Solubility of xenon in n-hexane between 257 and 333 K

Transcription

1 Fluid Phase Equilibria 193 (2002) Solubility of xenon in n-hexane between 257 and 333 K Rui P. Bonifácio a, Margarida F. Costa Gomes b, Eduardo J.M. Filipe a, a Centro de Química Estrutural, Instituto Superior Técnico, Lisboa, Portugal b Laboratoire de Thermodynamique des Solutions et des Polymères, UMR 6003, Université Blaise Pascal/CNRS, 24 Avenue des Landais, Aubière, France Received 21 June 2001; accepted 10 September 2001 Abstract Measurements of the solubility of xenon in liquid n-hexane are reported as a function of temperature from 257 to 333 K. A new experimental procedure is described and its accuracy is inferred to be 1% by comparing the data obtained with that reported in the literature in the smaller temperature range from 283 to 303 K. The data outside this temperature range are original in this work. The imprecision of the experimental data, considered as the average absolute deviations from appropriate smoothing equations, is less than 0.6%. The total volume occupied by the saturated solution was also determined experimentally and the data obtained was used to calculate the apparent molar volume of the solute in the solution as a function of the temperature from 277 to 325 K. From Henry s law coefficient and its variation with temperature, the partial molar functions of solvation such as the standard Gibbs energy, the enthalpy and entropy have been calculated from 255 to 335 K Elsevier Science B.V. All rights reserved. Keywords: Xenon; n-hexane; Henry s law coefficients; Apparent molar volumes; Partial molar thermodynamic properties 1. Introduction Mixtures involving n-alkanes and noble gases have been extensively studied and used as model systems for testing statistical theories of liquids. These chemical families provide a range of molecules whose physical properties gradually change within the homologous series or periodic group, and are therefore especially suited to study the role of size, shape, and flexibility on the thermodynamic properties of liquid mixtures. The interaction between xenon and the n-alkanes, in particular, has been extensively studied. Xenon is highly soluble in lipids and fats and shows anaesthetic properties at sub-atmospheric pressures. Given its chemical inertia, non-toxicity and non-flammability (which make it an easy and safe gas to handle), xenon could be considered the perfect anaesthetic. Very recently, its use has been Corresponding author. Tel.: ; fax: address: efilipe@ist.utl.pt (E.J.M. Filipe) /02/$ see front matter 2002 Elsevier Science B.V. All rights reserved. PII: S (01)

2 42 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) submitted for regulatory medical approval in Europe [1]. A further important application of xenon in nuclear medicine involves the use of 133 Xe isotope to study cerebral blood flow and pulmonary functions [2]. At the molecular level, xenon is a spherical and structureless particle, with a high polarisability that enhances dispersion forces. Its intermolecular potential is therefore relatively well characterised. These properties justify its frequent use as a prototype solute in the study of solute solvent interactions from first principles. In addition, one of xenon s most abundant natural isotopes, 129 Xe, has an NMR active nucleus whose shielding constant is very sensitive to the local environment. The 129 Xe particle can thus be used as a probe to study the properties of condensed phases, biological structures and microporous materials by NMR spectroscopy [3,4]. In previous work [5 7] we have reported low-temperature thermodynamic studies (from 160 to 200 K) of mixtures of xenon with the lighter alkanes (methane, ethane, propane, butane and i-butane). As expected, these mixtures are almost ideal and exhibit a behaviour that closely resembles that seen for mixtures of n-alkanes. The data, as interpreted by the statistical associating fluid theory (SAFT-VR) [8,9], seem to indicate that xenon can be represented as a sphere with almost the same diameter and intermolecular potential, as those suited to describe the segments of the n-alkanes. It is also interesting to see that the diameter of the xenon atom measured, for instance, in terms of van der Waals radii agrees well with that of the cross-sectional diameter of the n-alkanes. Solubility measurements often constitute an important source of information about the properties and structure of solutions [10]. Precise measurements covering sufficiently large ranges of temperature are frequently the only means of obtaining the enthalpy and heat capacity changes associated with the dissolution process. The solubility of gases in liquids has been determined in the past using various experimental methods. One of the most simple and accurate methods involves the saturation of a sample of pure degassed solvent with a given quantity of gas, and measuring the volume of the undissolved gas at constant pressure. This is the basis of the Ben Naim and Baer method [11] and of its multiple variations whose major improvements include automation of the measurements [12] and elimination of mercury from the experimental apparatus [13]. One possible modification of the saturation method involves the equilibration of known amounts of dry gas and degassed solvent at constant volume and temperature and measuring the equilibrium pressure of the saturated solution. This approach has the advantage of requiring only the use of an accurate manometer instead of a special manostatic system. Furthermore, the amounts of gas and liquid solvent can be considerably reduced as well as the overall volume of the experimental apparatus. This allows for considerable practical improvements such as the use of relatively small liquid thermostats. The main disadvantages of such an experimental method are the need of accurately measuring the volumes of both liquid and vapour phases in equilibrium and of knowing the saturation properties of the pure solvent. In the present work, a new experimental apparatus has been assembled for the accurate determination of the solubility of xenon in alkanes as a function of temperature. It makes use of the saturation method at constant volume whose principle was just described. The new experimental technique also allows the determination of apparent molar volumes of the solute in the solution as a function of temperature. For this measurement, the equilibrium cell works as a dilatometer, the apparent molar volume being calculated from the experimental determination of the amount of solute and solvent in the liquid solution as well as of its total volume.

