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Solubility of I2(s) and equilibrium concentration of the (I2+C6H6) charge transfer complex in supercritical xenon with added C6H6
J. Chem. Thermodynamics 1997, 29, 1209]1221
Solubility of I 2( s) and equilibrium concentration of the ( I 2 H C 6 H 6 ) charge transfer complex in supercritical xenon with added C 6 H 6 Hugo Destaillats Instituto de Quımica Fısica ´ ´ de Materiales, Ambiente y Energıa, ´ Facultad de Ciencias Exactas y Naturales, Uni¨ ersidad de Buenos Aires, Ciudad Uni¨ ersitaria Pabellon ´ II, 1428-Capital Federal, Argentina a and Roberto Fernandez-Prini ´
Instituto de Quımica Fısica ´ ´ de Materiales, Ambiente y Energıa, ´ Facultad de Ciencias Exactas y Naturales, Uni¨ ersidad de Buenos Aires, Ciudad Uni¨ ersitaria Pabellon ´ II, 1428-Capital Federal, and Unidad de Acti¨ adad Quımica, Comision ´ ´ Nacional de Energıa ´ Atomica, A¨ . Liberador 8350, 1429-Capital Federal, Argentina ´
The solubility of I 2 Žs. in supercritical xenon with and without added C 6 H 6 has been measured at the temperatures T s Ž300.79 " 0.04. K and Ž318.70 " 0.02. K over the pressure range from 5 MPa to 10 MPa. The u.v. absorbance due to the charge transfer interaction between I 2 Žacceptor. and C 6 H 6 Ždonor. was also measured when the fluid was saturated, and also when unsaturated, with I 2 . The enhancement of the solubility of I 2 Žs. due to added C 6 H 6 was moderate, supporting the view that the charge transfer process does not contribute significantly to the thermodynamic properties of donor and acceptor. The effect of density on the equilibrium concentration quotient for the formation of the donor]acceptor complex is discussed. Q 1997 Academic Press Limited KEYWORDS: solubility; supercritical fluid; iodine; charge transfer
1. Introduction The view that the strongly non-linear dependence on fluid density observed for many properties of solutes in dilute multicomponent supercritical fluids is due to the change in fluid density, and not to the position of the solvent’s critical points, is now gaining acceptance.Ž1 ] 3. This view explains why the maximum difference between observed and expected values of those properties often occurs at reduced densities between 0.3 and 0.7 and not at the solvent’s critical density. The possibility of describing theoretically the observed behaviour over the whole a To whom correspondence should be sent. Member of Carrera del Investigador CONICET ŽE-mail: [email protected]..
0021]9614r97r111209 q 13 $25.00r0rct970237
Q 1997 Academic Press Limited
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H. Destaillats and R. Fernandez-Prini ´
density range is hampered by the fact that at low fluid density microinhomogeneities may be present when solute] Žsolvent or co-solvent. interactions are strong.Ž4,5. Moreover, since the effective Hamiltonians which are used to describe intermolecular interactions are obtained by best-fitting fluid properties over limited density ranges, it is not surprising that they are unable to describe the whole fluid density range. We have previously reported values for the solubility of a series of simple solids in near-critical solvents,Ž6 ] 9. those studies form the basis of the present stage of our research into the behaviour of near-critical fluids, incorporating the study of the effect of fluid density upon charge transfer processes. In the present work we report the results of a study of dilute ŽI 2 q C 6 H 6 . in supercritical xenon at two temperatures close to the solvent’s critical temperature, Tc . We have determined the solubility of I 2 Žs. and calculated the concentration of donor]acceptor charge transfer complex by measurement of the visible and u.v. absorbance in the solution containing either I 2 or ŽI 2 q C 6 H 6 .. The equilibrium concentration quotient for the charge transfer complex was calculated and compared with the values obtained in the gas phase and in high density liquids. Observed changes in the concentration quotient for the charge transfer process introduced by the variation of supercritical solvent density appear to be related essentially to changes in infinite dilution activity coefficients of the species. No special features are observed in the neighbourhood of the solvent critical density, suggesting the absence of any clustering due to the position of the critical region.
2. Experimental In this study we have measured the u.v. and visible absorption of iodine dissolved in super-critical xenonŽ6. with and without added benzene. Our previous experience with solutions of I 2 in xenon suggested the convenience of employing a highpressure spectrophotometric cell and ancillary set-up, which minimizes the solutions’ exposure to stainless steel surfaces and avoiding iodine decomposition. Hence, a new high-pressure spectrophotometric cell was designed and built from titanium grade 1 Žfigure 1.. The 5 mm thick sapphire windows, 2, were located in two housings, 3, which were screwed onto the cell body, 1, so that their surfaces were pressed together defining the optical path of the cell; a longer path length was obtained by introducing a titanium ring as a spacer between the windows. One of the window housings had channels to allow the solution to fill the space between the two windows. The pressure seals, 7, were made of PTFE to avoid the presence of other materials which could react with iodine. An external magnet was rotated to stir the internal solution with a plastic-coated magnetic bar, thus ensuring equilibrium. Two different optical paths lengths in the spectrophotometric high-pressure cell could be chosen, thus affording some flexibility to optimize the conditions for the optical absorbance measurements. Their values, Ž1.15 " 0.02. mm and Ž5.16 " 0.02. mm, were determined by comparing the optical absorbance of two aqueous solutions Žpotassium ferricyanide and alkaline potassium chromate. in the high-
Solubility and charge transfer in supercritical xenon
1211
FIGURE 1. The titanium high-pressure optical cell. 1, cell body; 2, sapphire windows; 3, window housings, the spacer was positioned between the windows; 4, devices used to position the windows; 5, thermistor; 6, connecting socket for the tubing; 7, PTFE seals; 8, O-rings; 9, thermostatting jacket.
