21.3640 22.30419 0.2998 32.5610 0.12634 25.3487 1.0755 21.4919 21.3513 2.5546 21.3966 21.2473 23.9613 29.9076 30.7808 30.4039 30.5115 15.0238
5.0974 1.3046 6.9427 0.2472 4.9992 5.1317 3.7145 7.1753 4.0461 5.8246 0.7164 4.9568 5.0246 0.2369 4.9734 5.0142 5.6136 6.8061 6.4684 6.5553 6.9166 16.9799
17.9931 46.5869 30.8620 3.3653 18.19515 18.3510 12.2685 26.0779 7.4303 22.3593 9.7126 18.3037 18.1900 11.2417 18.7518 18.7059 24.7849 30.1467 33.1509 31.6337 30.7915 29.4155
3.3905 7.9524 5.8960 0.9580 3.1919 3.3834 2.0200 4.8683 3.30601 4.0841 1.2428 3.1243 3.2175 1.2643 3.0002 3.0399 3.5100 5.5849 1.0778 4.6130 5.7026 5.9000
2.98 3.04 3.43 5.90 6.17 5.34 12.21 4.54 4.84 5.18 4.01 4.90 5.50 5.22 4.86 3.76 3.51 3.83 2.04 1.08 3.46 1.66
0.032 0.007 0.057 0.004 0.008 0.003 0.002 0.010 0.004 0.003 0.002 0.002 0.003 0.004 0.003 0.002 0.010 0.006 0.005 0.006 0.005 0.030
a b
Data from reference [23]. Data from reference [22].
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TABLE 8 MSA-NRTL model parameters for the osmotic coefficients of studied solutions at 298.15 K (a = 0.2) Salt
s1mc;ac
s2mc;ac
scm
sam
r · 1010/m
d(U)
LiCl LiBr LiClO4 LiOAc NaCl NaBra NaBrb NaI NaSCN NaClO4 NaOAc kBr KI KOAc RbI CsI Et4NBr Bu4NBr Bu4NI Bu4NClO4 Am4NBr TMGP
0.2748 3.0545 3.6872 7.1906 3.4853 9.9371 4.8844 6.3400 0.9450 3.7966 4.53130 2.4387 6.6496 3.88540 1.12300 0.5565 2.8109 4.2440 1.6351 1.7034 4.0723 3.3534
1.4412 0.2328 1.5371 13.180 1.1076 17.1605 1.3957 1.9317 1.9966 1.7198 0.3228 1.7084 1.9189 1.4237 1.6030 0.9908 2.3390 2.6204 0.4919 0.3445 2.6195 2.6271
0.2711 3.1617 3.5530 2.9658 2.1763 4.1517 2.0181 1.6612 0.92401 1.6971 2.4752 1.6111 1.5249 2.8312 1.6458 0.84392 2.9858 3.1768 0.6278 0.3948 3.2184 3.1135
5.9083 2.9130 3.0866 5.108/0 4.0443 5.0252 2.2836 1.6590 1.33665 1.8992 2.7069 1.8495 1.5565 3.6208 2.6606 0.7815 3.0521 4.5160 2.1207 0.5818 4.3028 2.9744
1.52 1.42 1.18 1.03 6.09 13.89 4.49 5.51 4.54 4.85 4.34 4.90 5.38 5.45 4.83 3.60 3.35 4.34 2.13 1.14 3.80 2.21
0.088 0.069 0.115 0.009 0.010 0.005 0.008 0.059 0.009 0.012 0.003 0.003 0.006 0.001 0.002 0.002 0.011 0.005 0.005 0.007 0.005 0.031
a b
Data from reference [23]. Data from reference [22].
TABLE 9 EW model parameters for the osmotic coefficients of studied solutions at 298.15 K (C = 10) Salt
Eem/(kJ Æ mol1)
Eme/(kJ Æ mol1)
r · 1010/m
d(U)
LiBr LiCl LiOAc LiClO4 NaCl NaBra NaBrb NaI NaSCN NaClO4 NaOAc KBr KI RbI CsI KOAc Et4NBr Bu4NBr Bu4NI Bu4NClO4 Am4NBr TMGP
2.232 0.584 19.382 0.00012 1.994 10.410 4.956 0.760 5.103 11.952 14.911 16.220 6.465 18.254 4.676 4.535 60.456 33.557 16.987 26.956 27.373 1.461
188.405 215.294 133.449 5010.000 16.817 124.110 128.755 221.478 10.521 108.031 25.202 29.316 31.571 35.465 9.484 3.780 254.737 169.294 33.917 19.481 81.002 1.484
3.02 3.32 4.59 4.61 6.16 5.68 5.46 4.65 4.59 5.27 4.15 4.89 5.53 4.72 3.75 5.54 3.53 3.83 2.03 1.17 3.45 1.63
0.030 0.027 0.006 0.070 0.010 0.012 0.007 0.009 0.006 0.003 0.002 0.007 0.004 0.004 0.003 0.001 0.013 0.006 0.005 0.007 0.005 0.030
a b
Data from reference [23]. Data from reference [22].
