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Density, molar volume, thermal expansion and viscosity changes of (Ag,Tl)NO3 + dimethylsulfoxide + water systems at several temperatures
Pergamon PII:
Ekcrrochimica Am, Vol. 42, No. 1, pp. 107-113, 1997 Copyright 0 1996 Elsevier Science Ltd. Printed in Great Britain. All rights reserved SOO13-4686(~172-7 0013-4686/97 $17.00 + 0.00
Density, molar volume, thermal expansion and viscosity changes of (Ag,TI)N03 + dimethylsulfoxide + water systems at several temperatures Ioannis I. Ziogas and Georgios Papanastasiou Aristotle University of Thessaloniki,
Department of Chemistry, Laboratory 540 06 Thessaloniki. Greece
of Physical Chemistry,
(Received 18 December 1995; in revised form 15 April 1996) Abstract-Viscosities and densities of the system (Ago.~,Tlo,s)NO3+ DMSO + Hz0 were determined in the temperature range 376 < T/K < 394 K with the mole fraction of the mixed melt, xs, ranging between 0 and 0.9. This system, formed by the eutectic mixture of AgNOJ and TlNOj (eutectic point equal to 83”C, AgNO,/TlNO3 mole ratio equal to 1.062) and an equimolar mixture of dimethylsulfoxide with water, is liquid over the specified temperature and composition range. Parameters such as the molar volume, the volume coefficient of thermal expansion, the rheochor and the activation entropy and enthalpy in the Eyring’s equation were determined. An attempt has been made to express these properties by means of single equations, wherein the temperature and composition effects are involved. The behaviour of the system studied here is compared with that of the corresponding (A@.~,Tlo,s)N0, + DMSO systems, previously investigated. The results indicate that the partial replacement of DMSO with water decreases the cation-dipole interactions. Copyright 0 1996 Elsevier Science Ltd Key words: Molten salt, nitrate, viscosity, thermal expansion, hydrate melts.
1. INTRODUCTION
system, the use of DMSO, a high boiling point polar organic solvent, enabled us to extend the temperature range up to 121°C. However, in agreement with analogous literature data [12], we observed that this system presented a miscibility gap, in the temperature range 103 < T < 121°C and for mole fraction of the melt ranging between 0.55 and 0.75. This situation has motivated us to make a series of systematic measurements of density and viscosity of the (Ag,Tl)NOrDMSO-Hz0 systems, where the AgNOs/TlNOJ and HzO/DMSO mole ratios were equal to 1.062 and 1.0, respectively, over the whole composition range with temperatures from 103 to 121°C. We believe that these ternary systems, prepared from the corresponding aqueous mixtures by partial replacement of Hz0 with DMSO, are of considerable interest because it allows one to establish an experimental link between the behaviour of the corresponding binary (Ag,Tl)NOrH20 and (Ag,Tl)NO,-DMSO mixtures. Parameters such as the activation entropy and enthalpy in the Eyring’s equation, the molar volume, the rheochor and the coefficient of the thermal expansion of
For theoretical and various practical developments, the investigation of the so-called bridging systems (ie electrolyte systems extending in the liquid phase from a dilute solution in a polar molecular solvent such as water to a pure fused salt) has been the object of intense scrutiny. Unfortunately, the study of some physical properties of such hydrate systems over the entire composition range presents many difficulties due to the limited solubility of the salts at temperatures below 100°C or to the high vapour pressure at temperatures higher than 100°C. The system (Ag,Tl)NOJ-Hz0 formed by water and the eutectic mixture of AgNOj and T~NOJ (eutectic point equal to 83°C) is one of the few binary systems which are liquid over the entire composition range at temperatures below 100°C. This system has been extensively investigated by Abraham et al. [l-10]. In these frames, we examined in a previous paper the (Ag,Tl)NOrDMSO system, where the water has been replaced by dimethylsulfoxide [l 11. In this 107
108
I. I. Ziogas and G. Papanastasiou
the system studied were determined over the specified temperature and composition range. An attempt has been made to express these properties by means of single equations, wherein the temperature and composition effects are involved. It is noted that the physical behaviour of the above mentioned system, at various compositions and temperatures, seems not to have been investigated previously. 2. EXPERIMENTAL Chemicals Reagent-grade AgNO3 (Fluka, puriss. p.a. > 99.5%) was vacuum-desiccated at about 120°C and TlNO, (Fluka, purum stored over P205. p.a. > 99.0%) was re-crystallized in water, filtered, dried at 120°C in vacuum and stored over Pros. Conductivity water (conductance w 1.0 x 10e6 a-’ cm-‘) was used throughout. Reagent-grade dimethylsulfoxide (Merck, p.a. > 99.5%), containing not more than 0.03% water, was used and stored at room temperature over 4A molecular sieves. The systems xJAg,Tl)NOr + (1 - x,)(DMSO/HrO), x, being the mole fraction of the salt mixture, were obtained by addition of an equimolar solution of DMSO with water to the eutectic nitrate mixture having the following fixed composition in mole fractions: 0.515 AgNOsa.485 TlNOj. The salt and solvent mixtures are simply indicated as (Ag,Tl)NOs and DMSO/HrO respectively throughout this paper. All the solutions were gravimetrically prepared on a Mettler analytical balance just before their use. Measurements
Table 1 Experimental density p for the x,(Ag,TI)NO,+ (DMSO/HzO) system at various temperatures X-3
103°C
109°C 115°C P(g m-))
121°C
0.0
1.023 I .424 1.814 2.221 2.621 2.997 3.359 3.688 4.016 4.342
1.018 1.418 1.808 2.215 2.621 2.990 3.351 3.679 4.007 4.331
1.005 1.406 1.797 2.204 2.608 2.975 3.335 3.662 3.987 4.309
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.012 1.412 1.802 2.209 2.615 2.983 3.343 3.670 3.997 4.320
3. RESULTS AND DISCUSSION The experimental density (p) and viscosity (?I) of the systems x,(Ag,Tl)NOr + (1 - xx) (DMSO/HrO) with respect to the mole fraction x, of the melt are given in Tables 1 and 2 at various systems, contrary to temperatures. These x,(Ag,Tl)NOJ + (1 - x,)DMSO mixtures, are liquid over the entire composition range and temperatures from 103 to 121°C. On the other hand, the observed relative low vapour pressure of the above systems enabled the accurate determination of p and n.