pressure spectrophotometric cell with those obtained from the same solutions in two standard quartz cells having path lengths of 1.00 and 5.00 mm. The volumes inside the cell for the two path lengths were Ž3.04 " 0.05. cm3 and Ž3.48 " 0.05. cm3 , respectively. Xe was loaded into the cell through a six-port valve employing a manual displacement pump. An h.p.l.c. loop was attached to the six-port valve and filled with benzene Žco-solvent. by means of a syringe; the co-solvent was then swept from the loop into the cell with xenon. The system’s pressure was determined with a Wika transducer, and a thermistor, whose tip was placed inside the cell, was used to measure the temperature of the system. Both probes were property calibrated, the uncertainties being 0.001 MPa and 0.01 K, respectively. Measurements were taken at the temperatures of 300.79 K and 318.70 K and a pressure range of 5 MPa to 10 MPa; the fluid density was in the range 5 mol . dmy3 to 13 mol . dmy3 at the lower temperature and 3 mol . dmy3 to 9 mol . dmy3 at the higher temperature. Iodine was Mallinkrodt Žtrisublimed., it was purified by sublimation in the presence of molecular sieves to eliminate all traces of water. The xenon used was AGA of 0.99995 mass fraction and the benzene was Merck pro analysi, both were used without further purification. The high-pressure system was evacuated after
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H. Destaillats and R. Fernandez-Prini ´
each run by distillation of the fluid into a system with two high-pressure bottles, which allowed us to recover and purify the xenon by successive distillations. The density of fluid xenon was calculated with an equation of state obtained from that reported for Ar Ž10. and the law of corresponding states, as described elsewhere.Ž6. This formulation could be used over the entire experimental Ž p, V, T . range and we have checked that the densities obtained are within 1 per cent of those that were determined experimentally for xenon.Ž11,12. The change of fluid density produced by the addition of benzene was neglected, as it is considered to be within 1 per cent of that of pure Xe at the same pressure and temperature, whenever the fluid density differed more than 15 per cent from the critical density. Closer to the critical density the change may amount to about 10 per cent for the highest benzene concentration employed in this work. Since we were interested in studying near-critical behaviour, the highest temperature chosen was 29 K above the critical temperature of xenon Tc . Keeping the temperature not too far above Tc was important and imposed a severe limitation in the maximum concentration of benzene that could be dissolved in the fluid supercritical Xe phase. On the other hand, it was desirable to have the highest possible concentration of benzene in that phase in order to maximize the contribution of I 2 ]C 6 H 6 cross-interactions. On the basis of the vapour pressure Ž13. the density of pure C 6 H 6 vapour is 5.7 . 10y3 mol . dmy3 and 11.6 . 10y3 mol . dmy3 at T s 300.79 K and T s 318.70 K, respectively. We added between one and three 14.9 mm3 h.p.l.c. loops of C 6 H 6 to the cell, thus benzene densities in the supercritical fluid never exceeded 0.18 mol . dmy3 . It was observed that the value of the concentration of benzene c 3 , obtained from the known volume of the h.p.l.c. loop, could only be considered a rough indication of the real concentration of benzene present in the cell, probably due to incomplete displacement of the total liquid slug in the loop to the high pressure cell. The real value of c 3 in the cell was determined by calibration of the maximum absorbance in the u.v. peak of benzene at 260.0 nm as a function of the concentration of benzene. This peak was chosen because of its good linear Lambert]Beer behaviour in the c 3 range used in this work Žslope s 11.0 dm3 . moly1 .. The contribution of the charge transfer band at 260.0 nm was subtracted in every case by Gaussian fitting this band. The use of this procedure to determine c 3 significantly improved the consistency of the data and potentially enables quantitative information to be obtained even if the supercritical fluid were saturated with benzene. We have tried to measure the solubility of benzene in Xe, however, even at low fluid density the u.v. absorbance of the 260.0 nm benzene peak was much bigger than that of the maximum c 3 used to obtain the linear Lambert]Beer plot, and linearity could not be guaranteed. This test confirmed that all the added benzene was dissolved in xenon. For a given run a small increase in c 3 was observed when fluid density increased Ž ¨ ide infra., this is attributed to the difficulty of sweeping the benzene slug from the inlet piping with Xe when loading the cell. Runs performed in the presence of I 2 Žs. enabled the determination of iodine solubility in the fluid, as well as providing spectroscopic information about the charge transfer complex. Two runs with unsaturated I 2 solutions were also carried
Solubility and charge transfer in supercritical xenon
1213
out in order to obtain information about the charge transfer equilibrium under other operational conditions. The u.v. and visible spectra of the solutions were determined over the range 220 nm to 700 nm using a Shimadzu 3101-PC spectrophotometer. The optical absorbances at all wavelengths were determined by subtracting the absorption due to the sapphire windows and to the light scattered inside the xenon-filled cell, which depends on fluid density.Ž6,7. The molar absorptivity of I 2 at 523.0 nm, which is the position of the maximum of the visible absorption band, was determined at the lowest temperature by carefully weighing a small amount of I 2 Žs., f5 mg, which was introduced into the cell, which was then filled with enough Xe to dissolve all the solid. The measured molar absorptivity was 87.3 m2 . moly1 at T s 300.79 K, this value differs by less than 10 per cent from that previously reported by our laboratory using an instrument with different precision.Ž6. Since the experimental determination of the molar absorptivity is difficult, we calculated its value for I 2 at l max s Ž523.0 " 0.5. nm in the solutions at T s 318.70 K with the expression: Ž6.
e Ž T . s 116.3 tan1r2 Ž u 0r2T . " 4.4 4 m2 . moly1 ,
Ž 1.
where u 0 s 1.439 Ž n 0rcmy1 . is a characteristic temperature related to the vibrational wavenumber n 0 s 214.5 cmy1 .
FIGURE 2. Typical u.v. spectrum for ŽI 2 q C 6 H 6 q Xe. ŽT s 318.70 K, p s 9.28 MPa, c 2 s 10y3 mol . dmy3 , and c 3 s 0.081 mol . dmy3 .. - - - - -, the spectrum of ŽC 6 H 6 q Xe. under the same experimental conditions; . . . . . , shows the ŽI 2 q Xe. u.v. spectrum for the same value of c 2 .
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H. Destaillats and R. Fernandez-Prini ´
Figure 2 illustrates a typical u.v. spectrum for the ternary system. It also shows the small contribution of free I 2 and of C 6 H 6 to the charge transfer band. The u.v. absorbance due to the u.v. charge transfer band Žhaving maxima between 276 and 280 nm. involving I 2 as an acceptor and C 6 H 6 as the donor was determined from spectra of the type shown in figure 2. This required subtraction of the small contributions to the optical absorbance due to the free donor and acceptor. The optical absorbance of benzene at different fluid densities was negligible at the maximum wavelength of the charge transfer band, as illustrated by the spectrum in figure 2, except for a few points where the benzene concentration c 3 was higher than 0.1 mol . dmy3 ; and even then it never exceeded a 5 per cent of the total absorbance. The u.v. absorbance of free iodine, which is very low in the spectrum of figure 2, is due to the presence of I 2 and to I 4 , the latter having a larger molar absorptivity.Ž14,15. This correction was made on the basis of the spectra recorded for the binary ŽI 2 q Xe. system, their u.v. absorbances were fitted with a smooth function of the concentration of dissolved iodine c 2 . These values were always close to those calculated with the equilibrium constant for dimerization and the molar absorptivities reported in the literature for iodine vapour Ž14,15. extrapolated to the experimental temperatures of this study. This correction was between 10 per cent and 20 per cent of the total u.v. absorbance of the charge transfer band. Since the visible absorption band of I 2 is not modified by the charge transfer process it provided a means to calculate the total I 2 concentration in the fluid.
3. Results Table 1 reports the solubility of I 2 Žs. at the two experimental temperatures in the absence and in the presence of co-solvent. The logarithm of the solubility of iodine U is plotted against the xenon amount-of-substance density rn, 1 for T s 300.79 K in figure 3 and for T s 318.70 K in figure 4. The figures also show the curves calculated with the equations for the solubility of I 2 reported in a previous work Ž16. by interpolation for T s 300.79 K and extrapolation for T s 318.70 K. The agreement between the values obtained in the present work and those calculated is U very satisfactory, only at T s 318.70 K and high rn, 1 were differences in solubility amounting to a few per cent observed Ž cf. figure 4.. The new set of measurements of I 2 solubility in supercritical xenon were considered important to permit a more precise determination of the effect on solubility of added C 6 H 6 . The observed maxima of the u.v. absorbance peak at 276 nm is intermediate between the values of the maxima reported in the binary donor q acceptor ŽD q A. mixture in the vapour phase Ž268 nm.Ž17. and in non-polar liquids Ž297 nm for benzene Ž18. and 295 nm for carbon tetrachloride Ž19. ., but much closer to the vapour phase value. The product of the molar absorptivity of donor]acceptor complex DA multiplied by its concentration e ŽDA. c DA is the experimental quantity to which we had direct access from the u.v. optical absorbance and the optical path lengths of our cell. We have calculated c DA using the value reported for the binary ŽD q A. vapour phase for the molar absorptivity, assuming it is not affected by xenon density, even when we cannot exclude a small change of the molar absorptivity of DA with fluid density.
