- Email: [email protected]
Solubility of solids in near-critical fluids. V. CHI3in ethane and in carbon dioxide
J. Chem. Thermodynamics 1997, 29, 1077–1086
Solubility of solids in near-critical fluids V. CHI3 in ethane and in carbon dioxide Karin Gutkowski, Instituto de Quı´ mica Fı´ sica de Materiales, Ambiente y Energı´ a, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pabello´n II, 1428 -Capital Federal, Argentina
M. Laura Japas, Unidad de Actividad Quı´ mica, Comisio´n Nacional de Energı´ a Ato´mica, Av. Libertador 8250 , 1429 -Capital Federal, Argentina
and Roberto Ferna´ndez-Prini a Instituto de Quı´ mica Fı´ sica de Materiales, Ambiente y Energı´ a, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pabello´n II, 1428 -Capital Federal, Argentina, and Unidad de Actividad Quı´ mica, Comisio´n Nacional de Energı´ a Ato´mica, Av. Libertador 8250 , 1429 -Capital Federal, Argentina The solubilities of CHI3(s) in supercritical C2H6 and CO2 have been determined spectrophotometrically close to the solvents’ critical points at temperatures of 312.90 K and 327.00 K in C2H6, and 312.73 K and 326.95 K in CO2, over a range of fluid densities. Isothermal solubilities show the sharp change with pressure characteristic of near-critical behaviour. Solubilities are almost twice as large in CO2 than in C2H6 over the whole reduced density range. Enhancement factors E were calculated and compared to those of CHI3(s) in C2H4, CHF3, and SF6. The differences observed in E correlate well with the charge distribution, and hence multi-pole moments, of the solvent molecules. 7 1997 Academic Press Limited KEYWORDS: solubility; near-critical fluid; triiodomethane
1. Introduction The knowledge of the behaviour of simple solutes dissolved in supercritical fluids is of central interest in elucidating the influence of intermolecular interactions on the macroscopic properties of fluid systems. Thus, the use of supercritical solvents allows the exploration of the consequences of changes in fluid density, while the system changes continuously (with no phase transition) from liquid-like to gas-like densities, i.e. from the state where repulsions predominate to that where intermolecular attractions prevail.(1–3) a Member of Carrera del Investigador CONICET; to whom correspondence should be sent. E-mail address: rfprini.cnea.edu.ar.
0021–9614/97/101077 + 10 $25.00/0/ct970228
7 1997 Academic Press Limited
1078
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
We have reported values for the solubility of I2(s), CHI3(s), and CI4(s) in a series of near-critical solvents.(4–7) It was noted that the solubilities of CHI3 and of CI4 in ethene were appreciably larger than in CHF3. This was unexpected, especially in the case of the dipolar CHI3, due to the existence of dipole–dipole interactions between solute and solvent molecules. We have suggested(7) that such a result might be the consequence of charge transfer interactions between solute and solvent, for which some spectrophotometric evidence existed. On the other hand, there is an increasing awareness that collisionally induced (i.e. weak) charge transfer interactions,(8) typically exemplified by those present in (I2 + C6H6 ), do not contribute significantly to the thermodynamic properties of the solution.(9) In order to obtain more information about the observed difference in the behaviour of CHI3(s) when dissolved in different near-critical solvents, we decided to determine its solubility in supercritical ethane, with Lennard-Jones parameters close to those for ethene, and in carbon dioxide, a non-polar molecule having two symmetrical polar bonds.
2. Experimental We have measured the optical absorbance in the near u.v. of saturated solutions of CHI3 in near-critical ethane and in carbon dioxide at two temperatures and varying fluid densities. The high-pressure spectrophotometric cell and ancillary equipment have been described previously.(5) The temperature was controlled to 215 mK and the pressure was known to 0.2 per cent over the range 1 to 10 MPa. These uncertainties correspond to the maximum fluctuation of the thermodynamic parameters observed during any single run. In the present work we used a high-pressure spectrophotometric cell with two different optical path lengths fixed by introducing metal spacers between the two sapphire windows. This allowed us to maintain a relatively high precision over all the fluid density range covered in this study. The optical path lengths were (1.33 2 0.01) cm and (0.33 2 0.01) cm. Solubilities were determined by measuring the optical absorbance of the saturated solutions at the wavelength of maximum absorbance of the lowest energy u.v.-to-visible band of CHI3(5) which, for the two solvents in this work, was 347.0 nm for ethane, and 342.8 nm in carbon dioxide. The molar absorptivities o of CHI3 in ethane and carbon dioxide were determined by measuring the optical absorption of unsaturated solutions prepared by carefully weighing with a microbalance the appropriate amounts of solute (11 mg) and introducing it into the spectrophotometric cell. The volume of the cell was determined from the number of turns of the calibrated pressure hand-pump necessary to fill the cell at a given fluid pressure and temperature. The values obtained for o were 201.0 and 131.7 m2·mol−1 for C2H6 and CO2, respectively, the uncertainty in the molar absorptivities was 5 per cent. The molar absorptivities and wavelengths of the peak of CHI3 dissolved in different fluids are compared in table 1. In order to simplify the measurement of optical absorbance, the experimental procedure adopted in the present study was somewhat different from that described
1079
Solubility in near-critical fluids
TABLE 1. Wavelength l of the maximum absorption of CHI3 for the lowest u.v.–visible band and value of the molar absorptivity o for CHF3, C2H4, SF6, 2-methylheptane, acetonitrile, 2,2,3,3-tetrafluoropropanol, C2H6, and CO2
a b
Solvent
l/nm
o/(m2·mol−1 )
CHF3 C2H4 SF6 2-methylheptane acetonitrile 2,2,3,3-tetrafluoropropanol C2H6 CO2
342.0 345.5 345.5 349.4 336.4 341.5 347.0 342.8
175.6 a 171.4 a 173.6 a 214.0 a 193.0 a 166.0 a 201.0 b 131.7 b
Reference 7. Present work.