As previously [ 1l], the polynomial
The apparatus and procedure for the experimental measurements of density and viscosity were identical with those described previously [l 11. The overall estimated accuracy on the density and viscosity values was f0.04% and +0.2% respectively. Experiments were generally performed in at least five replicates for each composition and temperature and the results were averaged.
p(gcme3) = i
4X:
i-0
equation:
(1)
was fitted at each temperature and for 0 < x, < 0.9 by the least-squares technique. It was found that the optimum degree n was equal to 4, namely much less than the number of data points. The values of the
Table 2 Experimental viscosity q for the x,(Ag,Tl)NO, + (1 - x,)(DMSO/HQ
system at
various temperatures
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
(1 - x,)
103°C
106°C
109°C
112°C q(lOF Pas)
115°C
118°C
121°C
0.748 1.333 2.140 3.413 5.343 7.674 10.46 11.40 13.94 17.18
0.721 1.283 2.053 3.268 5.110 7.276 9.818 10.66 13.01 16.04
0.695 1.237 1.973 3.131 4.903 6.929 9.200 9.998 12.24 15.00
0.670 1.192 1.902 3.004 4.705 6.618 8.655 9.430 11.50 14.13
0.648 1.149 1.829 2.892 4.510 6.311 8.175 8.897 10.81 13.27
0.627 1.107 1.767 2.782 4.330 6.034 7.713 8.413 10.17 12.46
0.607 1.069 I .705 2.686 4.161 5.769 7.310 7.913 9.600 11.81
Changes in (Ag,Tl)NOl + DMSO systems at several temperatures
109
Table 3 Coefficients and standard error of estimate s for representations of p and [R] of the x,(Ag,Tl)NOJ f (1 - x~)(DMSO/HZO) system by equations (1) and (25) 106°C
103°C
XS
Equation (1) do 1.02591 dl 3.72926 d2 1.91193 d, -3.93212
109°C
112°C
115°C
1.02049 3.73155
1.89823
1.94566
1.94493
s
0.0067 1
0.00668
Equation (25) Ro 19.0837 RI 9.5626 s 0.1537
19.0517 9.3584 0.1510
adjustable coefficients d, are summarized along with the standard error of estimate correlation coefficient R. A comparison
19.0194 9.1729 0.1458
in Table 3 s and the
of experimental and calculated data at 109°C is presented as an example in Fig. 1. The effect of temperature on the density p of the systems was examined by assuming the validity of the following equation [ 131: p = po - bz-.
18.9643 8.8140 0.1438
18.9913 8.9927 0.1446
1.@_I770 3.74740 1.84174 -3.88217 I .92949 0.00678 18.9387 8.6414 0.1409
18.9166 8.4756 0.1429
calculated by least squares, the following relations were derived: PO= i
CiX: = 1.4060 + 3.4049X,
,=O
+ 3.1133~3 - 4.5606~; + 2.0756x,9
(2)
For each composition and over the temperature range 103-121°C it was found that the plots of p vs T, obtained from experimental density data, were perfectly linear; the correlation coefficient was better than 0.9992. However, in order to minimize any influence of the experimental error on the values of the parameters PO and b, corresponding to various values of Xs, we used smoothed density data calculated from equation (1). For each composition and over the temperature range studied, straight lines were obtained (the linear correlation coefficient was very close to unity). Using the values of PO and b,
121°C
1.01454 3.72846 1.91864 -3.97796 I .97363 0.00686
-3.92640
h
118°C
(3)
= 10.09 - 8.5485x, + 31.70x: - 16.38~: + 3.3034x:.
(4)
It follows that the equation relating the density to the temperature, T, and the mole fraction of x,, is
This equation fits the experimental data over the specified range of temperatures (103-121°C) and for 0.1 < xI < 0.9 with an uncertainty of 0.20%. Molar volume
5 ,
I
The molar volume of a mixed fused salt-mixed solvent system formed by the mixture of two salts and a mixture of two molecular polar solvents, where the mole ratios of the salts and the solvents are equal to rr and r2 respectively, is defined by:
v=
XIMI + x2M2 + x3M3 + x4M4 P
00 0
0.2
0.4
x
0.6
0.8
1
‘
Fig. 1. Density p as function of the salt mole fraction X, for the (Ag,Tl)NOj + DMSO + Hz0 system at 109°C: (a), experimentat values; (-), smoothed curve calculated from equation (1).
(6)
where MI and M2 are the molecular weights of the salts, Mr and M.+ the molecular weights of the solvents and XI, x2, x3 and x4 the corresponding mole fractions. However, taking into account that: Xl =
r1
x+s
(7)
I. I. Ziogas and G. Papanastasiou
110
x3=
*
(l-x,)
(
x4=
>
&
(l-x,)
(
>
(11)
x,=x1+x2
x,
=
1 - x, =
x3 +
x4
(12)
one obtains:
0
0.2
0.6
0.4 x
V=A+Bxs P
(13)
where A=
r2M3
+
A44
1 +r2
0.8
1
I
Fig. 2. VE as a function of the melt mole fraction x, for the (Ag,TI)NO>+ DMSO (data from Ref. 11) and (Ag,Tl)NOs + DMSO + Hz0 systems at 109°C. (a), experimental values; (-), smoothed curve calculated from equations (15), (16) and (5); (- - -) region where a miscibility gap occurs.
and B=
rlMl+M2_A
l+rl
’
(14)
It follows that for the system (Ag,TI)NOrDMSO, where rl = 1.062 and t-2= 1.0, equation (13) is reduced to the following expression: v = 48.073 + 168.60x, P .