3 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) Experimental 2.1. Materials The n-hexane used as solvent was from Lab-Scan, analytical reagent, with 99% mol/mol minimum stated purity. The liquid was purified by distillation in an inert atmosphere of dry nitrogen. The final purity was confirmed by checking its vapour pressure, after degasification. Deviations from literature values [14] were found to be less than 0.4%. The xenon used was from Linde Gas with 99.99% mol/mol minimum stated purity. The gas was used as received from the manufacturer Apparatus and operation The experimental apparatus is schematically represented in Fig. 1. The solubility measurements involve the equilibration of known amounts of dry gas and degassed solvent at constant volume and the determination of the equilibrium pressure for the saturated solution maintained at constant temperature. Fig. 1. Solubility apparatus: VB, vapour phase sampling bulb; EC, equilibrium cell; M, precise manometer; LR, pure degassed solvent reservoir; VG, vacuum gauge; TP, liquid nitrogen trap; VP, vacuum pump; T, liquid thermostat.

4 44 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) The pure solvent is first degassed by successive melting/freezing cycles, while vacuum pumping non-condensable gases. Up to eight cycles were necessary to degas the liquid n-hexane used as solvent. The degassed solvent is kept, under its own vapour pressure, in the reservoir indicated as LR in Fig. 1. The equilibrium cell (EC in Fig. 1) was built following the design of Carnicer et al. [15] and constitutes, together with the precise pressure transducer and the calibrated glass bulb (M and VB in Fig. 1, respectively), the equilibration section of the apparatus. The temperature is maintained in a 50 l water thermostat (T in Fig. 1) to within 0.01 K by means of a Hart Scientific PID temperature controller, and is measured with a previously calibrated Pt100 platinum resistance thermometer. The solubility measurements start with the introduction of a known quantity of the solute in the calibrated glass bulb (VB in Fig. 1). The quantity of gas is determined by measuring its pressure in the transducer M (Paroscientific model 0 7 bar, precision 0.01% FS) at constant temperature, correcting for gas imperfection. The volume of the glass bulb was previously calibrated with mercury (VB = ± cm 3 ). The degassed solvent is then transferred from the reservoir (LR in Fig. 1) into the equilibrium cell (EC in Fig. 1) at its own vapour pressure. The vapour pressure of the pure solvent was measured at this stage in order to check its purity. The level of liquid in capillaries h and k, as well as pressure and temperature are taken for the calculation of the initial quantity of pure solvent. The volume of the equilibrium cell was previously determined as a function of the level of liquid in the capillaries, with a precision of 0.01% and is of approximately 12.7 cm 3. Opening stopcock 2 and turning the liquid circulation on, initiates the equilibration process. The liquid is forced up the capillary arm h (see EC in Fig. 1.) and circulates through the capillary arm k. The readings of pressure during the dissolution process are recorded in a computer (via a serial-port interface) until a constant value is reached when equilibrium has been attained. The pressure, temperature and the level of the solution in the capillaries are then measured. Equilibrium is typically attained after 72 h. The measurement of solubility at different temperatures was done by simply changing the liquid thermostat set point and waiting for a new thermodynamic equilibrium. With a single loading it is thus possible to make measurements over a large temperature range. Several runs were performed in order to check the reproducibility of the results, both increasing and decreasing the temperature. 3. Experimental results and discussion 3.1. Data reduction The solubility of gaseous xenon in n-hexane can be expressed by the Henry s law coefficient, usually defined as [16] [ ] f2 (p,t,x 2 ) H 2,1 (p, T ) = lim (1) x2 0 x 2 The dependence of the Henry s law coefficient with pressure can be expressed as [17] H 2,1 (p, T ) = f 2(p,T,y 2 ) p [ V = H 2,1 (p1 sat x,t)exp 2 (p, T ) 2 RT p sat 1 ] dp (2)