previously.(5) The contribution to the measured optical absorbance due to the fraction of the light intensity which was dispersed by the fluid (i.e. stray light), which depends on fluid density but not on the wavelength, was evaluated directly from the spectra of the solutions recorded up to the visible region. The base line for each thermodynamic point was taken as the value of the optical absorbance at wavelengths greater than 500 nm and this value was substracted from that at the maximum of the near u.v. band used to determine the solubility of CHI3. In this way, it was possible to avoid the laborious measurement of the effect of density on the optical absorption of the pure solvent; moreover, the present procedure is considered to be more precise since the measurement of the base line absorption is made in the same solution where the solubility is being determined. Another change introduced in the experimental procedure was to determine the solubilities for increasing, and then for decreasing fluid density. This modification was adopted after careful verification that consistent values of the optical absorption were obtained when returning to the same lower density after a high fluid density excursion. The fact that the dissolution and precipitation of solute inside the spectrophotometric cell were found to be reversible to all practical purposes allowed us to obtain more experimental data points per run. The CHI3 was obtained from Aldrich with a purity of 0.99 mass fraction, and was used after recrystallation from ethanol. The solvents were AGA 0.9999 mass fraction. Optical absorption was measured with a Shimadzu 3101-PC spectrophotometer. The density of the near-critical fluid was calculated with the published equations of state for the two fluids.(10) The critical constants were Tc = 305.33 K and 304.13 K, −3 pc = 4.872 MPa and 7.375 MPa, r* and 10.63 mol·dm−3 for n,1,c = 6.87 mol·dm (10) ethane and carbon dioxide, respectively.
3. Results and discussion Measurements of the solubility of CHI3(s) were carried out at temperatures close to 312.9 K and 327.0 K in ethane and at (312.73 2 0.017) K and (326.95 2 0.015) K in
1080
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
TABLE 2. Solubility of CHI3 in fluid C2H6 at two temperatures, where r* n,1 denotes amount-of-substance solvent density, and c2 is isothernal solubility p/MPa
T/K
−3 r* ) n,1/(mol·dm
103·c2/(mol·dm−3 )
p/MPa
T/K
−3 r* ) n,1/(mol·dm
103·c2/(mol·dm−3 )
6.086 5.767 5.669 5.416 5.255 4.226 5.388 5.729 5.398 4.391 5.111 5.440
312.77 312.75 312.77 312.75 312.73 312.95 312.99 313.01 313.00 312.86 312.88 312.91
8.96 7.77 7.03 5.13 4.44 2.54 4.90 7.30 4.94 2.74 3.98 5.19
1.39 2 0.07 0.90 2 0.05 0.66 2 0.04 0.21 2 0.01 0.12 2 0.01 0.016 2 0.001 0.16 2 0.01 0.65 2 0.05 0.17 2 0.02 0.021 2 0.002 0.077 2 0.005 0.21 2 0.02
5.554 5.175 4.545 5.344 5.769 5.596 5.767 5.566 5.364 5.171 6.114
312.92 312.92 312.91 312.93 312.83 312.73 326.83 326.83 326.85 326.86 326.85
5.94 4.15 2.94 4.72 7.72 6.44 3.83 3.55 3.29 3.06 4.41
0.34 2 0.02 0.090 2 0.006 0.027 2 0.003 0.146 2 0.009 0.88 2 0.05 0.49 2 0.03 0.15 2 0.01 0.115 2 0.007 0.091 2 0.006 0.073 2 0.005 0.24 2 0.01
5.757 4.842 6.545 6.628 7.270 6.246 5.968 5.633 6.786 7.282 7.312
326.85 326.85 326.88 327.11 327.12 327.13 327.14 327.14 327.07 327.07 327.07
3.82 2.72 5.32 5.48 7.10 4.63 4.12 3.62 5.89 7.14 7.22
0.146 2 0.009 0.052 2 0.005 0.46 2 0.03 0.56 2 0.08 1.39 2 0.08 0.32 2 0.02 0.21 2 0.02 0.14 2 0.01 0.71 2 0.04 1.29 2 0.08 1.34 2 0.08
6.258 4.085 4.151 4.738 4.637 5.282 5.808 6.132 6.272 6.033 5.468
327.07 327.11 327.12 327.13 327.13 327.15 327.17 327.19 327.2 327.2 327.2
4.66 2.07 2.12 2.62 2.52 3.18 3.87 4.41 4.67 4.23 3.40
0.33 2 0.02 0.026 2 0.002 0.027 2 0.002 0.046 2 0.004 0.043 2 0.004 0.080 2 0.005 0.144 2 0.008 0.21 2 0.01 0.25 2 0.01 0.18 2 0.01 0.104 2 0.006
carbon dioxide. The solubilities are reported in tables 2 and 3 together with the corresponding values of the thermodynamic parameters characterizing each data point. All the runs contain data obtained, as described above, by increasing and then decreasing the density of the solvent. Figures 1 and 2 are plots of the solubilities in ethane and carbon dioxide, respectively, as a function of pressure. The data points show clearly the effect of the vicinity of the critical point of the fluids, the solubility increases more than one order of magnitude over the experimental pressure range TABLE 3. Solubility of CHI3 in fluid CO2 at two temperatures, where r* n,1 denotes amount-of-substance solvent density, and c2 is isothernal solubility p/MPa
T/K
−3 r* ) n,1/(mol·dm
103·c2/(mol·dm−3 )
p/MPa
T/K
−3 r* ) n,1/(mol·dm
103·c2/(mol·dm−3 )
9.976 9.434 9.089 8.888 8.242 7.829 9.468 9.404 9.396 8.357 8.949 8.856
326.94 326.94 326.94 326.93 326.95 326.96 326.97 326.97 312.72 312.73 312.73 312.74
7.59 6.61 6.07 5.78 4.97 4.52 6.66 6.55 13.21 7.64 11.22 10.62
0.63 2 0.02 0.39 2 0.01 0.30 2 0.01 0.28 2 0.01 0.16 2 0.01 0.119 2 0.005 0.40 2 0.02 0.38 2 0.01 2.7 2 0.1 0.37 2 0.02 1.43 2 0.05 1.16 2 0.05
8.738 8.479 9.085 8.682 8.393 7.783 8.523 7.968 8.042 8.100 8.210
312.74 312.74 312.74 312.71 312.71 312.72 312.72 312.73 312.73 312.73 312.73
9.8 8.22 11.97 9.45 7.81 5.88 8.47 6.33 6.54 6.71 7.07
0.86 2 0.03 0.47 2 0.02 1.82 2 0.07 0.68 2 0.03 0.34 2 0.01 0.12 2 0.01 0.46 2 0.02 0.161 2 0.007 0.182 2 0.007 0.199 2 0.008 0.24 2 0.01
Solubility in near-critical fluids
1081
FIGURE 1. Isothermal solubility c2 of CHI3(s) in ethane against pressure: W, T = 312.90 K; w, T = 327.00 K.