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Solubility and charge transfer in supercritical xenon
TABLE 1. Solubility of I 2 Žs. in fluid xenon at two temperatures with and without added benzene, and U values of Q for the ternary systems, where rn, 1 is the xenon amount-of-substance density, c 2 is the concentration of dissolved iodine, c 3 is the concentration of benzene, and Q is the equilibrium concentration ratio
MPa
U rn, 1 mol . dmy3
6.455 6.791 7.212 7.458 7.696 7.748 8.139 8.157 8.572 8.953 9.388 9.613 5.644 a 6.082 a 6.270 6.452 6.806 7.006 7.121 7.236 7.530 7.233 7.748 8.051 8.565 9.063 9.605
5.32 " 0.05 6.43 " 0.07 8.64 " 0.08 9.83 " 0.07 10.60 " 0.06 10.73 " 0.05 11.45 " 0.05 11.48 " 0.05 12.02 " 0.04 12.39 " 0.04 12.75 " 0.04 12.91 " 0.04 3.81 " 0.05 4.52 " 0.05 4.92 " 0.05 5.49 " 0.06 6.88 " 0.07 8.20 " 0.08 8.73 " 0.08 9.49 " 0.07 10.58 " 0.06 8.94 " 0.08 10.82 " 0.06 11.59 " 0.05 12.23 " 0.04 12.68 " 0.04 13.07 " 0.04
p
10 3 . c 2 mol . dmy3
10 2 . c 3 mol . dmy3
moly1 . dm3
3.5 " 0.2 4.2 " 0.2 4.5 " 0.2 7.9 " 0.4 8.3 " 0.4 8.2 " 0.4 8.8 " 0.4 8.6 " 0.4 8.7 " 0.4 9.7 " 0.5 10.5 " 0.5 9.5 " 0.5 9.6 " 0.5 9.7 " 0.5 9.6 " 0.5
5.1 " 0.5 4.1 " 0.4 4.7 " 0.5 4.3 " 0.4 3.3 " 0.2 2.5 " 0.1 2.3 " 0.1 2.2 " 0.1 1.9 " 0.1 2.3 " 0.1 1.9 " 0.1 1.6 " 0.1 1.5 " 0.1 1.4 " 0.1 1.4 " 0.1
Q
T s 300.79 K 0.84 " 0.05 1.53 " 0.06 3.89 " 0.12 5.63 " 0.17 6.94 " 0.21 7.08 " 0.21 8.54 " 0.26 8.81 " 0.26 10.12 " 0.30 11.12 " 0.33 12.23 " 0.37 12.70 " 0.38 0.34 " 0.01 0.57 " 0.02 0.79 " 0.02 1.19 " 0.05 2.97 " 0.09 4.36 " 0.13 5.13 " 0.15 5.79 " 0.17 7.37 " 0.22 5.83 " 0.17 8.36 " 0.25 9.37 " 0.28 10.97 " 0.33 12.2 " 0.37 13.4 " 0.40
Table 1 also reports the value of the equilibrium concentration ratio for the ternary systems Q of the ŽI 2 q C 6 H 6 . donor]acceptor complex ŽDA. to the product of concentrations of free I 2 and free C 6 H 6 for solutions saturated in iodine defined by: Q s c DA r Ž c 2 y c DA . Ž c 3 y c DA . 4 .
Ž 2.
Table 2 reports values of Q for ternary systems which were subsaturated in iodine. The slight decrease in c 2 with time observed in these runs is attributed to slow decomposition of I 2 on the small remaining surface of stainless steel in the inlets and outlets of the cell.
4. Discussion The solubility data obtained in the present work show that benzene produces an enhancement of iodine solubility, albeit a modest one. The experimental
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H. Destaillats and R. Fernandez-Prini ´ TABLE 1}continued
MPa
U rn, 1 . mol dmy3
4.741 5.430 6.143 6.778 7.462 7.886 8.402 8.656 8.825 9.043 9.242 9.434 9.620 4.752 5.433 6.168 6.794 7.381 6.287 6.884 7.481 8.035 8.068 8.503 8.924 9.162 9.416 9.616 8.829 9.053 9.277 9.422 9.627
2.39 " 0.03 2.91 " 0.03 3.53 " 0.04 4.19 " 0.04 5.05 " 0.05 5.68 " 0.05 6.59 " 0.06 7.09 " 0.06 7.43 " 0.06 7.86 " 0.06 8.28 " 0.06 8.64 " 0.04 8.98 " 0.04 2.40 " 0.03 2.90 " 0.03 3.55 " 0.04 4.20 " 0.05 4.93 " 0.04 3.66 " 0.04 4.29 " 0.05 5.06 " 0.05 5.94 " 0.05 5.98 " 0.05 6.76 " 0.06 7.62 " 0.05 8.12 " 0.06 8.58 " 0.04 8.91 " 0.04 7.45 " 0.05 7.91 " 0.06 8.33 " 0.05 8.62 " 0.04 9.02 " 0.04
p
3
10 . c 2 mol . dmy3
10 2 . c 3 mol . dmy3
Q y1 .
mol
dm3
T s 318.70 K
a
0.40 " 0.01 0.55 " 0.02 0.76 " 0.02 1.11 " 0.03 1.72 " 0.05 2.28 " 0.07 3.36 " 0.10 4.08 " 0.12 4.62 " 0.14 5.45 " 0.16 6.27 " 0.19 7.16 " 0.21 8.08 " 0.24 0.49 " 0.01 0.65 " 0.02 0.88 " 0.03 1.27 " 0.04 1.85 " 0.06 0.96 " 0.03 1.41 " 0.04 2.08 " 0.06 3.16 " 0.09 3.29 " 0.10 4.55 " 0.14 6.22 " 0.19 7.39 " 0.22 8.71 " 0.26 9.80 " 0.29 6.02 " 0.18 7.20 " 0.22 8.42 " 0.25 9.28 " 0.28 10.57 " 0.32
2.7 " 0.1 2.9 " 0.1 3.2 " 0.2 3.5 " 0.2 3.8 " 0.2 4.3 " 0.2 5.4 " 0.3 5.6 " 0.3 5.8 " 0.3 5.5 " 0.3 5.5 " 0.3 5.5 " 0.3 5.6 " 0.3 5.8 " 0.3 6.0 " 0.3 7.2 " 0.4 7.6 " 0.4 8.1 " 0.4 8.3 " 0.4 8.8 " 0.4
3.2 " 0.3 3.2 " 0.3 3.2 " 0.3 2.6 " 0.3 2.5 " 0.3 2.9 " 0.3 2.8 " 0.3 2.7 " 0.3 2.7 " 0.2 2.7 " 0.2 2.6 " 0.2 2.3 " 0.1 2.2 " 0.1 2.1 " 0.1 2.0 " 0.1 2.4 " 0.1 2.3 " 0.1 2.2 " 0.1 2.1 " 0.1 2.0 " 0.1
path length s 5.16 mm.
observations are in agreement with the conclusions of the molecular dynamics study of Danten et al.,Ž20. who were able to describe the observed thermodynamic and IR-spectroscopic behaviour of binary fluid mixtures of I 2 in C 6 H 6 on the basis of the intermolecular interactions arising from the contributions of the Lennard]Jones potential and the charge distribution of pure D and A. Thus, the observed increase in iodine solubility would be caused by the larger benzene]iodine cross-interaction, including quadrupolar interactions, compared with those present in the binary ŽI 2 q Xe. system with no C 6 H 6 , which are essentially restricted to Lennard]Jones interactions. Thus, the appearance of a new u.v. absorption band should not be taken as an indication that significant changes in the thermodynamic quantities of dissolved
Solubility and charge transfer in supercritical xenon
1217
FIGURE 3. Logarithm of the isothermal solubility of I 2 Žs. c 2 at T s 300.79 K against the solvent U . y3 . \ B, 0.0; `, 0.04; ^, 0.08; e, 0.1. The solid Ž amount-of-substance density rn, 1 . For c 3 r mol dm curve gives the solubility of iodine in the absence of benzene calculated with the expressions in reference 16.
iodine occur or that a new stable species DA is formed. As demonstrated by Orgel and MullikenŽ21. the charge transfer u.v. band may originate in the collisions of D and A, which generate a new electronic level. The charge transfer equilibrium concentration quotient has frequently been reported in the literature in place of the thermodynamic equilibrium constant for the charge transfer complex formation. This would be valid only under two conditions: that the concentrations of the species are within the Henrian limit and that the solvent medium does not change. Rigorously then, the equilibrium constant is equal to Q multiplied by the quotient of infinite dilution activity coefficients, because solutions are usually very dilute, a condition also valid in the present study. The second condition, however, is not fulfilled, since the infinite dilution activity coefficients will change with the fluid density. The literature reports different values for the molar absorptivities of DA in the vapour phase and in triple-point liquids, but these are only apparent molar absorptivities as they were calculated with the assumption that the real
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H. Destaillats and R. Fernandez-Prini ´
FIGURE 4. Logarithm of the isothermal solubility of I 2 Žs. c 2 at T s 318.70 K against the solvent U . y3 . \ B, 0.0; I, 0.03; `, 0.05, e, 0.08. The solid Ž amount-of-substance density rn, 1 . For c 3 r mol dm curve gives the solubility of iodine in the absence of benzene calculated with the expressions in reference 16.