(15)
The excess molar volume is detined by: VE=V-
I@= V-(x,~+(l-x,)~~m,)
(16)
where rP, and c are, respectively, the molar volumes of the solvent and the liquid salt mixture. At each temperature, these quantities have been calculated from the following relationships: rp_ A:B s PI
216.67 =D PS
(17)
(18) pf and p: being, respectively, the densities of the pure melt and the equimolar solvent mixture at the corresponding temperature. Using equations (15) and (16) and smoothed density data calculated from equation (5), the values of VE as a function of xs were calculated at various temperatures T. In these calculations, the values of c were obtained at each temperature from data reported in literature[ 141.In all temperatures studied, it was found that the values of VE are negative, and the corresponding curves VE =f(x,) at each temperature present a pronounced minimum at x, s 0.40, as it is shown by the example in Fig. 2. In general, solute-solvent interactions increase density and decrease molar volume; the negative values of VE could be attributed to this behaviour. On the other hand, Kodejs and Sacchetto derived an
equation, based on a statistical mechanical treatment of the quasi-lattice model, for the dependence of the molar volume of fused salt-water mixtures on molar composition [ 151. This theoretical model ascribes negative deviations from the ideality in the case where a contraction of the solvent molar volume at sites near ions occurs; this contraction is induced by the ion-solvent interactions. So, assuming the validity of this model we can attribute the negative values of VE mainly to the above mentioned “contraction effect”. A point of interest is that the minimum values of VE (maximum ion-solvent interactions), are observed for all temperatures at mole ratio, n,/n,, of mixedsolvent/salt around 1.5:l {x3 = l/[l + (n,/n,)] x 0.40). At this composition, assuming that all the solvent molecules are adsorbed on the melt, it follows that the corresponding mole ratio nm/nrr equal to 1.5, expresses the mean number r of sites offered by one “molecule” of the melt for adsorption of DMSO and water molecules. This value is very close with those of the system AgNOj-DMSO and LiNOj-DMSO, equal to 1.5 and 1.7 respectively at 373.2 K, recently obtained from determinations of the solvent activity[ 161. As it is shown from the plots of Fig. 2, which are given as an example, the observed “contraction effect” of the systems studied in this investigation is significantly weaker than that of the (Ag,Tl)NOJDMSO mixtures studied previously [l 1, 121. The differences observed between the VE values of the two systems can be attributed to the fact that the ion-solvent interactions are stronger in the (Ag,Tl)NOJ-DMSO systems than in the corresponding mixtures, where DMSO was partially replaced by HzO. Assuming that all the above mentioned interactions are principally ion-dipole electrostatic interactions, this behaviour can be correlated to the fact that DMSO is more polar (pu~so = 3.96 D) than water (pu*o = 1.83 D). It is worth noting that the
111
Changes in (Ag,Tl)NOJ + DMSO systems at several temperatures experimental study of the enthalpies of transfer of various cations from water to DMSO in dilute solutions evidenced that the cation-dipole interactions are stronger in DMSO solutions than those of the aqueous ones [ 171. Coefficient of thermal expansion
interactions. viisIties As previously [ 11, l&20], in order to establish correlation functions relating the viscosity t) to the mixture composition at various temperatures, the rheochor [R] of the mixtures was calculated from the following equation by using smoothed density data:
The coefficient of thermal expansion K of the fused salt-solvent systems have been determined from the following equation derived previously [ 111:
[R] = y
$iS = P,l/S
(23)
where (M) = 48.073 + 168.60x,.
(24)
It was found that the plots of [R] vs x, are linear (R > 0.9988) and that the corresponding data at each temperature and for 0 < xs < 1 can be fitted, by least-squares, to the following equation This equation permits the determination of K at any value of x, and T lying within the specified range of temperatures (103-121°C) and compositions (0.1 < x, < 0.9). The ideal coefficient of thermal expansion lcidof a mixture can be determined by the following relationship [ 111:
106([R]/(m3.(Pa s)iie mol-I)) = Ro + RlxI (25) whose coefficients RO and RI are summarized in Table 3. By combining equations (l), (23)-(25) one obtains: (Ro + RIX,) l/8 = rl
where e0 is the molar volume of the pure solvent, K:. and K," are respectively the coefficients of thermal expansion of the equimolar solvent mixture and the pure melt. The excess coefficient of thermal expansion is defined by: KE = K _ Kid= _b _ Kid. P For the system (Ag,Tl)NOJ-DMSO-HZO, nation of the above equations gives:
i d,x: ( i=O >
48.073 + 168.60x,
(26)
’
As previously [ 11, 18-201, it was found in this investigation that, in all cases, equation (26) fits the viscosity data better than a simple polynomial of 4 degrees relating q with x,. A comparison of experimental and calculated data at 109°C is presented as an example in Fig. 3. The variation of viscosity with temperature was correlated by the Eyring’s equation. This equation for a simple liquid is given by [l 11:
(21) combi-
q= {$$exp(
(27)
- y)}exp(g)
where NA and h are respectively the Avogadro’s and Plan&s constants and AH+ is the activation
*O L -
xs cK,o
+
-I
(1 - xs)~~so,~~~&o,~~~
x,q+(l
. (22) - &) VODMso,H*O
Using equation (22), the values of ~~ as a function of xs were calculated at various temperatures T. In these calculations, the values of K,” were obtained at each temperature from data reported in the literature [ 141.In all temperatures studied, it was found that the values of ~~ are negative, and the corresponding curves K' =f(x,) at each temperature present a pronounced minimum. This behaviour could be attributed, as in the case of FE, to various ion-solvent
1
0
0
0.2
0.4
0.6 x
0.8
1
I
Fig. 3. Viscosity q as function of the salt mole fraction xI for the (Ag,Tl)NO, + DMSO + Hz0 system at 109°C: (O), experimental values; (-), smoothed curve calculated from equation (26).
112
I. I. Ziogas and G. Papanastasiou
enthalpy of viscous flow. In the case of a binary mixture, the molar volume V is defined by equation (13). Since AS+ is taken as constant, equation (27) predicts a linear relationship between ln(qV) and l/T. Alternatively, the experimental confirmation of such a correlation is evidence of the validity of the Eyring’s equation over the specified range of temperatures. Smoothed viscosity and molar volume data, calculated using equations (26), (15) and (l), were used in the plots of ln(vV) vs l/T. For each composition and over the temperature range 376.15 < T < 394.15, it was found that the graphs ln(qV) vs l/T were perfectly linear (R > 0.9998). The obtained parameters are graphically represented in Fig. 4. The following relations were obtained: AH*/(kJ mol-I) = i HiXi = 13.23 - 5.327~~ i-0 + 92.82~; - 190.6x: + 221.4x: - 140.7x; + 37.44x; (R’ x 1.0, SA,,= 2.8 W3 kJ)
(28)
AS+/(J mol-* K-r) = i Sixi = - 1.941 - 60.23x, i-0 + 233.7~; - 377.4~: +401.3x:
- 250.1~;
+ 64.74x: (R* z 1.00, sk = 6.7 x 10s3 J mol-’ K-r). Consequently, by combining (27)-(29) we can write:
equations
(29)
(5), (15),
25 I
g 20
0
0.2
0.4 a 0.6
0.8
1
‘ Fig. 4. Activation enthalpy of viscous flow AH+ and activation entropy of viscous flow AS+‘, obtained using calculated molar volume and viscosity data from equations (15) and (26), as functions of the salt mole fraction x, for the (Ag,Tl)NO, + DMSO (data from Ref. 11) and (Ag,Tl)NOJ + DMSO + Hz0 systems. (- - -) region where a miscibility gap occurs.