5 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) where f 2 is the fugacity of component 2 (taken here to be the gaseous solute), x 2 its molar fraction in the liquid solution, V2 the partial molar volume of the solute at infinite dilution and p1 sat is the vapour pressure of the pure solvent. The amount of solvent present in the gaseous phase in equilibrium with the liquid solution, n g 1, can be calculated from experimentally measured quantities assuming the validity of Raoult s law: n g 1 = psat 1 (T )x 1V vap Z 12 (p, T )RT and equivalently for the quantity of solute, n g 2 : (3) n g [p psat 1 2 = (T )x 1]V vap (4) Z 12 (p, T )RT where p is the equilibrium pressure of the saturated solution and x 1 the molar fraction of component 1 in the liquid solution. V vap is the volume of the gaseous phase in equilibrium, which is given by V vap = (V tot V liq ), the difference between the total volume of the apparatus, V tot, accurately known from a previous calibration, and the volume of the liquid solution, V liq. Z 12 is the compressibility factor for the solution [16]: Z 12 = 1 + p RT (y 1B 11 + y 2 B 22 + y 1 y 2 δ 12 ) (5) where B 11 and B 22 are the second virial coefficients for the pure solvent and the pure solute, respectively, and δ 12 = 2B 12 B 11 B 22, where B 12 is the solute solvent crossed second virial coefficient. The amount of solute and solvent present in the liquid solution (n l 2 and nl 1, respectively) are determined from the difference between the quantities calculated from Eqs. (3) and (4) and the total initial amounts. The latter are determined from experimental quantities as previously described. The fugacity of component 2 can then be determined in the usual way [18]: f 2 (p,t,y 2 ) = φ 2 (p, T )y 2 p (6) with [ p(b22 (T ) + y1 2 φ 2 (p, T ) = exp δ ] 12(T )) (7) RT where φ 2 is the fugacity coefficient of component 2. The equilibrium compositions are calculated iteratively. The process starts with initial guesses for the molar fractions in both phases and continues with the determination of the quantities of solute and solvent present in the two phases (Eqs. (3) and (4)). The process converges rapidly and coherent values for y i and x i are obtained after a few iterations. The calculation of Henry s law coefficients is then immediate, using Eqs. (1), (5) and (6) [17]. Although only one solubility measurement was carried out at each temperature, it is assumed that the Henry s law coefficient obtained for each state point is independent of the molar fraction of the solute. The pressure dependence for H 2,1 was taken into account following Eq. (2). The apparent molar volume of the solute in the solvent, V φ 2, can also be obtained during the solubility experiment by measuring the total volume occupied by the saturated solution [19]: ( V φ 2 (T ) = Vliq n l 1 V 1 sat(t ) ) (8) n l 2

6 46 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) where V liq is the total volume occupied by the liquid solution and V sat 1 the orthobaric molar volume of the solvent. The vapour pressure of n-hexane was calculated using a Wagner s type equation of state reported by Ambrose and Walton [14]. The molar volume of n-hexane was calculated using the equation reported by Cibulka [20]. The second virial coefficients for pure n-hexane were taken from Dymond et al. [21], and for pure xenon from the compilation of Dymond and Smith [22]. The crossed virial coefficient for the mixture was estimated using the Tsonopoulos correlation [23]. As a first approximation, the partial molar volumes of xenon in n-hexane, necessary for the calculation of the Henry s law coefficients (Eq. (2)), were estimated using the method described by Tiepel and Gubbins [24,25], which is based on a first-order perturbation theory. This method has been applied to calculate the partial molar volume of several gases in water and proved to be accurate to within 3%. This uncertainty affects negligibly the values of the Henry s law constant. These estimated partial molar volumes for xenon in n-hexane can be expressed in the temperature range from 255 to 333 K as ln(v 2 cm 3 mol 1 ) = T K (9) The Henry s law coefficients can be calculated using these values or the apparent molar volumes determined experimentally (this approximation is considered valid for the solutions studied). The two sets of data do not differ significantly the latter were preferred for the calculation of H 2, Experimental results Henry s law coefficients, H 2,1 (p1 sat,t), for xenon in n-hexane for temperatures ranging from 257 to 333 K are recorded in Table 1 and plotted in Fig. 2. For each experimental point, the value of temperature, equilibrium pressure and molar fractions of xenon in the liquid and gaseous phases in equilibrium are indicated. The temperatures are reported on the ITS-90 temperature scale. The relative atomic masses were taken from the IUPAC tables [26] and the value for the gas constant was taken as J mol 1 K 1 [27]. Fig. 2. Henry s law coefficients for xenon in water: ( ) experimental data of Pollack and Himm [31]; ( ) experimental data of Clever [32]; ( ) this work.