TABLE 2. Values of Q determined in iodine-subsaturated ternary systems, at T s 300.79 K, where U rn, 1 is the xenon amount-of-substance density, c 2 is the concentration of dissolved iodine, c 3 is the concentration of benzene, and Q is the equilibrium concentration ratio
MPa
U rn, 1 . mol dmy3
10 3 . c 2 mol . dmy3
10 2 . c3 mol . dmy3
7.773 8.427 8.962 9.380 9.645 7.255 7.743 9.032 9.352 9.623
10.85 " 0.06 11.90 " 0.05 12.43 " 0.04 12.77 " 0.04 12.95 " 0.04 8.98 " 0.08 10.71 " 0.06 12.47 " 0.04 12.72 " 0.04 12.91 " 0.04
3.68 " 0.11 3.66 " 0.11 3.66 " 0.11 3.66 " 0.11 3.64 " 0.11 3.69 " 0.11 3.34 " 0.10 3.35 " 0.10 3.35 " 0.10 3.33 " 0.10
4.3 " 0.2 4.5 " 0.2 4.5 " 0.2 4.5 " 0.2 4.5 " 0.2 16.8 " 0.8 16.8 " 0.8 17.5 " 0.9 17.4 " 0.9 17.4 " 0.9
p
Q y1 .
mol
dm3
1.9 " 0.1 1.5 " 0.1 1.5 " 0.1 1.5 " 0.1 1.4 " 0.1 2.4 " 0.1 2.1 " 0.1 1.6 " 0.1 1.6 " 0.1 1.5 " 0.1
Solubility and charge transfer in supercritical xenon
1219
FIGURE 5. Concentration quotient Q for charge transfer complex against the solvent amount-ofU substance density rn, 1 . The arrows indicate the values reported in the literature for Q in the vapour phase. B, T s 300.8 K saturated in I 2 ; v, T s 300.8 K, unsaturated in I 2 ; I, T s 318.7 K, saturated in I 2 . The error bars indicate the uncertainty in Q.
concentration of DA may be obtained from Q. Considering that the molar absorptivity reported for the gaseous DA complex, e s Ž165 " 10. m2 . moly1 Ž17. is quite probably not affected by non-ideal behaviour, we have used it to calculate Q for supercritical xenon at both temperatures. This assumption implies that the transition probability between ground and excited states is not appreciably affected by changes in the density of the weakly interacting Xe atoms. The experimental range of densities in the present study only extends to half the packing fraction of xenon at the triple point and in this range intermolecular attractions prevail.Ž2. Moreover, when a change of molar absorptivity of the charge transfer complex has been reported, lmax of DA is shifted,Ž22. whereas this is not the case in our study. U Here, Q is plotted against rn, 1 in figure 5 for the cases where the fluid was saturated, and unsaturated, in I 2 . At the lower temperature there is an increase in U the scatter of the Q values for low rn, 1 due to the low value of c DA . Figure 5 also shows the limiting value of Q reported for C 6 H 6 and I 2 in the gas phase at both temperatures,Ž17. these are about 30 times larger than the typical values obtained
1220
H. Destaillats and R. Fernandez-Prini ´
for Q in high density fluids at room temperature Ž e. g. 0.157 in carbon tetrachloride and 0.105 in heptane..Ž18. U The results of the present study do not suggest any peculiar behaviour when rn, 1 is close to the critical value. Moreover, the smooth increase of Q with decreasing density does not require the ad-hoc assumption of critical clustering to explain the behaviour in the near-critical region. On account of the collisional nature of the charge transfer band and the fact that the activity coefficients of D, A, and DA at infinite dilution will be density-dependent, the results suggest that the change in the infinite dilution activity coefficients of the species involved are responsible for the observed changes in Q with fluid density. The concept of sociation introduced by GuggenheimŽ23. is very relevant to the present discussion,Ž24. it may be used for all types of intermolecular interactions, from weak intermolecular interactions to association by covalent bonding. This generalization could be the basis of a quantitative description of the thermodynamic behaviour of the weak charge transfer ŽI 2 q C 6 H 6 . complex.Ž24. Its study in supercritical fluids appears to give a good opportunity to elucidate this issue. Sociation is equivalent to an enhanced local concentration of donor close to molecules of the acceptor; this enhancement leads to an increase in the number of collisional encounters between D and A. It has been shownŽ25. that for Lennard]Jones fluids the excess local density which enhances cross-interactions is larger in density ranges where excluded volume effects are not relevant; i.e., for densities which are smaller than roughly twice the critical density. However, to obtain values for the activity coefficients at infinite dilution and establish the constancy of the molar absorptivity of DA, new experimental or theoretical studies are still necessary. Preliminary results for the ŽI 2 q mesitylene. charge transfer complex in SF6 support the interpretation given here to the behaviour observed in the ŽI 2 q C 6 H 6 . system. Thanks are given to the Universidad de Buenos Aires ŽUBACyT. and CONICET for partial economic support. H.D. is grateful to UBACyT for a research fellowship. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Carlier, C.; Randolph, T. W. AIChE J. 1993, 39, 876]884. Fernandez-Prini, R.; Japas, M. L. Chem. Soc. Re¨ . 1994, 23, 155]163. ´ Bennet, G. E.; Rossky, P. J.; Johnston, K. P. J. Phys. Chem. 1995, 99, 16136]16143. Fernandez-Prini, R. Pure Appl. Chem. 1995, 67, 519]526. ´ Fernandez-Prini, R. The Role of Chemistry in the Preser¨ ation of the En¨ ironment. Workshop ´ NSF-CONICET: Buenos Aires. 1996, p. 26. Fernadez, D. P.; Fernandez-Prini, R. J. Chem. Thermodynamics 1992, 24, 377]386. ´ ´ Marceca, E.; Fernandez-Prini, R. J. Chem. Thermodynamics 1993, 25, 237]247. ´ Marceca, E.; Fernandez-Prini, R. J. Chem. Thermodynamics 1994, 26, 651]661. ´ Gutkowski, K.; Japas, M. L.; Fernandez-Prini, R. J. Chem. Thermodynamics 1997, 29, 1077]1086. ´ Stewart, R. B.; Jacobsen, R. T. J. Phys. Chem. Ref. Data 1989, 18, 639]656. Habgood, H. W.; Schneider, W. G. Can. J. Chem. 1954, 32, 98]111. Michels, A.; Wassenaar, T.; Louwerse, P. Physica 1954, 20, 99]106. Lide, D. R. Handbook of Chemistry and Physics Ž75th edition.. CRC Press. 1995, pp. 3]208. Tamres, M.; Duerksen, W. K.; Goodenow, J. M. J. Phys. Chem. 1968, 72, 966]970.