indicating that, as expected,(2) the solute’s partial molar volume is very large in dilute near-critical solutions. In order to compare the solubility data for different near-critical solvents which were obtained at different temperatures, it is very important to eliminate the change in solubility directly attributable to the change of solute vapour pressure with temperature and pressure. This is easily done by calculating the enhancement factor E defined by, E = x/xid = xp/p* 2 ( p,T),
(1)
where x is the solute’s mole fraction when the solution is saturated and x id is the ideal solubility given by the ratio of the solute’s vapour pressure p* 2 to the total pressure p. In reference 7 E was defined as the ratio of the molar concentration to the ideal molar concentration of the saturated solution.
1082
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
FIGURE 2. Isothermal solubility c2 of CHI3(s) in carbon dioxide against pressure: R, T = 312.73 K; r, T = 326.93 K.
The Poynting effect has been taken into account to correct p* 2 by the effect of total pressure upon the chemical potential of the solid solute in equilibrium with the saturated solution. The increase in the solute’s vapour pressure is: p* 2 ( p,T) = p* 2 (T)exp{V* 2 (T)( p − p* 2 )/(RT)},
(2)
where p* 2 (T) and V* 2 (T) are, respectively, the vapour pressure and the molar volume of pure solid CHI3 at the experimental temperature. The temperature dependence of the vapour pressure of CHI3(s) was taken from Marceca and Ferna´ndez-Prini,(7) 3 −1 (11) the molar volume of the solid V* . Taking 2 was taken to be equal to 98.2 cm ·mol into account the fact that solutions are very dilute, the approximation x 1 c2/r* n,1 was used to calculate the mole fraction of the saturated solutions. The Poynting correction is appreciable leading to an increase of p* 2 (T) of between 15 and 40 per cent for the systems studied.
1083
Solubility in near-critical fluids
TABLE 4. Dependence of ln E for CHI3(s) on the reduced density of ethane and carbon dioxide at near-critical temperatures, a0, a1, and a2 are coefficients {see equation (4)} Solvent
T/K
a0
a1
a2
C2H6
312.90 327.00
(−0.200 2 0.131) (−0.058 2 0.131)
(8.517 2 0.405) (7.684 2 0.405)
(−2.945 2 0.292) (−2.539 2 0.292)
CO2
312.73 326.95
(1.066 2 0.276) (0.511 2 0.060)
(6.684 2 0.656) (7.642 2 0.216)
(−1.833 2 0.371) (−2.752 2 0.191)
The enhancement factors calculated for the two experimental isotherms in C2H6 and CO2 were fitted as a function of the reduced density with the following polynomial expression: ln E = a0 + a1r 1red + a2(r 1red )2,
(3)
where r is the reduced density of the solvent equal to the ratio of r* n,1, the amount-of-substance solvent density, and r* n,1,c, its critical value. Table 4 reports the values obtained for the coefficients of equation (4) and their standard deviations. The E is found to change very little with temperature, so the coefficients in equation (4) for data corresponding to a given isotherm were the same (within experimental uncertainty) in spite of small differences in the actual experimental temperature. The ln E is plotted in figure 3 for the five solvent systems against the solvents’ reduced density. It can be seen that at high and intermediate densities the enhancement factors are largest for C2H4 and lowest for SF6. In CO2 and C2H6, enhancement factors are intermediate. The difference in E(CHI3 ) in the hydrocarbon solvents is more than one order of magnitude at high fluid density. The case of CHF3 is very interesting: figure 3 shows that at low density E(CHI3 ) in this dipolar solvent is the largest one in the series. However, the change of solubility with density over the experimental density range (intermediate density range) is much smaller for CHF3 than for any of the other fluids studied, with the possible exception of SF6. As a consequence, ln E in CHF3 at high density is as low as in C2H6. At very low fluid density, the limiting slope of ln E against density is related to the second virial coefficients according to: red 1
red lim ln E = (B11 − 2B12 )r* n,1 = (B11 − 2B12 )r 1 ,
r* n ,1 : 0
(4)
where B11 and B12 are the second virial coefficients of the pure solvent and the cross-second virial coefficient respectively, and Bij = Bij r* n,1,c. As the fluid density increases, higher order virial coefficients will have to be taken into account to describe the density dependence of ln E. For dimethylamino benzonitrile dissolved in supercritical C2H6, Morita and Kajimoto(12) have observed the limiting linear behaviour for r 1red R 0.4. This range is close to the lower end of our experimental density range. The ln E data in SF6 and C2H6 shown in figure 3 appear to extrapolate linearly to zero for r 1red = 0; for the latter solvent the small values of the a0 coefficients in table 4 support this contention. The deviations from limiting linear behaviour are
1084
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
FIGURE 3. Logarithm of the enhancement factor E of CHI3(s) against the solvent’s reduced density rired: q, C2H4; t, CO2; r, CHF3; w, C2H6; r, SF6. One curve is drawn for each solvent in order to guide the eye.