rl=
48.073 + 168.6x,
x exp
Equation (30), expressing rj as a function of xr and T, fits the experimental data over the specified range of temperatures (103-121°C) and for 0.1 < x, Q 0.9. This equation predicts the experimental data with an overall uncertainty of k2.0 x 10e4 Pa s. Figure 4 shows that AH+ decreases as the mole fraction of the mixed solvent xX,(= 1 - xs) increases. This behaviour could be explained by assuming a mechanism of hole formation in the process of viscous flow. Indeed, the activation energy for viscous flow, being close to the formation energy of a hole, decreases when the number of holes in the liquid increases [4,21]. By analogy with the (Ag,Tl)N03-Hz0 and (Ag,Tl)NOrDMSO systems [4, 111, we can assume that the number of holes increases when the equimolar solvent mixture of DMSO and Hz0 is progressively added to the melt. One can see from Fig. 4 that, the activation enthalpy of viscous flow of the (Ag,Tl)NOJ-DMSO mixtures, AH&,, is significantly greater than that of the corresponding (Ag,Tl)NOrDMSO-Hz0 ones. As previously, this effect could be attributed to the fact that the cation-dipole interactions decrease by the partial replacement of the more polar component DMSO (~DMSO= 3.96 D) by water &O = 1.83 D). However, for xs < 0.18, where the main participating component in the viscous flow is the corresponding solvent, one observes AH&so,~~o ’ AH&so. This behaviour could be attributed to various water-water and water-DMSO interactions. Indeed, it has been argued in literature that when DMSO is added to water, the hydrogen bond network of Hz0 is enhanced [17,22-241. On the other hand, there is experimental evidence for intermolecular associations between DMSO and water [ 17,241. Consequently, taking into account the above remarks, we can attribute the observed behaviour to all these effects. The variation of the entropy of activation AS+ vs xs is given in Fig. 4. It can be seen from Fig. 4 that the shape of this plot presenting a pronounced minimum is quite different from that observed in the case of the (Ag,Tl)NOrDMSO mixtures, where the corresponding graph increased continuously with xJ [l 11. It is noted that AS+ alters its sign for mixtures with high salt content, while its minimum, at mole fraction x,““, lies within the composition
Changes in (Ag,Tl)N03 + DMSO systems at several temperatures range where AH&,W,H20 becomes greater than AH&so. According to Abraham et al. the change in the sign of AS+ and the existence of a minimum indicate that there is presumably no unique and simple mechanism of viscous flow, but several and competing mechanisms are likely to occur in different sections of the liquid [5]. According to the above authors, a very simplified picture describes the liquid as consisting of only two types of structures. One of them has a high degree of order, close to that of a crystal, while the other is relatively disordered. In the highly ordered type, hole formation could be associated with a lowering of the local degree of order. Consequently, the passage of a unit of flow from one equilibrium position to another is accompanied by a positive contribution to the entropy of activation. In the relatively disordered structure of the liquid, the mechanism of flow is eventually associated with an increase of the local degree of order. So, a negative contribution to AS may be observed. The activation entropy of viscous flow becomes positive for mixtures with high salt content where the salt is the main participating component in the viscous flow. This behaviour could be interpreted by assuming that the predominant structure of these liquids presents a relatively high degree of order. As the mole fraction of the solvent, x,., increases, the salt-solvent mixtures become less ordered decreasing the activation entropy. However, for mixtures with high solvent content (x, < xp), where the main participating component in the viscous flow is the solvent, one can see from Fig. 4 that AS+ increases as x, decreases. As previously, this behaviour could be attributed to various water-water and water-DMSO interactions, by assuming, in agreement with literature data [17], that these interactions contribute positively to the order of the system. REFERENCES 1. M.-C. Abraham,
M. Abraham, A. Combey and J. Sangster, J. Chem. Eng. Data 28, 259 (1983).
113
2. M. Abraham, J. Chim. Phys. 81, 207 (1984). 3. M. Abraham and M.-C. Abraham, Electrochim. Acta 31, 821 (1986). 4. M. Abraham and M.-C. Abraham, Electrochim. Acta 32. 1475 (1987). 5. M: Abraham and M.-C. Abraham, Electrochim. Acta 33, 967 (1988). 6. M. Abraham and M.-C. Abraham, J. Phys. Chem. 94, 900 (1990). 7. M. Abraham, I. Ziogas and M.-C. Abraham, J. Solution Chem. 19, 693 (1990). 8. M. Abraham, M.-C. Abraham and I. Ziogas, J. Am. Chem. Sot. 113, 8383 (1991). 9. I. Ziogas, M.-C. Abraham and M. Abraham, Electrochim. Acta 37, 349 (1992). 10. M. Abraham, M.-C. Abraham, I. Ziogas and Z. Kodejs, J. Am. Chem. Sot. 115, 4300 (1993). 11. I. Ziogas and G. Papanastasiou, Electrochim. Acta 39, 2517 (1994). 12. G. A.‘Saccheto and Z. Kodejs, Material Science Forum (Edited by M. Chemla and D. Devilhers), Vol. 73-75, p. 227. Trans. Tech. Publications, Switzerland (1991). 13. G. J. Janz, Molten Salts Handbook, p. 39. Academic Press, New York (1972). 14. M.-C. Abraham, M. Abraham and J. Sangster, J. Chem. Eng. Data 27, 200 (1982). 15. Z. Kodejs and G. Sacchetto, J. Chem. Sot., Faraday Trans. I, 78, 3529 (1982). 16. G. A. Sacchetto and Z. Kodejs, J. Chem. Sot., Faraday Trans. IS4, 2885 (1988). 17. H. H. Szmant, Dimethyl Sulfoxide (Edited by S. W. Jacob, E. E. Rosenbaum and D. C. Wood) Vol. 1, pp. 6, 34,39. Marcel Dekker, New York (1971) and references cited therein. 18. G. Papanastasiou, A. Papoutsis and G. Kokkinidis, J. Chem. Eng. Data 32, 377 (1987). 19. G. Papanastasiou and I. Ziogas, J. Chem. Eng. Data 36, 46 (1991). 20. G. Papanastasiou and I. Ziogas, J. Chem. Eng. Data 37, 167 (1992). 21. S. Glassstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes, p. 488. McGraw-Hill Co., New York (1941). 22. J. T. W. Lai, F. W. Lau, D. Robb, P. Westh, G. Nielsen, C. Trandum, A. Hvidt and Y. Koga, J. Solution Chem. 24, 89 (1995). 23. C. De Visser, W. J. M. Heuvelsland, L. A. Dunn and G. Somsen, Trans. Faraday Sot. 74, 1159 (1978). 24. G. J. Safford, P. C. Schaffer, P. S. Leung, G. F. Doebbler, G. W. Brady and E. F. X. Lyden, J. Chem. Phys. SO, 2140 (1969).