Solubility and charge transfer in supercritical xenon 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
Passchier, A. A.; Gregory, N. W. J. Phys. Chem. 1968, 72, 2697]2702. Fernandez, D. P. Thesis, Universidad de Buenos Aires. 1991. ´ Lang, F. T.; Strong, R. L. J. Am. Chem. Soc. 1965, 87, 2345]2349. Benesi, H. A.; Hildebrand, J. H. J. Am. Chem. Soc. 1949, 71, 2703]2708. Tamres, M.; Virzi, D.; Searles, S. J. Am. Chem. Soc. 1953, 75, 4358]4363. Denten, Y.; Guillot, B.; Guissani, Y. J. Chem. Phys. 1992, 96, 3782]3794. Orgel, L. E.; Mulliken, R. S. J. Am. Chem. Soc. 1957, 79, 4839]4846. Tamres, M. Molecular Complexes 1973, 1, 49]116. Guggenheim, E. A. Trans. Faraday Soc. 1960, 56, 1159]1164. Prue, J. E. J. Chem. Soc. 1965, 7534]7535. Fernandez-Prini, R.; Japas, M. L. J. Phys. Chem. 1992, 96, 5115]5121. ´
(Recei¨ ed 7 January 1997; in final form 13 March 1997)
WA97r001
1221
Solubility of I 2( s) and equilibrium concentration of the ( I 2 H C 6 H 6 ) charge transfer complex in supercritical xenon with added C 6 H 6 Hugo Destaillats Instituto de Quımica Fısica ´ ´ de Materiales, Ambiente y Energıa, ´ Facultad de Ciencias Exactas y Naturales, Uni¨ ersidad de Buenos Aires, Ciudad Uni¨ ersitaria Pabellon ´ II, 1428-Capital Federal, Argentina a and Roberto Fernandez-Prini ´
Instituto de Quımica Fısica ´ ´ de Materiales, Ambiente y Energıa, ´ Facultad de Ciencias Exactas y Naturales, Uni¨ ersidad de Buenos Aires, Ciudad Uni¨ ersitaria Pabellon ´ II, 1428-Capital Federal, and Unidad de Acti¨ adad Quımica, Comision ´ ´ Nacional de Energıa ´ Atomica, A¨ . Liberador 8350, 1429-Capital Federal, Argentina ´
The solubility of I 2 Žs. in supercritical xenon with and without added C 6 H 6 has been measured at the temperatures T s Ž300.79 " 0.04. K and Ž318.70 " 0.02. K over the pressure range from 5 MPa to 10 MPa. The u.v. absorbance due to the charge transfer interaction between I 2 Žacceptor. and C 6 H 6 Ždonor. was also measured when the fluid was saturated, and also when unsaturated, with I 2 . The enhancement of the solubility of I 2 Žs. due to added C 6 H 6 was moderate, supporting the view that the charge transfer process does not contribute significantly to the thermodynamic properties of donor and acceptor. The effect of density on the equilibrium concentration quotient for the formation of the donor]acceptor complex is discussed. Q 1997 Academic Press Limited KEYWORDS: solubility; supercritical fluid; iodine; charge transfer
1. Introduction The view that the strongly non-linear dependence on fluid density observed for many properties of solutes in dilute multicomponent supercritical fluids is due to the change in fluid density, and not to the position of the solvent’s critical points, is now gaining acceptance.Ž1 ] 3. This view explains why the maximum difference between observed and expected values of those properties often occurs at reduced densities between 0.3 and 0.7 and not at the solvent’s critical density. The possibility of describing theoretically the observed behaviour over the whole a To whom correspondence should be sent. Member of Carrera del Investigador CONICET ŽE-mail: [email protected]..
0021]9614r97r111209 q 13 $25.00r0rct970237
Q 1997 Academic Press Limited
1210
H. Destaillats and R. Fernandez-Prini ´
density range is hampered by the fact that at low fluid density microinhomogeneities may be present when solute] Žsolvent or co-solvent. interactions are strong.Ž4,5. Moreover, since the effective Hamiltonians which are used to describe intermolecular interactions are obtained by best-fitting fluid properties over limited density ranges, it is not surprising that they are unable to describe the whole fluid density range. We have previously reported values for the solubility of a series of simple solids in near-critical solvents,Ž6 ] 9. those studies form the basis of the present stage of our research into the behaviour of near-critical fluids, incorporating the study of the effect of fluid density upon charge transfer processes. In the present work we report the results of a study of dilute ŽI 2 q C 6 H 6 . in supercritical xenon at two temperatures close to the solvent’s critical temperature, Tc . We have determined the solubility of I 2 Žs. and calculated the concentration of donor]acceptor charge transfer complex by measurement of the visible and u.v. absorbance in the solution containing either I 2 or ŽI 2 q C 6 H 6 .. The equilibrium concentration quotient for the charge transfer complex was calculated and compared with the values obtained in the gas phase and in high density liquids. Observed changes in the concentration quotient for the charge transfer process introduced by the variation of supercritical solvent density appear to be related essentially to changes in infinite dilution activity coefficients of the species. No special features are observed in the neighbourhood of the solvent critical density, suggesting the absence of any clustering due to the position of the critical region.
2. Experimental In this study we have measured the u.v. and visible absorption of iodine dissolved in super-critical xenonŽ6. with and without added benzene. Our previous experience with solutions of I 2 in xenon suggested the convenience of employing a highpressure spectrophotometric cell and ancillary set-up, which minimizes the solutions’ exposure to stainless steel surfaces and avoiding iodine decomposition. Hence, a new high-pressure spectrophotometric cell was designed and built from titanium grade 1 Žfigure 1.. The 5 mm thick sapphire windows, 2, were located in two housings, 3, which were screwed onto the cell body, 1, so that their surfaces were pressed together defining the optical path of the cell; a longer path length was obtained by introducing a titanium ring as a spacer between the windows. One of the window housings had channels to allow the solution to fill the space between the two windows. The pressure seals, 7, were made of PTFE to avoid the presence of other materials which could react with iodine. An external magnet was rotated to stir the internal solution with a plastic-coated magnetic bar, thus ensuring equilibrium. Two different optical paths lengths in the spectrophotometric high-pressure cell could be chosen, thus affording some flexibility to optimize the conditions for the optical absorbance measurements. Their values, Ž1.15 " 0.02. mm and Ž5.16 " 0.02. mm, were determined by comparing the optical absorbance of two aqueous solutions Žpotassium ferricyanide and alkaline potassium chromate. in the high-
Solubility and charge transfer in supercritical xenon
1211
FIGURE 1. The titanium high-pressure optical cell. 1, cell body; 2, sapphire windows; 3, window housings, the spacer was positioned between the windows; 4, devices used to position the windows; 5, thermistor; 6, connecting socket for the tubing; 7, PTFE seals; 8, O-rings; 9, thermostatting jacket.