appreciable for CHI3 in CO2 and C2H4, and very notable for CHF3. Apart from the effect of higher order virial coefficients mentioned above, the departure of ln E from a linear behaviour may be due to stronger non-spherical solvent–solvent interactions, e.g. dipolar interactions and/or hydrogen bonding, as discussed below. In spite of these complications, the slopes of the lines joining the low density data with the origin of coordinates in figure 3 may be taken as lower boundaries for the limiting slopes (B11 − 2B12 ) for all the systems considered in this work. In fact, they are in the order CHF3C2H4 q CO2 q C2H6SF6. The values of these limiting slopes reflect mainly the magnitude of the cross-second virial coefficients because the value of B11, which for the five solvents considered do not differ too much,(13) is much smaller than B12. The Lennard–Jones parameters of C2H6 and C2H4 are similar,(14, 15) hence they cannot be the cause for the large difference in the solubility of CHI3 in these two
1085
Solubility in near-critical fluids
TABLE 5. Electrostatic characteristics of solvent molecules, where dq denotes the fraction of the proton charge on the atoms; m denotes dipole moment; a denotes polarizability; Q denotes quadrupole moment or its components (taken from reference 19). Values of Q calculated with the charge distribution reported in this table are given in parenthesis 1030·m C·m
1030·a m3
1040·Q C·m2
Solvent
dq
C 2H 6
C: 0.0073 H: −0.0024 C: −0.325 H: 0.162
0
4.50
0
4.205
CO2
C: 0.66 O: −0.33
0
2.639
CHF3
C: 0.319 H: 0.138 F: −0.152 S: 0.366 F: −0.061
5.50
3.6
16.2
0
6.56
0
C2H4
SF6
−2.67 (−0.05) (xx): −10.84 (−10.37) (yy): 5.40 (2.97) (zz): 5.44 (7.40) −15.2 (−15.1) (11.9)
fluids. Taking into account the dipolar nature of the solute CHI3, it seems important to know the charge distribution on the solvent molecules. Table 5 summarizes some molecular characteristics of the five solvent molecules related to multipolar electrostatic interactions. It seems clear that the large limiting slope observed in CHF3 is due to the permanent dipole moment of this molecule, but this is of no use to explain the trend of E in non-polar solvents. In general, the charge distribution on the solvent molecules should provide an indication of the relative magnitude of the solvent–solute interactions, as suggested by Reynolds et al.(16) in a recent study of solvation dynamics. We report in table 5 the charge distribution on the atoms of the five solvent molecules analysed in this work. The electrostatic potential around the molecules was determined using a density functional theory calculation in the local density approximation.(17, 18) The charge distributions in C2H6 and C2H4 are found to be very different, even the signs of the partial charges in carbon and hydrogen atoms are opposite. As shown in table 5, the quadrupole moments calculated using the molecular charge distributions agree quite well with the experimental quadrupole moments.(19) Hence, it may be concluded that the dipole and quadrupole moments of the molecules reflect correctly the observed trend in the magnitude of solute–solvent interactions. For CHF3 at higher density, E is not much greater than is observed for C2H6, a remarkable change from the low density behaviour noted above. At smaller r 1red than that of the triple point, attractive interactions will predominate and in dilute solutions solvent dipole–dipole interactions will be the dominant factor in determining the fluid’s structure. As the fluid density increases, the structure of the pure solvent will not provide the optimum orientation of solvent molecules around the solute particle to maximize interactions with the dipolar solute.
1086
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
The results we have discussed support the view(2) that at low density there is an inhomogeneous region in the vicinity of the solute molecule and that the microinhomogeneity increases with the strength of the solute–solvent interaction. They also indicate that charge transfer between solute and solvent need not be invoked to explain the difference in solubility observed for CHI3(s) in C2H6 and in C2H4. The calculations of the molecular charge distributions were done by Dr Darı´ o Estrin to whom we are very grateful. Thanks are given to the Universidad de Buenos Aires (UBACyT) and CONICET for partial economic support. K. G. is grateful to UBACyT for a research student’s fellowship. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
Carlier, C.; Randolph, T. W. AIChE J. 1993, 39, 876–884. Ferna´ndez-Prini, R.; Japas, M. L. Chem. Soc. Rev. 1994, 23, 155–163. Bennet, G. E.; Rossky, P. J.; Johnston, K. P. J. Phys. Chem. 1995, 99, 16136–16143. Ferna´ndez, D. P.; Ferna´ndez-Prini, R. J. Chem. Thermodynamics 1992, 24, 377–386. Marceca, E.; Ferna´ndez-Prini, R. J. Chem. Thermodynamics 1993, 25, 237–247. Marceca, E.; Ferna´ndez-Prini, R. J. Chem. Thermodynamics 1993, 25, 719–728. Marceca, E.; Ferna´ndez-Prini, R. J. Chem. Thermodynamics 1994, 26, 651–661. Orgel, L. E.; Mulliken, R. S. J. Am. Chem. Soc. 1957, 79, 4839–4846. Danten, Y.; Guillot, B.; Guissani, Y. J. Chem. Phys. 1992, 96, 3782–3794. Lemmon, E. W.; Jacobsen, R. T.; Pensonelle, S. G.; Beyerlein, S. W. Report 93 -1 . Center of Applied Thermodynamic Studies, University of Idaho. 1993. Lide, D. R. Handbook of Chemistry and Physics. CRC Press: Boca Raton. 1995, 75th edition, pp. 3–208. Morita, A.; Kajimoto, O. J. Phys. Chem. 1990, 94, 6420–6425. Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures. Clarendon Press: Oxford. 1980. Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids. J. Wiley and Sons: New York. 1996. Reed, T. M.; Gubbins, K. E. Applied Statistical Mechanics. McGraw Hill Kagakusho: Tokyo. 1973. Reynolds, L.; Gardecki, J. A.; Frankland, S. J. V.; Horng, M. L.; Maroncelli, M. J. Phys. Chem. 1996, 100, 10337–10357. Breneman, C. M.; Wiberg, K. B. J. Comp. Chem. 1990, 11, 361–370. Estrin, D. A.; Paglieri, L.; Corongiu, G. J. Phys. Chem. 1994, 98, 5653–5660. Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids. Clarenden Press: Oxford. 1984, Vol. 1.