Ekcrrochimica Am, Vol. 42, No. 1, pp. 107-113, 1997 Copyright 0 1996 Elsevier Science Ltd. Printed in Great Britain. All rights reserved SOO13-4686(~172-7 0013-4686/97 $17.00 + 0.00
Density, molar volume, thermal expansion and viscosity changes of (Ag,TI)N03 + dimethylsulfoxide + water systems at several temperatures Ioannis I. Ziogas and Georgios Papanastasiou Aristotle University of Thessaloniki,
Department of Chemistry, Laboratory 540 06 Thessaloniki. Greece
of Physical Chemistry,
(Received 18 December 1995; in revised form 15 April 1996) Abstract-Viscosities and densities of the system (Ago.~,Tlo,s)NO3+ DMSO + Hz0 were determined in the temperature range 376 < T/K < 394 K with the mole fraction of the mixed melt, xs, ranging between 0 and 0.9. This system, formed by the eutectic mixture of AgNOJ and TlNOj (eutectic point equal to 83”C, AgNO,/TlNO3 mole ratio equal to 1.062) and an equimolar mixture of dimethylsulfoxide with water, is liquid over the specified temperature and composition range. Parameters such as the molar volume, the volume coefficient of thermal expansion, the rheochor and the activation entropy and enthalpy in the Eyring’s equation were determined. An attempt has been made to express these properties by means of single equations, wherein the temperature and composition effects are involved. The behaviour of the system studied here is compared with that of the corresponding (A@.~,Tlo,s)N0, + DMSO systems, previously investigated. The results indicate that the partial replacement of DMSO with water decreases the cation-dipole interactions. Copyright 0 1996 Elsevier Science Ltd Key words: Molten salt, nitrate, viscosity, thermal expansion, hydrate melts.
1. INTRODUCTION
system, the use of DMSO, a high boiling point polar organic solvent, enabled us to extend the temperature range up to 121°C. However, in agreement with analogous literature data [12], we observed that this system presented a miscibility gap, in the temperature range 103 < T < 121°C and for mole fraction of the melt ranging between 0.55 and 0.75. This situation has motivated us to make a series of systematic measurements of density and viscosity of the (Ag,Tl)NOrDMSO-Hz0 systems, where the AgNOs/TlNOJ and HzO/DMSO mole ratios were equal to 1.062 and 1.0, respectively, over the whole composition range with temperatures from 103 to 121°C. We believe that these ternary systems, prepared from the corresponding aqueous mixtures by partial replacement of Hz0 with DMSO, are of considerable interest because it allows one to establish an experimental link between the behaviour of the corresponding binary (Ag,Tl)NOrH20 and (Ag,Tl)NO,-DMSO mixtures. Parameters such as the activation entropy and enthalpy in the Eyring’s equation, the molar volume, the rheochor and the coefficient of the thermal expansion of
For theoretical and various practical developments, the investigation of the so-called bridging systems (ie electrolyte systems extending in the liquid phase from a dilute solution in a polar molecular solvent such as water to a pure fused salt) has been the object of intense scrutiny. Unfortunately, the study of some physical properties of such hydrate systems over the entire composition range presents many difficulties due to the limited solubility of the salts at temperatures below 100°C or to the high vapour pressure at temperatures higher than 100°C. The system (Ag,Tl)NOJ-Hz0 formed by water and the eutectic mixture of AgNOj and T~NOJ (eutectic point equal to 83°C) is one of the few binary systems which are liquid over the entire composition range at temperatures below 100°C. This system has been extensively investigated by Abraham et al. [l-10]. In these frames, we examined in a previous paper the (Ag,Tl)NOrDMSO system, where the water has been replaced by dimethylsulfoxide [l 11. In this 107
108
I. I. Ziogas and G. Papanastasiou
the system studied were determined over the specified temperature and composition range. An attempt has been made to express these properties by means of single equations, wherein the temperature and composition effects are involved. It is noted that the physical behaviour of the above mentioned system, at various compositions and temperatures, seems not to have been investigated previously. 2. EXPERIMENTAL Chemicals Reagent-grade AgNO3 (Fluka, puriss. p.a. > 99.5%) was vacuum-desiccated at about 120°C and TlNO, (Fluka, purum stored over P205. p.a. > 99.0%) was re-crystallized in water, filtered, dried at 120°C in vacuum and stored over Pros. Conductivity water (conductance w 1.0 x 10e6 a-’ cm-‘) was used throughout. Reagent-grade dimethylsulfoxide (Merck, p.a. > 99.5%), containing not more than 0.03% water, was used and stored at room temperature over 4A molecular sieves. The systems xJAg,Tl)NOr + (1 - x,)(DMSO/HrO), x, being the mole fraction of the salt mixture, were obtained by addition of an equimolar solution of DMSO with water to the eutectic nitrate mixture having the following fixed composition in mole fractions: 0.515 AgNOsa.485 TlNOj. The salt and solvent mixtures are simply indicated as (Ag,Tl)NOs and DMSO/HrO respectively throughout this paper. All the solutions were gravimetrically prepared on a Mettler analytical balance just before their use. Measurements
Table 1 Experimental density p for the x,(Ag,TI)NO,+ (DMSO/HzO) system at various temperatures X-3
103°C
109°C 115°C P(g m-))
121°C
0.0
1.023 I .424 1.814 2.221 2.621 2.997 3.359 3.688 4.016 4.342
1.018 1.418 1.808 2.215 2.621 2.990 3.351 3.679 4.007 4.331
1.005 1.406 1.797 2.204 2.608 2.975 3.335 3.662 3.987 4.309
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
1.012 1.412 1.802 2.209 2.615 2.983 3.343 3.670 3.997 4.320
3. RESULTS AND DISCUSSION The experimental density (p) and viscosity (?I) of the systems x,(Ag,Tl)NOr + (1 - xx) (DMSO/HrO) with respect to the mole fraction x, of the melt are given in Tables 1 and 2 at various systems, contrary to temperatures. These x,(Ag,Tl)NOJ + (1 - x,)DMSO mixtures, are liquid over the entire composition range and temperatures from 103 to 121°C. On the other hand, the observed relative low vapour pressure of the above systems enabled the accurate determination of p and n.