pressure spectrophotometric cell with those obtained from the same solutions in two standard quartz cells having path lengths of 1.00 and 5.00 mm. The volumes inside the cell for the two path lengths were Ž3.04 " 0.05. cm3 and Ž3.48 " 0.05. cm3 , respectively. Xe was loaded into the cell through a six-port valve employing a manual displacement pump. An h.p.l.c. loop was attached to the six-port valve and filled with benzene Žco-solvent. by means of a syringe; the co-solvent was then swept from the loop into the cell with xenon. The system’s pressure was determined with a Wika transducer, and a thermistor, whose tip was placed inside the cell, was used to measure the temperature of the system. Both probes were property calibrated, the uncertainties being 0.001 MPa and 0.01 K, respectively. Measurements were taken at the temperatures of 300.79 K and 318.70 K and a pressure range of 5 MPa to 10 MPa; the fluid density was in the range 5 mol . dmy3 to 13 mol . dmy3 at the lower temperature and 3 mol . dmy3 to 9 mol . dmy3 at the higher temperature. Iodine was Mallinkrodt Žtrisublimed., it was purified by sublimation in the presence of molecular sieves to eliminate all traces of water. The xenon used was AGA of 0.99995 mass fraction and the benzene was Merck pro analysi, both were used without further purification. The high-pressure system was evacuated after
1212
H. Destaillats and R. Fernandez-Prini ´
each run by distillation of the fluid into a system with two high-pressure bottles, which allowed us to recover and purify the xenon by successive distillations. The density of fluid xenon was calculated with an equation of state obtained from that reported for Ar Ž10. and the law of corresponding states, as described elsewhere.Ž6. This formulation could be used over the entire experimental Ž p, V, T . range and we have checked that the densities obtained are within 1 per cent of those that were determined experimentally for xenon.Ž11,12. The change of fluid density produced by the addition of benzene was neglected, as it is considered to be within 1 per cent of that of pure Xe at the same pressure and temperature, whenever the fluid density differed more than 15 per cent from the critical density. Closer to the critical density the change may amount to about 10 per cent for the highest benzene concentration employed in this work. Since we were interested in studying near-critical behaviour, the highest temperature chosen was 29 K above the critical temperature of xenon Tc . Keeping the temperature not too far above Tc was important and imposed a severe limitation in the maximum concentration of benzene that could be dissolved in the fluid supercritical Xe phase. On the other hand, it was desirable to have the highest possible concentration of benzene in that phase in order to maximize the contribution of I 2 ]C 6 H 6 cross-interactions. On the basis of the vapour pressure Ž13. the density of pure C 6 H 6 vapour is 5.7 . 10y3 mol . dmy3 and 11.6 . 10y3 mol . dmy3 at T s 300.79 K and T s 318.70 K, respectively. We added between one and three 14.9 mm3 h.p.l.c. loops of C 6 H 6 to the cell, thus benzene densities in the supercritical fluid never exceeded 0.18 mol . dmy3 . It was observed that the value of the concentration of benzene c 3 , obtained from the known volume of the h.p.l.c. loop, could only be considered a rough indication of the real concentration of benzene present in the cell, probably due to incomplete displacement of the total liquid slug in the loop to the high pressure cell. The real value of c 3 in the cell was determined by calibration of the maximum absorbance in the u.v. peak of benzene at 260.0 nm as a function of the concentration of benzene. This peak was chosen because of its good linear Lambert]Beer behaviour in the c 3 range used in this work Žslope s 11.0 dm3 . moly1 .. The contribution of the charge transfer band at 260.0 nm was subtracted in every case by Gaussian fitting this band. The use of this procedure to determine c 3 significantly improved the consistency of the data and potentially enables quantitative information to be obtained even if the supercritical fluid were saturated with benzene. We have tried to measure the solubility of benzene in Xe, however, even at low fluid density the u.v. absorbance of the 260.0 nm benzene peak was much bigger than that of the maximum c 3 used to obtain the linear Lambert]Beer plot, and linearity could not be guaranteed. This test confirmed that all the added benzene was dissolved in xenon. For a given run a small increase in c 3 was observed when fluid density increased Ž ¨ ide infra., this is attributed to the difficulty of sweeping the benzene slug from the inlet piping with Xe when loading the cell. Runs performed in the presence of I 2 Žs. enabled the determination of iodine solubility in the fluid, as well as providing spectroscopic information about the charge transfer complex. Two runs with unsaturated I 2 solutions were also carried
Solubility and charge transfer in supercritical xenon
1213
out in order to obtain information about the charge transfer equilibrium under other operational conditions. The u.v. and visible spectra of the solutions were determined over the range 220 nm to 700 nm using a Shimadzu 3101-PC spectrophotometer. The optical absorbances at all wavelengths were determined by subtracting the absorption due to the sapphire windows and to the light scattered inside the xenon-filled cell, which depends on fluid density.Ž6,7. The molar absorptivity of I 2 at 523.0 nm, which is the position of the maximum of the visible absorption band, was determined at the lowest temperature by carefully weighing a small amount of I 2 Žs., f5 mg, which was introduced into the cell, which was then filled with enough Xe to dissolve all the solid. The measured molar absorptivity was 87.3 m2 . moly1 at T s 300.79 K, this value differs by less than 10 per cent from that previously reported by our laboratory using an instrument with different precision.Ž6. Since the experimental determination of the molar absorptivity is difficult, we calculated its value for I 2 at l max s Ž523.0 " 0.5. nm in the solutions at T s 318.70 K with the expression: Ž6.
e Ž T . s 116.3 tan1r2 Ž u 0r2T . " 4.4 4 m2 . moly1 ,
Ž 1.
where u 0 s 1.439 Ž n 0rcmy1 . is a characteristic temperature related to the vibrational wavenumber n 0 s 214.5 cmy1 .
FIGURE 2. Typical u.v. spectrum for ŽI 2 q C 6 H 6 q Xe. ŽT s 318.70 K, p s 9.28 MPa, c 2 s 10y3 mol . dmy3 , and c 3 s 0.081 mol . dmy3 .. - - - - -, the spectrum of ŽC 6 H 6 q Xe. under the same experimental conditions; . . . . . , shows the ŽI 2 q Xe. u.v. spectrum for the same value of c 2 .
1214
H. Destaillats and R. Fernandez-Prini ´
Figure 2 illustrates a typical u.v. spectrum for the ternary system. It also shows the small contribution of free I 2 and of C 6 H 6 to the charge transfer band. The u.v. absorbance due to the u.v. charge transfer band Žhaving maxima between 276 and 280 nm. involving I 2 as an acceptor and C 6 H 6 as the donor was determined from spectra of the type shown in figure 2. This required subtraction of the small contributions to the optical absorbance due to the free donor and acceptor. The optical absorbance of benzene at different fluid densities was negligible at the maximum wavelength of the charge transfer band, as illustrated by the spectrum in figure 2, except for a few points where the benzene concentration c 3 was higher than 0.1 mol . dmy3 ; and even then it never exceeded a 5 per cent of the total absorbance. The u.v. absorbance of free iodine, which is very low in the spectrum of figure 2, is due to the presence of I 2 and to I 4 , the latter having a larger molar absorptivity.Ž14,15. This correction was made on the basis of the spectra recorded for the binary ŽI 2 q Xe. system, their u.v. absorbances were fitted with a smooth function of the concentration of dissolved iodine c 2 . These values were always close to those calculated with the equilibrium constant for dimerization and the molar absorptivities reported in the literature for iodine vapour Ž14,15. extrapolated to the experimental temperatures of this study. This correction was between 10 per cent and 20 per cent of the total u.v. absorbance of the charge transfer band. Since the visible absorption band of I 2 is not modified by the charge transfer process it provided a means to calculate the total I 2 concentration in the fluid.
3. Results Table 1 reports the solubility of I 2 Žs. at the two experimental temperatures in the absence and in the presence of co-solvent. The logarithm of the solubility of iodine U is plotted against the xenon amount-of-substance density rn, 1 for T s 300.79 K in figure 3 and for T s 318.70 K in figure 4. The figures also show the curves calculated with the equations for the solubility of I 2 reported in a previous work Ž16. by interpolation for T s 300.79 K and extrapolation for T s 318.70 K. The agreement between the values obtained in the present work and those calculated is U very satisfactory, only at T s 318.70 K and high rn, 1 were differences in solubility amounting to a few per cent observed Ž cf. figure 4.. The new set of measurements of I 2 solubility in supercritical xenon were considered important to permit a more precise determination of the effect on solubility of added C 6 H 6 . The observed maxima of the u.v. absorbance peak at 276 nm is intermediate between the values of the maxima reported in the binary donor q acceptor ŽD q A. mixture in the vapour phase Ž268 nm.Ž17. and in non-polar liquids Ž297 nm for benzene Ž18. and 295 nm for carbon tetrachloride Ž19. ., but much closer to the vapour phase value. The product of the molar absorptivity of donor]acceptor complex DA multiplied by its concentration e ŽDA. c DA is the experimental quantity to which we had direct access from the u.v. optical absorbance and the optical path lengths of our cell. We have calculated c DA using the value reported for the binary ŽD q A. vapour phase for the molar absorptivity, assuming it is not affected by xenon density, even when we cannot exclude a small change of the molar absorptivity of DA with fluid density.