(Received 21 November 1996; in final form 13 March 1997)
WE-084
Solubility of solids in near-critical fluids V. CHI3 in ethane and in carbon dioxide Karin Gutkowski, Instituto de Quı´ mica Fı´ sica de Materiales, Ambiente y Energı´ a, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pabello´n II, 1428 -Capital Federal, Argentina
M. Laura Japas, Unidad de Actividad Quı´ mica, Comisio´n Nacional de Energı´ a Ato´mica, Av. Libertador 8250 , 1429 -Capital Federal, Argentina
and Roberto Ferna´ndez-Prini a Instituto de Quı´ mica Fı´ sica de Materiales, Ambiente y Energı´ a, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, Ciudad Universitaria Pabello´n II, 1428 -Capital Federal, Argentina, and Unidad de Actividad Quı´ mica, Comisio´n Nacional de Energı´ a Ato´mica, Av. Libertador 8250 , 1429 -Capital Federal, Argentina The solubilities of CHI3(s) in supercritical C2H6 and CO2 have been determined spectrophotometrically close to the solvents’ critical points at temperatures of 312.90 K and 327.00 K in C2H6, and 312.73 K and 326.95 K in CO2, over a range of fluid densities. Isothermal solubilities show the sharp change with pressure characteristic of near-critical behaviour. Solubilities are almost twice as large in CO2 than in C2H6 over the whole reduced density range. Enhancement factors E were calculated and compared to those of CHI3(s) in C2H4, CHF3, and SF6. The differences observed in E correlate well with the charge distribution, and hence multi-pole moments, of the solvent molecules. 7 1997 Academic Press Limited KEYWORDS: solubility; near-critical fluid; triiodomethane
1. Introduction The knowledge of the behaviour of simple solutes dissolved in supercritical fluids is of central interest in elucidating the influence of intermolecular interactions on the macroscopic properties of fluid systems. Thus, the use of supercritical solvents allows the exploration of the consequences of changes in fluid density, while the system changes continuously (with no phase transition) from liquid-like to gas-like densities, i.e. from the state where repulsions predominate to that where intermolecular attractions prevail.(1–3) a Member of Carrera del Investigador CONICET; to whom correspondence should be sent. E-mail address: rfprini.cnea.edu.ar.
0021–9614/97/101077 + 10 $25.00/0/ct970228
7 1997 Academic Press Limited
1078
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
We have reported values for the solubility of I2(s), CHI3(s), and CI4(s) in a series of near-critical solvents.(4–7) It was noted that the solubilities of CHI3 and of CI4 in ethene were appreciably larger than in CHF3. This was unexpected, especially in the case of the dipolar CHI3, due to the existence of dipole–dipole interactions between solute and solvent molecules. We have suggested(7) that such a result might be the consequence of charge transfer interactions between solute and solvent, for which some spectrophotometric evidence existed. On the other hand, there is an increasing awareness that collisionally induced (i.e. weak) charge transfer interactions,(8) typically exemplified by those present in (I2 + C6H6 ), do not contribute significantly to the thermodynamic properties of the solution.(9) In order to obtain more information about the observed difference in the behaviour of CHI3(s) when dissolved in different near-critical solvents, we decided to determine its solubility in supercritical ethane, with Lennard-Jones parameters close to those for ethene, and in carbon dioxide, a non-polar molecule having two symmetrical polar bonds.
2. Experimental We have measured the optical absorbance in the near u.v. of saturated solutions of CHI3 in near-critical ethane and in carbon dioxide at two temperatures and varying fluid densities. The high-pressure spectrophotometric cell and ancillary equipment have been described previously.(5) The temperature was controlled to 215 mK and the pressure was known to 0.2 per cent over the range 1 to 10 MPa. These uncertainties correspond to the maximum fluctuation of the thermodynamic parameters observed during any single run. In the present work we used a high-pressure spectrophotometric cell with two different optical path lengths fixed by introducing metal spacers between the two sapphire windows. This allowed us to maintain a relatively high precision over all the fluid density range covered in this study. The optical path lengths were (1.33 2 0.01) cm and (0.33 2 0.01) cm. Solubilities were determined by measuring the optical absorbance of the saturated solutions at the wavelength of maximum absorbance of the lowest energy u.v.-to-visible band of CHI3(5) which, for the two solvents in this work, was 347.0 nm for ethane, and 342.8 nm in carbon dioxide. The molar absorptivities o of CHI3 in ethane and carbon dioxide were determined by measuring the optical absorption of unsaturated solutions prepared by carefully weighing with a microbalance the appropriate amounts of solute (11 mg) and introducing it into the spectrophotometric cell. The volume of the cell was determined from the number of turns of the calibrated pressure hand-pump necessary to fill the cell at a given fluid pressure and temperature. The values obtained for o were 201.0 and 131.7 m2·mol−1 for C2H6 and CO2, respectively, the uncertainty in the molar absorptivities was 5 per cent. The molar absorptivities and wavelengths of the peak of CHI3 dissolved in different fluids are compared in table 1. In order to simplify the measurement of optical absorbance, the experimental procedure adopted in the present study was somewhat different from that described
1079
Solubility in near-critical fluids
TABLE 1. Wavelength l of the maximum absorption of CHI3 for the lowest u.v.–visible band and value of the molar absorptivity o for CHF3, C2H4, SF6, 2-methylheptane, acetonitrile, 2,2,3,3-tetrafluoropropanol, C2H6, and CO2
a b
Solvent
l/nm
o/(m2·mol−1 )
CHF3 C2H4 SF6 2-methylheptane acetonitrile 2,2,3,3-tetrafluoropropanol C2H6 CO2
342.0 345.5 345.5 349.4 336.4 341.5 347.0 342.8
175.6 a 171.4 a 173.6 a 214.0 a 193.0 a 166.0 a 201.0 b 131.7 b
Reference 7. Present work.