As previously [ 1l], the polynomial
The apparatus and procedure for the experimental measurements of density and viscosity were identical with those described previously [l 11. The overall estimated accuracy on the density and viscosity values was f0.04% and +0.2% respectively. Experiments were generally performed in at least five replicates for each composition and temperature and the results were averaged.
p(gcme3) = i
4X:
i-0
equation:
(1)
was fitted at each temperature and for 0 < x, < 0.9 by the least-squares technique. It was found that the optimum degree n was equal to 4, namely much less than the number of data points. The values of the
Table 2 Experimental viscosity q for the x,(Ag,Tl)NO, + (1 - x,)(DMSO/HQ
system at
various temperatures
0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
(1 - x,)
103°C
106°C
109°C
112°C q(lOF Pas)
115°C
118°C
121°C
0.748 1.333 2.140 3.413 5.343 7.674 10.46 11.40 13.94 17.18
0.721 1.283 2.053 3.268 5.110 7.276 9.818 10.66 13.01 16.04
0.695 1.237 1.973 3.131 4.903 6.929 9.200 9.998 12.24 15.00
0.670 1.192 1.902 3.004 4.705 6.618 8.655 9.430 11.50 14.13
0.648 1.149 1.829 2.892 4.510 6.311 8.175 8.897 10.81 13.27
0.627 1.107 1.767 2.782 4.330 6.034 7.713 8.413 10.17 12.46
0.607 1.069 I .705 2.686 4.161 5.769 7.310 7.913 9.600 11.81
Changes in (Ag,Tl)NOl + DMSO systems at several temperatures
109
Table 3 Coefficients and standard error of estimate s for representations of p and [R] of the x,(Ag,Tl)NOJ f (1 - x~)(DMSO/HZO) system by equations (1) and (25) 106°C
103°C
XS
Equation (1) do 1.02591 dl 3.72926 d2 1.91193 d, -3.93212
109°C
112°C
115°C
1.02049 3.73155
1.89823
1.94566
1.94493
s
0.0067 1
0.00668
Equation (25) Ro 19.0837 RI 9.5626 s 0.1537
19.0517 9.3584 0.1510
adjustable coefficients d, are summarized along with the standard error of estimate correlation coefficient R. A comparison
19.0194 9.1729 0.1458
in Table 3 s and the
of experimental and calculated data at 109°C is presented as an example in Fig. 1. The effect of temperature on the density p of the systems was examined by assuming the validity of the following equation [ 131: p = po - bz-.
18.9643 8.8140 0.1438
18.9913 8.9927 0.1446
1.@_I770 3.74740 1.84174 -3.88217 I .92949 0.00678 18.9387 8.6414 0.1409
18.9166 8.4756 0.1429
calculated by least squares, the following relations were derived: PO= i
CiX: = 1.4060 + 3.4049X,
,=O
+ 3.1133~3 - 4.5606~; + 2.0756x,9
(2)
For each composition and over the temperature range 103-121°C it was found that the plots of p vs T, obtained from experimental density data, were perfectly linear; the correlation coefficient was better than 0.9992. However, in order to minimize any influence of the experimental error on the values of the parameters PO and b, corresponding to various values of Xs, we used smoothed density data calculated from equation (1). For each composition and over the temperature range studied, straight lines were obtained (the linear correlation coefficient was very close to unity). Using the values of PO and b,
121°C
1.01454 3.72846 1.91864 -3.97796 I .97363 0.00686
-3.92640
h
118°C
(3)
= 10.09 - 8.5485x, + 31.70x: - 16.38~: + 3.3034x:.
(4)
It follows that the equation relating the density to the temperature, T, and the mole fraction of x,, is
This equation fits the experimental data over the specified range of temperatures (103-121°C) and for 0.1 < xI < 0.9 with an uncertainty of 0.20%. Molar volume
5 ,
I
The molar volume of a mixed fused salt-mixed solvent system formed by the mixture of two salts and a mixture of two molecular polar solvents, where the mole ratios of the salts and the solvents are equal to rr and r2 respectively, is defined by:
v=
XIMI + x2M2 + x3M3 + x4M4 P
00 0
0.2
0.4
x
0.6
0.8
1
‘
Fig. 1. Density p as function of the salt mole fraction X, for the (Ag,Tl)NOj + DMSO + Hz0 system at 109°C: (a), experimentat values; (-), smoothed curve calculated from equation (1).
(6)
where MI and M2 are the molecular weights of the salts, Mr and M.+ the molecular weights of the solvents and XI, x2, x3 and x4 the corresponding mole fractions. However, taking into account that: Xl =
r1
x+s
(7)
I. I. Ziogas and G. Papanastasiou
110
x3=
*
(l-x,)
(
x4=
>
&
(l-x,)
(
>
(11)
x,=x1+x2
x,
=
1 - x, =
x3 +
x4
(12)
one obtains:
0
0.2
0.6
0.4 x
V=A+Bxs P
(13)
where A=
r2M3
+
A44
1 +r2
0.8
1
I
Fig. 2. VE as a function of the melt mole fraction x, for the (Ag,TI)NO>+ DMSO (data from Ref. 11) and (Ag,Tl)NOs + DMSO + Hz0 systems at 109°C. (a), experimental values; (-), smoothed curve calculated from equations (15), (16) and (5); (- - -) region where a miscibility gap occurs.
and B=
rlMl+M2_A
l+rl
’
(14)
It follows that for the system (Ag,TI)NOrDMSO, where rl = 1.062 and t-2= 1.0, equation (13) is reduced to the following expression: v = 48.073 + 168.60x, P .