1215
Solubility and charge transfer in supercritical xenon
TABLE 1. Solubility of I 2 Žs. in fluid xenon at two temperatures with and without added benzene, and U values of Q for the ternary systems, where rn, 1 is the xenon amount-of-substance density, c 2 is the concentration of dissolved iodine, c 3 is the concentration of benzene, and Q is the equilibrium concentration ratio
MPa
U rn, 1 mol . dmy3
6.455 6.791 7.212 7.458 7.696 7.748 8.139 8.157 8.572 8.953 9.388 9.613 5.644 a 6.082 a 6.270 6.452 6.806 7.006 7.121 7.236 7.530 7.233 7.748 8.051 8.565 9.063 9.605
5.32 " 0.05 6.43 " 0.07 8.64 " 0.08 9.83 " 0.07 10.60 " 0.06 10.73 " 0.05 11.45 " 0.05 11.48 " 0.05 12.02 " 0.04 12.39 " 0.04 12.75 " 0.04 12.91 " 0.04 3.81 " 0.05 4.52 " 0.05 4.92 " 0.05 5.49 " 0.06 6.88 " 0.07 8.20 " 0.08 8.73 " 0.08 9.49 " 0.07 10.58 " 0.06 8.94 " 0.08 10.82 " 0.06 11.59 " 0.05 12.23 " 0.04 12.68 " 0.04 13.07 " 0.04
p
10 3 . c 2 mol . dmy3
10 2 . c 3 mol . dmy3
moly1 . dm3
3.5 " 0.2 4.2 " 0.2 4.5 " 0.2 7.9 " 0.4 8.3 " 0.4 8.2 " 0.4 8.8 " 0.4 8.6 " 0.4 8.7 " 0.4 9.7 " 0.5 10.5 " 0.5 9.5 " 0.5 9.6 " 0.5 9.7 " 0.5 9.6 " 0.5
5.1 " 0.5 4.1 " 0.4 4.7 " 0.5 4.3 " 0.4 3.3 " 0.2 2.5 " 0.1 2.3 " 0.1 2.2 " 0.1 1.9 " 0.1 2.3 " 0.1 1.9 " 0.1 1.6 " 0.1 1.5 " 0.1 1.4 " 0.1 1.4 " 0.1
Q
T s 300.79 K 0.84 " 0.05 1.53 " 0.06 3.89 " 0.12 5.63 " 0.17 6.94 " 0.21 7.08 " 0.21 8.54 " 0.26 8.81 " 0.26 10.12 " 0.30 11.12 " 0.33 12.23 " 0.37 12.70 " 0.38 0.34 " 0.01 0.57 " 0.02 0.79 " 0.02 1.19 " 0.05 2.97 " 0.09 4.36 " 0.13 5.13 " 0.15 5.79 " 0.17 7.37 " 0.22 5.83 " 0.17 8.36 " 0.25 9.37 " 0.28 10.97 " 0.33 12.2 " 0.37 13.4 " 0.40
Table 1 also reports the value of the equilibrium concentration ratio for the ternary systems Q of the ŽI 2 q C 6 H 6 . donor]acceptor complex ŽDA. to the product of concentrations of free I 2 and free C 6 H 6 for solutions saturated in iodine defined by: Q s c DA r Ž c 2 y c DA . Ž c 3 y c DA . 4 .
Ž 2.
Table 2 reports values of Q for ternary systems which were subsaturated in iodine. The slight decrease in c 2 with time observed in these runs is attributed to slow decomposition of I 2 on the small remaining surface of stainless steel in the inlets and outlets of the cell.
4. Discussion The solubility data obtained in the present work show that benzene produces an enhancement of iodine solubility, albeit a modest one. The experimental
1216
H. Destaillats and R. Fernandez-Prini ´ TABLE 1}continued
MPa
U rn, 1 . mol dmy3
4.741 5.430 6.143 6.778 7.462 7.886 8.402 8.656 8.825 9.043 9.242 9.434 9.620 4.752 5.433 6.168 6.794 7.381 6.287 6.884 7.481 8.035 8.068 8.503 8.924 9.162 9.416 9.616 8.829 9.053 9.277 9.422 9.627
2.39 " 0.03 2.91 " 0.03 3.53 " 0.04 4.19 " 0.04 5.05 " 0.05 5.68 " 0.05 6.59 " 0.06 7.09 " 0.06 7.43 " 0.06 7.86 " 0.06 8.28 " 0.06 8.64 " 0.04 8.98 " 0.04 2.40 " 0.03 2.90 " 0.03 3.55 " 0.04 4.20 " 0.05 4.93 " 0.04 3.66 " 0.04 4.29 " 0.05 5.06 " 0.05 5.94 " 0.05 5.98 " 0.05 6.76 " 0.06 7.62 " 0.05 8.12 " 0.06 8.58 " 0.04 8.91 " 0.04 7.45 " 0.05 7.91 " 0.06 8.33 " 0.05 8.62 " 0.04 9.02 " 0.04
p
3
10 . c 2 mol . dmy3
10 2 . c 3 mol . dmy3
Q y1 .
mol
dm3
T s 318.70 K
a
0.40 " 0.01 0.55 " 0.02 0.76 " 0.02 1.11 " 0.03 1.72 " 0.05 2.28 " 0.07 3.36 " 0.10 4.08 " 0.12 4.62 " 0.14 5.45 " 0.16 6.27 " 0.19 7.16 " 0.21 8.08 " 0.24 0.49 " 0.01 0.65 " 0.02 0.88 " 0.03 1.27 " 0.04 1.85 " 0.06 0.96 " 0.03 1.41 " 0.04 2.08 " 0.06 3.16 " 0.09 3.29 " 0.10 4.55 " 0.14 6.22 " 0.19 7.39 " 0.22 8.71 " 0.26 9.80 " 0.29 6.02 " 0.18 7.20 " 0.22 8.42 " 0.25 9.28 " 0.28 10.57 " 0.32
2.7 " 0.1 2.9 " 0.1 3.2 " 0.2 3.5 " 0.2 3.8 " 0.2 4.3 " 0.2 5.4 " 0.3 5.6 " 0.3 5.8 " 0.3 5.5 " 0.3 5.5 " 0.3 5.5 " 0.3 5.6 " 0.3 5.8 " 0.3 6.0 " 0.3 7.2 " 0.4 7.6 " 0.4 8.1 " 0.4 8.3 " 0.4 8.8 " 0.4
3.2 " 0.3 3.2 " 0.3 3.2 " 0.3 2.6 " 0.3 2.5 " 0.3 2.9 " 0.3 2.8 " 0.3 2.7 " 0.3 2.7 " 0.2 2.7 " 0.2 2.6 " 0.2 2.3 " 0.1 2.2 " 0.1 2.1 " 0.1 2.0 " 0.1 2.4 " 0.1 2.3 " 0.1 2.2 " 0.1 2.1 " 0.1 2.0 " 0.1
path length s 5.16 mm.
observations are in agreement with the conclusions of the molecular dynamics study of Danten et al.,Ž20. who were able to describe the observed thermodynamic and IR-spectroscopic behaviour of binary fluid mixtures of I 2 in C 6 H 6 on the basis of the intermolecular interactions arising from the contributions of the Lennard]Jones potential and the charge distribution of pure D and A. Thus, the observed increase in iodine solubility would be caused by the larger benzene]iodine cross-interaction, including quadrupolar interactions, compared with those present in the binary ŽI 2 q Xe. system with no C 6 H 6 , which are essentially restricted to Lennard]Jones interactions. Thus, the appearance of a new u.v. absorption band should not be taken as an indication that significant changes in the thermodynamic quantities of dissolved
Solubility and charge transfer in supercritical xenon
1217
FIGURE 3. Logarithm of the isothermal solubility of I 2 Žs. c 2 at T s 300.79 K against the solvent U . y3 . \ B, 0.0; `, 0.04; ^, 0.08; e, 0.1. The solid Ž amount-of-substance density rn, 1 . For c 3 r mol dm curve gives the solubility of iodine in the absence of benzene calculated with the expressions in reference 16.
iodine occur or that a new stable species DA is formed. As demonstrated by Orgel and MullikenŽ21. the charge transfer u.v. band may originate in the collisions of D and A, which generate a new electronic level. The charge transfer equilibrium concentration quotient has frequently been reported in the literature in place of the thermodynamic equilibrium constant for the charge transfer complex formation. This would be valid only under two conditions: that the concentrations of the species are within the Henrian limit and that the solvent medium does not change. Rigorously then, the equilibrium constant is equal to Q multiplied by the quotient of infinite dilution activity coefficients, because solutions are usually very dilute, a condition also valid in the present study. The second condition, however, is not fulfilled, since the infinite dilution activity coefficients will change with the fluid density. The literature reports different values for the molar absorptivities of DA in the vapour phase and in triple-point liquids, but these are only apparent molar absorptivities as they were calculated with the assumption that the real
1218
H. Destaillats and R. Fernandez-Prini ´
FIGURE 4. Logarithm of the isothermal solubility of I 2 Žs. c 2 at T s 318.70 K against the solvent U . y3 . \ B, 0.0; I, 0.03; `, 0.05, e, 0.08. The solid Ž amount-of-substance density rn, 1 . For c 3 r mol dm curve gives the solubility of iodine in the absence of benzene calculated with the expressions in reference 16.