tive for all salts. This means that the attraction between two oppositely charged ions in solution is stronger than attraction between an ion and a solvent molecule. The solvent parameter is also positive, that is the oppositely charged ions interact in the solution most powerful than two solvent molecules. 4.3. The MNRTL model The model parameters for the MNRTL model have been collected in table 7. In this case as the same as aqueous solutions [17], the model parameters vary considerably between studied systems. This means that the parameters are quite strongly correlated. 4.4. The MSA-NRTL model The results of MSA-NRTL model have been presented in table 8. Behavior of the model parameters are similar to the aqueous solutions [18], except for the s2mc;ac , that is negative for aqueous solutions and positive for studied systems. However, this is in agreement with the positive nature of smc,ac as the difference of the anion–cation and ion–solvent interaction ðsmc;ac ¼ s1mc;ac þ x1 s2mc;ac Þ [18].
4.2. The NRF model 4.5. The EW model The parameters of NRF model are collected in table 6. These results show that the model parameters are consistent. The electrolyte parameter of this model is nega-
Table 9 contained the model parameters of the EW model. In contrast to the other studied models, the
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TABLE 10 Standard deviations in osmotic coefficients obtained from various models Salt
Pitzer
NRTL
NRF
MNRTL
MSA-NRTL
EW
LiBr LiCl LiClO4 LiOAc NaCl NaBra NaBrb NaI NaSCN NaClO4 NaOAc KBr KI KOAc RbI CsI Et4NBr Bu4NBr Bu4NI Bu4NClO4 Am4NBr TMGP
0.009 0.012 0.013 0.003 0.005 0.002 0.001 0.007 0.006 0.004 0.002 0.002 0.002 0.0003 0.003 0.002 0.006 0.004 0.005 0.007 0.005 0.015
0.040 0.043 0.046 0.005 0.006 0.003 0.002 0.050 0.008 0.004 0.003 0.003 0.002 0.001 0.003 0.002 0.010 0.005 0.005 0.006 0.005 0.039
0.017 0.023 0.006 0.004 0.004 0.002 0.003 0.026 0.006 0.003 0.004 0.003 0.003 0.001 0.002 0.002 0.010 0.005 0.005 0.006 0.005 0.037
0.007 0.032 0.057 0.004 0.008 0.002 0.003 0.010 0.004 0.003 0.002 0.002 0.003 0.004 0.003 0.002 0.010 0.006 0.005 0.006 0.005 0.037
0.069 0.088 0.115 0.009 0.010 0.005 0.008 0.048 0.009 0.012 0.003 0.003 0.006 0.001 0.002 0.002 0.011 0.005 0.005 0.007 0.005 0.051
0.030 0.027 0.070 0.006 0.010 0.012 0.007 0.009 0.006 0.003 0.002 0.007 0.004 0.001 0.004 0.003 0.013 0.006 0.005 0.007 0.005 0.037
0.013
0.008
0.010
0.022
0.012
Average 0.005 a Data from reference [23]. b Data from reference [22].
model parameters of the EW model are not dimensionless. Their dimension is determined by units of R. We used R in J Æ mol1 Æ K1 (8.314 J Æ mol1 Æ K1), hence, the parameters are expressed in kJ Æ mol1. The Ee1 parameter of the EW model is proportional to difference in ion–solvent and solvent–solvent interactions and the E1e parameter is proportional to the difference in solvent–ion and ion–ion interactions [19] The sign of these parameters, in contrast other LC models, both in this study for non-aqueous solutions and in the case of aqueous systems [19], is not in accordance with the nature of these interactions. This fact can be regarded as the failing of this model. Therefore, one cannot elucidate some information about interactions in the solutions using the EW model parameters. 5. Conclusions The published osmotic coefficient data for some 1:1 salts in methanol along with new data for tetramethylguanidinium perchlorate are correlated using the local composition models with the MSA equation as the long-range contribution. For the methanol solutions of NaBr, NaSCN, NaOAc and KOAc at 298.15 K, osmotic coefficients recalculated according to the reported isopiestic equilibrium molalities and new Pitzer parameters were calculated from the recalculated osmotic coefficients. Model parameters for the studied LC models are interpreted in terms of ion–ion and ion–solvent inter-
actions occurring in the solutions. A comparison of the models with Pitzer model is also presented in table 10. It is evident from this Table that the models provide satisfactory correlation for most of the studied systems. Higher standard deviations for some solutions in the LC models (solutions of LiCl, LiClO4, NaI, Et4NBr, and TMGP in methanol) may relate to the point that in these models ion association has not been considered.
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JCT 04-216