(15)
The excess molar volume is detined by: VE=V-
I@= V-(x,~+(l-x,)~~m,)
(16)
where rP, and c are, respectively, the molar volumes of the solvent and the liquid salt mixture. At each temperature, these quantities have been calculated from the following relationships: rp_ A:B s PI
216.67 =D PS
(17)
(18) pf and p: being, respectively, the densities of the pure melt and the equimolar solvent mixture at the corresponding temperature. Using equations (15) and (16) and smoothed density data calculated from equation (5), the values of VE as a function of xs were calculated at various temperatures T. In these calculations, the values of c were obtained at each temperature from data reported in literature[ 141.In all temperatures studied, it was found that the values of VE are negative, and the corresponding curves VE =f(x,) at each temperature present a pronounced minimum at x, s 0.40, as it is shown by the example in Fig. 2. In general, solute-solvent interactions increase density and decrease molar volume; the negative values of VE could be attributed to this behaviour. On the other hand, Kodejs and Sacchetto derived an
equation, based on a statistical mechanical treatment of the quasi-lattice model, for the dependence of the molar volume of fused salt-water mixtures on molar composition [ 151. This theoretical model ascribes negative deviations from the ideality in the case where a contraction of the solvent molar volume at sites near ions occurs; this contraction is induced by the ion-solvent interactions. So, assuming the validity of this model we can attribute the negative values of VE mainly to the above mentioned “contraction effect”. A point of interest is that the minimum values of VE (maximum ion-solvent interactions), are observed for all temperatures at mole ratio, n,/n,, of mixedsolvent/salt around 1.5:l {x3 = l/[l + (n,/n,)] x 0.40). At this composition, assuming that all the solvent molecules are adsorbed on the melt, it follows that the corresponding mole ratio nm/nrr equal to 1.5, expresses the mean number r of sites offered by one “molecule” of the melt for adsorption of DMSO and water molecules. This value is very close with those of the system AgNOj-DMSO and LiNOj-DMSO, equal to 1.5 and 1.7 respectively at 373.2 K, recently obtained from determinations of the solvent activity[ 161. As it is shown from the plots of Fig. 2, which are given as an example, the observed “contraction effect” of the systems studied in this investigation is significantly weaker than that of the (Ag,Tl)NOJDMSO mixtures studied previously [l 1, 121. The differences observed between the VE values of the two systems can be attributed to the fact that the ion-solvent interactions are stronger in the (Ag,Tl)NOJ-DMSO systems than in the corresponding mixtures, where DMSO was partially replaced by HzO. Assuming that all the above mentioned interactions are principally ion-dipole electrostatic interactions, this behaviour can be correlated to the fact that DMSO is more polar (pu~so = 3.96 D) than water (pu*o = 1.83 D). It is worth noting that the
111
Changes in (Ag,Tl)NOJ + DMSO systems at several temperatures experimental study of the enthalpies of transfer of various cations from water to DMSO in dilute solutions evidenced that the cation-dipole interactions are stronger in DMSO solutions than those of the aqueous ones [ 171. Coefficient of thermal expansion
interactions. viisIties As previously [ 11, l&20], in order to establish correlation functions relating the viscosity t) to the mixture composition at various temperatures, the rheochor [R] of the mixtures was calculated from the following equation by using smoothed density data:
The coefficient of thermal expansion K of the fused salt-solvent systems have been determined from the following equation derived previously [ 111:
[R] = y
$iS = P,l/S
(23)
where (M) = 48.073 + 168.60x,.
(24)
It was found that the plots of [R] vs x, are linear (R > 0.9988) and that the corresponding data at each temperature and for 0 < xs < 1 can be fitted, by least-squares, to the following equation This equation permits the determination of K at any value of x, and T lying within the specified range of temperatures (103-121°C) and compositions (0.1 < x, < 0.9). The ideal coefficient of thermal expansion lcidof a mixture can be determined by the following relationship [ 111:
106([R]/(m3.(Pa s)iie mol-I)) = Ro + RlxI (25) whose coefficients RO and RI are summarized in Table 3. By combining equations (l), (23)-(25) one obtains: (Ro + RIX,) l/8 = rl
where e0 is the molar volume of the pure solvent, K:. and K," are respectively the coefficients of thermal expansion of the equimolar solvent mixture and the pure melt. The excess coefficient of thermal expansion is defined by: KE = K _ Kid= _b _ Kid. P For the system (Ag,Tl)NOJ-DMSO-HZO, nation of the above equations gives:
i d,x: ( i=O >
48.073 + 168.60x,
(26)
’
As previously [ 11, 18-201, it was found in this investigation that, in all cases, equation (26) fits the viscosity data better than a simple polynomial of 4 degrees relating q with x,. A comparison of experimental and calculated data at 109°C is presented as an example in Fig. 3. The variation of viscosity with temperature was correlated by the Eyring’s equation. This equation for a simple liquid is given by [l 11:
(21) combi-
q= {$$exp(
(27)
- y)}exp(g)
where NA and h are respectively the Avogadro’s and Plan&s constants and AH+ is the activation
*O L -
xs cK,o
+
-I
(1 - xs)~~so,~~~&o,~~~
x,q+(l
. (22) - &) VODMso,H*O
Using equation (22), the values of ~~ as a function of xs were calculated at various temperatures T. In these calculations, the values of K,” were obtained at each temperature from data reported in the literature [ 141.In all temperatures studied, it was found that the values of ~~ are negative, and the corresponding curves K' =f(x,) at each temperature present a pronounced minimum. This behaviour could be attributed, as in the case of FE, to various ion-solvent
1
0
0
0.2
0.4
0.6 x
0.8
1
I
Fig. 3. Viscosity q as function of the salt mole fraction xI for the (Ag,Tl)NO, + DMSO + Hz0 system at 109°C: (O), experimental values; (-), smoothed curve calculated from equation (26).
112
I. I. Ziogas and G. Papanastasiou
enthalpy of viscous flow. In the case of a binary mixture, the molar volume V is defined by equation (13). Since AS+ is taken as constant, equation (27) predicts a linear relationship between ln(qV) and l/T. Alternatively, the experimental confirmation of such a correlation is evidence of the validity of the Eyring’s equation over the specified range of temperatures. Smoothed viscosity and molar volume data, calculated using equations (26), (15) and (l), were used in the plots of ln(vV) vs l/T. For each composition and over the temperature range 376.15 < T < 394.15, it was found that the graphs ln(qV) vs l/T were perfectly linear (R > 0.9998). The obtained parameters are graphically represented in Fig. 4. The following relations were obtained: AH*/(kJ mol-I) = i HiXi = 13.23 - 5.327~~ i-0 + 92.82~; - 190.6x: + 221.4x: - 140.7x; + 37.44x; (R’ x 1.0, SA,,= 2.8 W3 kJ)
(28)
AS+/(J mol-* K-r) = i Sixi = - 1.941 - 60.23x, i-0 + 233.7~; - 377.4~: +401.3x:
- 250.1~;
+ 64.74x: (R* z 1.00, sk = 6.7 x 10s3 J mol-’ K-r). Consequently, by combining (27)-(29) we can write:
equations
(29)
(5), (15),
25 I
g 20
0
0.2
0.4 a 0.6
0.8
1
‘ Fig. 4. Activation enthalpy of viscous flow AH+ and activation entropy of viscous flow AS+‘, obtained using calculated molar volume and viscosity data from equations (15) and (26), as functions of the salt mole fraction x, for the (Ag,Tl)NO, + DMSO (data from Ref. 11) and (Ag,Tl)NOJ + DMSO + Hz0 systems. (- - -) region where a miscibility gap occurs.