previously.(5) The contribution to the measured optical absorbance due to the fraction of the light intensity which was dispersed by the fluid (i.e. stray light), which depends on fluid density but not on the wavelength, was evaluated directly from the spectra of the solutions recorded up to the visible region. The base line for each thermodynamic point was taken as the value of the optical absorbance at wavelengths greater than 500 nm and this value was substracted from that at the maximum of the near u.v. band used to determine the solubility of CHI3. In this way, it was possible to avoid the laborious measurement of the effect of density on the optical absorption of the pure solvent; moreover, the present procedure is considered to be more precise since the measurement of the base line absorption is made in the same solution where the solubility is being determined. Another change introduced in the experimental procedure was to determine the solubilities for increasing, and then for decreasing fluid density. This modification was adopted after careful verification that consistent values of the optical absorption were obtained when returning to the same lower density after a high fluid density excursion. The fact that the dissolution and precipitation of solute inside the spectrophotometric cell were found to be reversible to all practical purposes allowed us to obtain more experimental data points per run. The CHI3 was obtained from Aldrich with a purity of 0.99 mass fraction, and was used after recrystallation from ethanol. The solvents were AGA 0.9999 mass fraction. Optical absorption was measured with a Shimadzu 3101-PC spectrophotometer. The density of the near-critical fluid was calculated with the published equations of state for the two fluids.(10) The critical constants were Tc = 305.33 K and 304.13 K, −3 pc = 4.872 MPa and 7.375 MPa, r* and 10.63 mol·dm−3 for n,1,c = 6.87 mol·dm (10) ethane and carbon dioxide, respectively.
3. Results and discussion Measurements of the solubility of CHI3(s) were carried out at temperatures close to 312.9 K and 327.0 K in ethane and at (312.73 2 0.017) K and (326.95 2 0.015) K in
1080
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
TABLE 2. Solubility of CHI3 in fluid C2H6 at two temperatures, where r* n,1 denotes amount-of-substance solvent density, and c2 is isothernal solubility p/MPa
T/K
−3 r* ) n,1/(mol·dm
103·c2/(mol·dm−3 )
p/MPa
T/K
−3 r* ) n,1/(mol·dm
103·c2/(mol·dm−3 )
6.086 5.767 5.669 5.416 5.255 4.226 5.388 5.729 5.398 4.391 5.111 5.440
312.77 312.75 312.77 312.75 312.73 312.95 312.99 313.01 313.00 312.86 312.88 312.91
8.96 7.77 7.03 5.13 4.44 2.54 4.90 7.30 4.94 2.74 3.98 5.19
1.39 2 0.07 0.90 2 0.05 0.66 2 0.04 0.21 2 0.01 0.12 2 0.01 0.016 2 0.001 0.16 2 0.01 0.65 2 0.05 0.17 2 0.02 0.021 2 0.002 0.077 2 0.005 0.21 2 0.02
5.554 5.175 4.545 5.344 5.769 5.596 5.767 5.566 5.364 5.171 6.114
312.92 312.92 312.91 312.93 312.83 312.73 326.83 326.83 326.85 326.86 326.85
5.94 4.15 2.94 4.72 7.72 6.44 3.83 3.55 3.29 3.06 4.41
0.34 2 0.02 0.090 2 0.006 0.027 2 0.003 0.146 2 0.009 0.88 2 0.05 0.49 2 0.03 0.15 2 0.01 0.115 2 0.007 0.091 2 0.006 0.073 2 0.005 0.24 2 0.01
5.757 4.842 6.545 6.628 7.270 6.246 5.968 5.633 6.786 7.282 7.312
326.85 326.85 326.88 327.11 327.12 327.13 327.14 327.14 327.07 327.07 327.07
3.82 2.72 5.32 5.48 7.10 4.63 4.12 3.62 5.89 7.14 7.22
0.146 2 0.009 0.052 2 0.005 0.46 2 0.03 0.56 2 0.08 1.39 2 0.08 0.32 2 0.02 0.21 2 0.02 0.14 2 0.01 0.71 2 0.04 1.29 2 0.08 1.34 2 0.08
6.258 4.085 4.151 4.738 4.637 5.282 5.808 6.132 6.272 6.033 5.468
327.07 327.11 327.12 327.13 327.13 327.15 327.17 327.19 327.2 327.2 327.2
4.66 2.07 2.12 2.62 2.52 3.18 3.87 4.41 4.67 4.23 3.40
0.33 2 0.02 0.026 2 0.002 0.027 2 0.002 0.046 2 0.004 0.043 2 0.004 0.080 2 0.005 0.144 2 0.008 0.21 2 0.01 0.25 2 0.01 0.18 2 0.01 0.104 2 0.006
carbon dioxide. The solubilities are reported in tables 2 and 3 together with the corresponding values of the thermodynamic parameters characterizing each data point. All the runs contain data obtained, as described above, by increasing and then decreasing the density of the solvent. Figures 1 and 2 are plots of the solubilities in ethane and carbon dioxide, respectively, as a function of pressure. The data points show clearly the effect of the vicinity of the critical point of the fluids, the solubility increases more than one order of magnitude over the experimental pressure range TABLE 3. Solubility of CHI3 in fluid CO2 at two temperatures, where r* n,1 denotes amount-of-substance solvent density, and c2 is isothernal solubility p/MPa
T/K
−3 r* ) n,1/(mol·dm
103·c2/(mol·dm−3 )
p/MPa
T/K
−3 r* ) n,1/(mol·dm
103·c2/(mol·dm−3 )
9.976 9.434 9.089 8.888 8.242 7.829 9.468 9.404 9.396 8.357 8.949 8.856
326.94 326.94 326.94 326.93 326.95 326.96 326.97 326.97 312.72 312.73 312.73 312.74
7.59 6.61 6.07 5.78 4.97 4.52 6.66 6.55 13.21 7.64 11.22 10.62
0.63 2 0.02 0.39 2 0.01 0.30 2 0.01 0.28 2 0.01 0.16 2 0.01 0.119 2 0.005 0.40 2 0.02 0.38 2 0.01 2.7 2 0.1 0.37 2 0.02 1.43 2 0.05 1.16 2 0.05
8.738 8.479 9.085 8.682 8.393 7.783 8.523 7.968 8.042 8.100 8.210
312.74 312.74 312.74 312.71 312.71 312.72 312.72 312.73 312.73 312.73 312.73
9.8 8.22 11.97 9.45 7.81 5.88 8.47 6.33 6.54 6.71 7.07
0.86 2 0.03 0.47 2 0.02 1.82 2 0.07 0.68 2 0.03 0.34 2 0.01 0.12 2 0.01 0.46 2 0.02 0.161 2 0.007 0.182 2 0.007 0.199 2 0.008 0.24 2 0.01
Solubility in near-critical fluids
1081
FIGURE 1. Isothermal solubility c2 of CHI3(s) in ethane against pressure: W, T = 312.90 K; w, T = 327.00 K.