TABLE 2. Values of Q determined in iodine-subsaturated ternary systems, at T s 300.79 K, where U rn, 1 is the xenon amount-of-substance density, c 2 is the concentration of dissolved iodine, c 3 is the concentration of benzene, and Q is the equilibrium concentration ratio
MPa
U rn, 1 . mol dmy3
10 3 . c 2 mol . dmy3
10 2 . c3 mol . dmy3
7.773 8.427 8.962 9.380 9.645 7.255 7.743 9.032 9.352 9.623
10.85 " 0.06 11.90 " 0.05 12.43 " 0.04 12.77 " 0.04 12.95 " 0.04 8.98 " 0.08 10.71 " 0.06 12.47 " 0.04 12.72 " 0.04 12.91 " 0.04
3.68 " 0.11 3.66 " 0.11 3.66 " 0.11 3.66 " 0.11 3.64 " 0.11 3.69 " 0.11 3.34 " 0.10 3.35 " 0.10 3.35 " 0.10 3.33 " 0.10
4.3 " 0.2 4.5 " 0.2 4.5 " 0.2 4.5 " 0.2 4.5 " 0.2 16.8 " 0.8 16.8 " 0.8 17.5 " 0.9 17.4 " 0.9 17.4 " 0.9
p
Q y1 .
mol
dm3
1.9 " 0.1 1.5 " 0.1 1.5 " 0.1 1.5 " 0.1 1.4 " 0.1 2.4 " 0.1 2.1 " 0.1 1.6 " 0.1 1.6 " 0.1 1.5 " 0.1
Solubility and charge transfer in supercritical xenon
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FIGURE 5. Concentration quotient Q for charge transfer complex against the solvent amount-ofU substance density rn, 1 . The arrows indicate the values reported in the literature for Q in the vapour phase. B, T s 300.8 K saturated in I 2 ; v, T s 300.8 K, unsaturated in I 2 ; I, T s 318.7 K, saturated in I 2 . The error bars indicate the uncertainty in Q.
concentration of DA may be obtained from Q. Considering that the molar absorptivity reported for the gaseous DA complex, e s Ž165 " 10. m2 . moly1 Ž17. is quite probably not affected by non-ideal behaviour, we have used it to calculate Q for supercritical xenon at both temperatures. This assumption implies that the transition probability between ground and excited states is not appreciably affected by changes in the density of the weakly interacting Xe atoms. The experimental range of densities in the present study only extends to half the packing fraction of xenon at the triple point and in this range intermolecular attractions prevail.Ž2. Moreover, when a change of molar absorptivity of the charge transfer complex has been reported, lmax of DA is shifted,Ž22. whereas this is not the case in our study. U Here, Q is plotted against rn, 1 in figure 5 for the cases where the fluid was saturated, and unsaturated, in I 2 . At the lower temperature there is an increase in U the scatter of the Q values for low rn, 1 due to the low value of c DA . Figure 5 also shows the limiting value of Q reported for C 6 H 6 and I 2 in the gas phase at both temperatures,Ž17. these are about 30 times larger than the typical values obtained
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H. Destaillats and R. Fernandez-Prini ´
for Q in high density fluids at room temperature Ž e. g. 0.157 in carbon tetrachloride and 0.105 in heptane..Ž18. U The results of the present study do not suggest any peculiar behaviour when rn, 1 is close to the critical value. Moreover, the smooth increase of Q with decreasing density does not require the ad-hoc assumption of critical clustering to explain the behaviour in the near-critical region. On account of the collisional nature of the charge transfer band and the fact that the activity coefficients of D, A, and DA at infinite dilution will be density-dependent, the results suggest that the change in the infinite dilution activity coefficients of the species involved are responsible for the observed changes in Q with fluid density. The concept of sociation introduced by GuggenheimŽ23. is very relevant to the present discussion,Ž24. it may be used for all types of intermolecular interactions, from weak intermolecular interactions to association by covalent bonding. This generalization could be the basis of a quantitative description of the thermodynamic behaviour of the weak charge transfer ŽI 2 q C 6 H 6 . complex.Ž24. Its study in supercritical fluids appears to give a good opportunity to elucidate this issue. Sociation is equivalent to an enhanced local concentration of donor close to molecules of the acceptor; this enhancement leads to an increase in the number of collisional encounters between D and A. It has been shownŽ25. that for Lennard]Jones fluids the excess local density which enhances cross-interactions is larger in density ranges where excluded volume effects are not relevant; i.e., for densities which are smaller than roughly twice the critical density. However, to obtain values for the activity coefficients at infinite dilution and establish the constancy of the molar absorptivity of DA, new experimental or theoretical studies are still necessary. Preliminary results for the ŽI 2 q mesitylene. charge transfer complex in SF6 support the interpretation given here to the behaviour observed in the ŽI 2 q C 6 H 6 . system. Thanks are given to the Universidad de Buenos Aires ŽUBACyT. and CONICET for partial economic support. H.D. is grateful to UBACyT for a research fellowship. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14.
Carlier, C.; Randolph, T. W. AIChE J. 1993, 39, 876]884. Fernandez-Prini, R.; Japas, M. L. Chem. Soc. Re¨ . 1994, 23, 155]163. ´ Bennet, G. E.; Rossky, P. J.; Johnston, K. P. J. Phys. Chem. 1995, 99, 16136]16143. Fernandez-Prini, R. Pure Appl. Chem. 1995, 67, 519]526. ´ Fernandez-Prini, R. The Role of Chemistry in the Preser¨ ation of the En¨ ironment. Workshop ´ NSF-CONICET: Buenos Aires. 1996, p. 26. Fernadez, D. P.; Fernandez-Prini, R. J. Chem. Thermodynamics 1992, 24, 377]386. ´ ´ Marceca, E.; Fernandez-Prini, R. J. Chem. Thermodynamics 1993, 25, 237]247. ´ Marceca, E.; Fernandez-Prini, R. J. Chem. Thermodynamics 1994, 26, 651]661. ´ Gutkowski, K.; Japas, M. L.; Fernandez-Prini, R. J. Chem. Thermodynamics 1997, 29, 1077]1086. ´ Stewart, R. B.; Jacobsen, R. T. J. Phys. Chem. Ref. Data 1989, 18, 639]656. Habgood, H. W.; Schneider, W. G. Can. J. Chem. 1954, 32, 98]111. Michels, A.; Wassenaar, T.; Louwerse, P. Physica 1954, 20, 99]106. Lide, D. R. Handbook of Chemistry and Physics Ž75th edition.. CRC Press. 1995, pp. 3]208. Tamres, M.; Duerksen, W. K.; Goodenow, J. M. J. Phys. Chem. 1968, 72, 966]970.
Solubility and charge transfer in supercritical xenon 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25.
Passchier, A. A.; Gregory, N. W. J. Phys. Chem. 1968, 72, 2697]2702. Fernandez, D. P. Thesis, Universidad de Buenos Aires. 1991. ´ Lang, F. T.; Strong, R. L. J. Am. Chem. Soc. 1965, 87, 2345]2349. Benesi, H. A.; Hildebrand, J. H. J. Am. Chem. Soc. 1949, 71, 2703]2708. Tamres, M.; Virzi, D.; Searles, S. J. Am. Chem. Soc. 1953, 75, 4358]4363. Denten, Y.; Guillot, B.; Guissani, Y. J. Chem. Phys. 1992, 96, 3782]3794. Orgel, L. E.; Mulliken, R. S. J. Am. Chem. Soc. 1957, 79, 4839]4846. Tamres, M. Molecular Complexes 1973, 1, 49]116. Guggenheim, E. A. Trans. Faraday Soc. 1960, 56, 1159]1164. Prue, J. E. J. Chem. Soc. 1965, 7534]7535. Fernandez-Prini, R.; Japas, M. L. J. Phys. Chem. 1992, 96, 5115]5121. ´
(Recei¨ ed 7 January 1997; in final form 13 March 1997)
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