rl=
48.073 + 168.6x,
x exp
Equation (30), expressing rj as a function of xr and T, fits the experimental data over the specified range of temperatures (103-121°C) and for 0.1 < x, Q 0.9. This equation predicts the experimental data with an overall uncertainty of k2.0 x 10e4 Pa s. Figure 4 shows that AH+ decreases as the mole fraction of the mixed solvent xX,(= 1 - xs) increases. This behaviour could be explained by assuming a mechanism of hole formation in the process of viscous flow. Indeed, the activation energy for viscous flow, being close to the formation energy of a hole, decreases when the number of holes in the liquid increases [4,21]. By analogy with the (Ag,Tl)N03-Hz0 and (Ag,Tl)NOrDMSO systems [4, 111, we can assume that the number of holes increases when the equimolar solvent mixture of DMSO and Hz0 is progressively added to the melt. One can see from Fig. 4 that, the activation enthalpy of viscous flow of the (Ag,Tl)NOJ-DMSO mixtures, AH&,, is significantly greater than that of the corresponding (Ag,Tl)NOrDMSO-Hz0 ones. As previously, this effect could be attributed to the fact that the cation-dipole interactions decrease by the partial replacement of the more polar component DMSO (~DMSO= 3.96 D) by water &O = 1.83 D). However, for xs < 0.18, where the main participating component in the viscous flow is the corresponding solvent, one observes AH&so,~~o ’ AH&so. This behaviour could be attributed to various water-water and water-DMSO interactions. Indeed, it has been argued in literature that when DMSO is added to water, the hydrogen bond network of Hz0 is enhanced [17,22-241. On the other hand, there is experimental evidence for intermolecular associations between DMSO and water [ 17,241. Consequently, taking into account the above remarks, we can attribute the observed behaviour to all these effects. The variation of the entropy of activation AS+ vs xs is given in Fig. 4. It can be seen from Fig. 4 that the shape of this plot presenting a pronounced minimum is quite different from that observed in the case of the (Ag,Tl)NOrDMSO mixtures, where the corresponding graph increased continuously with xJ [l 11. It is noted that AS+ alters its sign for mixtures with high salt content, while its minimum, at mole fraction x,““, lies within the composition
Changes in (Ag,Tl)N03 + DMSO systems at several temperatures range where AH&,W,H20 becomes greater than AH&so. According to Abraham et al. the change in the sign of AS+ and the existence of a minimum indicate that there is presumably no unique and simple mechanism of viscous flow, but several and competing mechanisms are likely to occur in different sections of the liquid [5]. According to the above authors, a very simplified picture describes the liquid as consisting of only two types of structures. One of them has a high degree of order, close to that of a crystal, while the other is relatively disordered. In the highly ordered type, hole formation could be associated with a lowering of the local degree of order. Consequently, the passage of a unit of flow from one equilibrium position to another is accompanied by a positive contribution to the entropy of activation. In the relatively disordered structure of the liquid, the mechanism of flow is eventually associated with an increase of the local degree of order. So, a negative contribution to AS may be observed. The activation entropy of viscous flow becomes positive for mixtures with high salt content where the salt is the main participating component in the viscous flow. This behaviour could be interpreted by assuming that the predominant structure of these liquids presents a relatively high degree of order. As the mole fraction of the solvent, x,., increases, the salt-solvent mixtures become less ordered decreasing the activation entropy. However, for mixtures with high solvent content (x, < xp), where the main participating component in the viscous flow is the solvent, one can see from Fig. 4 that AS+ increases as x, decreases. As previously, this behaviour could be attributed to various water-water and water-DMSO interactions, by assuming, in agreement with literature data [17], that these interactions contribute positively to the order of the system. REFERENCES 1. M.-C. Abraham,
M. Abraham, A. Combey and J. Sangster, J. Chem. Eng. Data 28, 259 (1983).
113
2. M. Abraham, J. Chim. Phys. 81, 207 (1984). 3. M. Abraham and M.-C. Abraham, Electrochim. Acta 31, 821 (1986). 4. M. Abraham and M.-C. Abraham, Electrochim. Acta 32. 1475 (1987). 5. M: Abraham and M.-C. Abraham, Electrochim. Acta 33, 967 (1988). 6. M. Abraham and M.-C. Abraham, J. Phys. Chem. 94, 900 (1990). 7. M. Abraham, I. Ziogas and M.-C. Abraham, J. Solution Chem. 19, 693 (1990). 8. M. Abraham, M.-C. Abraham and I. Ziogas, J. Am. Chem. Sot. 113, 8383 (1991). 9. I. Ziogas, M.-C. Abraham and M. Abraham, Electrochim. Acta 37, 349 (1992). 10. M. Abraham, M.-C. Abraham, I. Ziogas and Z. Kodejs, J. Am. Chem. Sot. 115, 4300 (1993). 11. I. Ziogas and G. Papanastasiou, Electrochim. Acta 39, 2517 (1994). 12. G. A.‘Saccheto and Z. Kodejs, Material Science Forum (Edited by M. Chemla and D. Devilhers), Vol. 73-75, p. 227. Trans. Tech. Publications, Switzerland (1991). 13. G. J. Janz, Molten Salts Handbook, p. 39. Academic Press, New York (1972). 14. M.-C. Abraham, M. Abraham and J. Sangster, J. Chem. Eng. Data 27, 200 (1982). 15. Z. Kodejs and G. Sacchetto, J. Chem. Sot., Faraday Trans. I, 78, 3529 (1982). 16. G. A. Sacchetto and Z. Kodejs, J. Chem. Sot., Faraday Trans. IS4, 2885 (1988). 17. H. H. Szmant, Dimethyl Sulfoxide (Edited by S. W. Jacob, E. E. Rosenbaum and D. C. Wood) Vol. 1, pp. 6, 34,39. Marcel Dekker, New York (1971) and references cited therein. 18. G. Papanastasiou, A. Papoutsis and G. Kokkinidis, J. Chem. Eng. Data 32, 377 (1987). 19. G. Papanastasiou and I. Ziogas, J. Chem. Eng. Data 36, 46 (1991). 20. G. Papanastasiou and I. Ziogas, J. Chem. Eng. Data 37, 167 (1992). 21. S. Glassstone, K. J. Laidler and H. Eyring, The Theory of Rate Processes, p. 488. McGraw-Hill Co., New York (1941). 22. J. T. W. Lai, F. W. Lau, D. Robb, P. Westh, G. Nielsen, C. Trandum, A. Hvidt and Y. Koga, J. Solution Chem. 24, 89 (1995). 23. C. De Visser, W. J. M. Heuvelsland, L. A. Dunn and G. Somsen, Trans. Faraday Sot. 74, 1159 (1978). 24. G. J. Safford, P. C. Schaffer, P. S. Leung, G. F. Doebbler, G. W. Brady and E. F. X. Lyden, J. Chem. Phys. SO, 2140 (1969).