indicating that, as expected,(2) the solute’s partial molar volume is very large in dilute near-critical solutions. In order to compare the solubility data for different near-critical solvents which were obtained at different temperatures, it is very important to eliminate the change in solubility directly attributable to the change of solute vapour pressure with temperature and pressure. This is easily done by calculating the enhancement factor E defined by, E = x/xid = xp/p* 2 ( p,T),
(1)
where x is the solute’s mole fraction when the solution is saturated and x id is the ideal solubility given by the ratio of the solute’s vapour pressure p* 2 to the total pressure p. In reference 7 E was defined as the ratio of the molar concentration to the ideal molar concentration of the saturated solution.
1082
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
FIGURE 2. Isothermal solubility c2 of CHI3(s) in carbon dioxide against pressure: R, T = 312.73 K; r, T = 326.93 K.
The Poynting effect has been taken into account to correct p* 2 by the effect of total pressure upon the chemical potential of the solid solute in equilibrium with the saturated solution. The increase in the solute’s vapour pressure is: p* 2 ( p,T) = p* 2 (T)exp{V* 2 (T)( p − p* 2 )/(RT)},
(2)
where p* 2 (T) and V* 2 (T) are, respectively, the vapour pressure and the molar volume of pure solid CHI3 at the experimental temperature. The temperature dependence of the vapour pressure of CHI3(s) was taken from Marceca and Ferna´ndez-Prini,(7) 3 −1 (11) the molar volume of the solid V* . Taking 2 was taken to be equal to 98.2 cm ·mol into account the fact that solutions are very dilute, the approximation x 1 c2/r* n,1 was used to calculate the mole fraction of the saturated solutions. The Poynting correction is appreciable leading to an increase of p* 2 (T) of between 15 and 40 per cent for the systems studied.
1083
Solubility in near-critical fluids
TABLE 4. Dependence of ln E for CHI3(s) on the reduced density of ethane and carbon dioxide at near-critical temperatures, a0, a1, and a2 are coefficients {see equation (4)} Solvent
T/K
a0
a1
a2
C2H6
312.90 327.00
(−0.200 2 0.131) (−0.058 2 0.131)
(8.517 2 0.405) (7.684 2 0.405)
(−2.945 2 0.292) (−2.539 2 0.292)
CO2
312.73 326.95
(1.066 2 0.276) (0.511 2 0.060)
(6.684 2 0.656) (7.642 2 0.216)
(−1.833 2 0.371) (−2.752 2 0.191)
The enhancement factors calculated for the two experimental isotherms in C2H6 and CO2 were fitted as a function of the reduced density with the following polynomial expression: ln E = a0 + a1r 1red + a2(r 1red )2,
(3)
where r is the reduced density of the solvent equal to the ratio of r* n,1, the amount-of-substance solvent density, and r* n,1,c, its critical value. Table 4 reports the values obtained for the coefficients of equation (4) and their standard deviations. The E is found to change very little with temperature, so the coefficients in equation (4) for data corresponding to a given isotherm were the same (within experimental uncertainty) in spite of small differences in the actual experimental temperature. The ln E is plotted in figure 3 for the five solvent systems against the solvents’ reduced density. It can be seen that at high and intermediate densities the enhancement factors are largest for C2H4 and lowest for SF6. In CO2 and C2H6, enhancement factors are intermediate. The difference in E(CHI3 ) in the hydrocarbon solvents is more than one order of magnitude at high fluid density. The case of CHF3 is very interesting: figure 3 shows that at low density E(CHI3 ) in this dipolar solvent is the largest one in the series. However, the change of solubility with density over the experimental density range (intermediate density range) is much smaller for CHF3 than for any of the other fluids studied, with the possible exception of SF6. As a consequence, ln E in CHF3 at high density is as low as in C2H6. At very low fluid density, the limiting slope of ln E against density is related to the second virial coefficients according to: red 1
red lim ln E = (B11 − 2B12 )r* n,1 = (B11 − 2B12 )r 1 ,
r* n ,1 : 0
(4)
where B11 and B12 are the second virial coefficients of the pure solvent and the cross-second virial coefficient respectively, and Bij = Bij r* n,1,c. As the fluid density increases, higher order virial coefficients will have to be taken into account to describe the density dependence of ln E. For dimethylamino benzonitrile dissolved in supercritical C2H6, Morita and Kajimoto(12) have observed the limiting linear behaviour for r 1red R 0.4. This range is close to the lower end of our experimental density range. The ln E data in SF6 and C2H6 shown in figure 3 appear to extrapolate linearly to zero for r 1red = 0; for the latter solvent the small values of the a0 coefficients in table 4 support this contention. The deviations from limiting linear behaviour are
1084
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
FIGURE 3. Logarithm of the enhancement factor E of CHI3(s) against the solvent’s reduced density rired: q, C2H4; t, CO2; r, CHF3; w, C2H6; r, SF6. One curve is drawn for each solvent in order to guide the eye.
appreciable for CHI3 in CO2 and C2H4, and very notable for CHF3. Apart from the effect of higher order virial coefficients mentioned above, the departure of ln E from a linear behaviour may be due to stronger non-spherical solvent–solvent interactions, e.g. dipolar interactions and/or hydrogen bonding, as discussed below. In spite of these complications, the slopes of the lines joining the low density data with the origin of coordinates in figure 3 may be taken as lower boundaries for the limiting slopes (B11 − 2B12 ) for all the systems considered in this work. In fact, they are in the order CHF3C2H4 q CO2 q C2H6SF6. The values of these limiting slopes reflect mainly the magnitude of the cross-second virial coefficients because the value of B11, which for the five solvents considered do not differ too much,(13) is much smaller than B12. The Lennard–Jones parameters of C2H6 and C2H4 are similar,(14, 15) hence they cannot be the cause for the large difference in the solubility of CHI3 in these two
1085
Solubility in near-critical fluids
TABLE 5. Electrostatic characteristics of solvent molecules, where dq denotes the fraction of the proton charge on the atoms; m denotes dipole moment; a denotes polarizability; Q denotes quadrupole moment or its components (taken from reference 19). Values of Q calculated with the charge distribution reported in this table are given in parenthesis 1030·m C·m
1030·a m3
1040·Q C·m2
Solvent
dq
C 2H 6
C: 0.0073 H: −0.0024 C: −0.325 H: 0.162
0
4.50
0
4.205
CO2
C: 0.66 O: −0.33
0
2.639
CHF3
C: 0.319 H: 0.138 F: −0.152 S: 0.366 F: −0.061
5.50
3.6
16.2
0
6.56
0
C2H4
SF6
−2.67 (−0.05) (xx): −10.84 (−10.37) (yy): 5.40 (2.97) (zz): 5.44 (7.40) −15.2 (−15.1) (11.9)
fluids. Taking into account the dipolar nature of the solute CHI3, it seems important to know the charge distribution on the solvent molecules. Table 5 summarizes some molecular characteristics of the five solvent molecules related to multipolar electrostatic interactions. It seems clear that the large limiting slope observed in CHF3 is due to the permanent dipole moment of this molecule, but this is of no use to explain the trend of E in non-polar solvents. In general, the charge distribution on the solvent molecules should provide an indication of the relative magnitude of the solvent–solute interactions, as suggested by Reynolds et al.(16) in a recent study of solvation dynamics. We report in table 5 the charge distribution on the atoms of the five solvent molecules analysed in this work. The electrostatic potential around the molecules was determined using a density functional theory calculation in the local density approximation.(17, 18) The charge distributions in C2H6 and C2H4 are found to be very different, even the signs of the partial charges in carbon and hydrogen atoms are opposite. As shown in table 5, the quadrupole moments calculated using the molecular charge distributions agree quite well with the experimental quadrupole moments.(19) Hence, it may be concluded that the dipole and quadrupole moments of the molecules reflect correctly the observed trend in the magnitude of solute–solvent interactions. For CHF3 at higher density, E is not much greater than is observed for C2H6, a remarkable change from the low density behaviour noted above. At smaller r 1red than that of the triple point, attractive interactions will predominate and in dilute solutions solvent dipole–dipole interactions will be the dominant factor in determining the fluid’s structure. As the fluid density increases, the structure of the pure solvent will not provide the optimum orientation of solvent molecules around the solute particle to maximize interactions with the dipolar solute.
1086
K. Gutkowski, M. L. Japas, and R. Ferna´ndez-Prini
The results we have discussed support the view(2) that at low density there is an inhomogeneous region in the vicinity of the solute molecule and that the microinhomogeneity increases with the strength of the solute–solvent interaction. They also indicate that charge transfer between solute and solvent need not be invoked to explain the difference in solubility observed for CHI3(s) in C2H6 and in C2H4. The calculations of the molecular charge distributions were done by Dr Darı´ o Estrin to whom we are very grateful. Thanks are given to the Universidad de Buenos Aires (UBACyT) and CONICET for partial economic support. K. G. is grateful to UBACyT for a research student’s fellowship. REFERENCES 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19.
Carlier, C.; Randolph, T. W. AIChE J. 1993, 39, 876–884. Ferna´ndez-Prini, R.; Japas, M. L. Chem. Soc. Rev. 1994, 23, 155–163. Bennet, G. E.; Rossky, P. J.; Johnston, K. P. J. Phys. Chem. 1995, 99, 16136–16143. Ferna´ndez, D. P.; Ferna´ndez-Prini, R. J. Chem. Thermodynamics 1992, 24, 377–386. Marceca, E.; Ferna´ndez-Prini, R. J. Chem. Thermodynamics 1993, 25, 237–247. Marceca, E.; Ferna´ndez-Prini, R. J. Chem. Thermodynamics 1993, 25, 719–728. Marceca, E.; Ferna´ndez-Prini, R. J. Chem. Thermodynamics 1994, 26, 651–661. Orgel, L. E.; Mulliken, R. S. J. Am. Chem. Soc. 1957, 79, 4839–4846. Danten, Y.; Guillot, B.; Guissani, Y. J. Chem. Phys. 1992, 96, 3782–3794. Lemmon, E. W.; Jacobsen, R. T.; Pensonelle, S. G.; Beyerlein, S. W. Report 93 -1 . Center of Applied Thermodynamic Studies, University of Idaho. 1993. Lide, D. R. Handbook of Chemistry and Physics. CRC Press: Boca Raton. 1995, 75th edition, pp. 3–208. Morita, A.; Kajimoto, O. J. Phys. Chem. 1990, 94, 6420–6425. Dymond, J. H.; Smith, E. B. The Virial Coefficients of Pure Gases and Mixtures. Clarendon Press: Oxford. 1980. Hirschfelder, J. O.; Curtiss, C. F.; Bird, R. B. Molecular Theory of Gases and Liquids. J. Wiley and Sons: New York. 1996. Reed, T. M.; Gubbins, K. E. Applied Statistical Mechanics. McGraw Hill Kagakusho: Tokyo. 1973. Reynolds, L.; Gardecki, J. A.; Frankland, S. J. V.; Horng, M. L.; Maroncelli, M. J. Phys. Chem. 1996, 100, 10337–10357. Breneman, C. M.; Wiberg, K. B. J. Comp. Chem. 1990, 11, 361–370. Estrin, D. A.; Paglieri, L.; Corongiu, G. J. Phys. Chem. 1994, 98, 5653–5660. Gray, C. G.; Gubbins, K. E. Theory of Molecular Fluids. Clarenden Press: Oxford. 1984, Vol. 1.
(Received 21 November 1996; in final form 13 March 1997)
WE-084