7 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) Table 1 Values for the Henry s law coefficients, equilibrium pressure, p, molar fraction for xenon in gaseous and liquid phases at equilibrium between 257 and 333 K T (K) p (kpa) x 2 (10 2 ) y 2 H 2,1 (p1 sat, T) (MPa) Numerous methods are reported in the literature [28] for representing the dependence of the Henry s law coefficient in relatively narrow temperature ranges. In the present case, two smoothing equations were used for the correlation of the experimental data. Clarke and Glew [29] proposed: ln[h 2,1 (T, p1 sat )] = A A T/K + A 2 ln(10 2 T/K) + A 3 (10 2 T/K) + A 4 (10 2 T/K) 2 + (10) and Benson and Krause [30] suggested n ln[h 2,1 (T, p1 sat Pa)] = B i (T /K) i (11) i=0 The coefficients A i and B i for the two equations, as well as the average absolute deviations (AAD) obtained in each case are listed in Table 2. A plot of the Clarke and Glew smoothing equation is also included in Fig. 2. The relative deviations of the experimental results from the same smoothing correlation are represented in Fig. 3 as a function of temperature. As can be observed the data are uniformly distributed and deviations from the correlation do not exceed ±1% (AAD of 0.6%). The solubility of xenon in n-hexane has been previously measured by Pollack and Himm [31] and by Clever [32]. The former reported measurements at only three temperatures, with stated uncertainties of the order of 1 2%, and the later reports measurements from 289 to 316 K claiming uncertainties of about

8 48 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) Table 2 Coefficients for Eqs. (10) and (11) and AAD of the different correlations from experimental data Eq. (10) Eq. (11) A B A B A B AAD 0.6% AAD 0.6% 1%. The two sets of results differ by about 4% at 20 C and show relative deviations from our data of up to 6%. Part of this difference can probably be ascribed to the impurities of the solvent or to different data reduction methods, which are often a source of misleading comparisons between different sets of gas solubility data [33]. Furthermore, our results are systematically above the literature values. From the analysis of all these data as well as a careful study of the sources and order of magnitude of the systematic errors during our experiments, it is believed that the values for the Henry s law coefficients reported in this work are accurate to within 1% Thermodynamic functions The exact expression for the change in partial molar Gibbs energy when the solute is transferred, at temperature T, from the pure perfect gas state at standard pressure to the dilute state in the solvent (standard Gibbs energy of solvation [34]) is [17] ( G 2 (T, psat 1 ) = RT ln H2,1 (T, p1 sat) ) (12) p where p is the standard state pressure, considered as Pa. The partial molar differences in enthalpy and entropy between the two states can be obtained by calculating the corresponding partial derivatives of the Gibbs energy with respect to temperature at Fig. 3. Deviations of the Henry s law coefficients of xenon in n-hexane from the correlation of the experimental values of this work: ( ) experimental data of Pollack and Himm [31]; ( ) experimental data of Clever [32]; ( ) this work.

9 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) Table 3 Partial molar thermodynamic functions of solution for xenon in n-hexane at several discrete temperatures between 255 and 335 K a T (K) G 2 (psat 1, T) (kj mol 1 ) H 2 (psat 1, T) (kj mol 1 ) S 2 (psat 1, T) (J mol 1 K 1 ) a G 2 is the partial molar Gibbs energy, H 2 the partial molar enthalpy and S 2 the partial molar entropy. The values are based on the ideal gas state at Pa. constant pressure. The result for the enthalpy of solution at temperature T and at the vapour pressure of pure solvent is [ ( d ln H 2 (T, psat 1 ) H2,1 (T, p = RT2 1 sat) ) V 2 (T ) ( dp sat 1 (T ) )] (13) dt p RT dt while the difference in the partial molar entropy is given by S 2 (T, psat 1 ) = R ln(h 2,1(T, p1 sat)) RT d ( ln H2,1 (T, p sat p dt p 1 ) ) ( dp + V2 sat (T ) 1 (T ) dt Partial molar thermodynamic functions of solution were calculated from the smoothing equation proposed by Clarke and Glew (Eq. (10)) and are listed in Table 3. The results agree with the data from [31] to within the combined uncertainties (1.2% average deviation for the partial molar Gibbs energy in the temperature range reported, 15 and 8.6% for the partial molar enthalpy and for the partial molar entropy of solution at K, respectively). No values obtained directly by calorimetric determinations were found for comparison Apparent molar volumes The values of the apparent molar volumes were calculated in Eq. (8) using the experimental values of the total volume occupied by the saturated solution, V liq, and the amount of solvent and solute present in the liquid phase, n l 1 and nl 2, respectively. The values obtained for the apparent molar volumes of xenon in n-hexane in the temperature range from 277 to 325 K (13 experimental points), although with a large dispersion, follow the Eq. (15) with and AAD of 11% (with a maximum absolute deviation of 23%). ln(v φ 2 /cm3 mol 1 ) = T/K (15) ) (14)

10 50 R.P. Bonifácio et al. / Fluid Phase Equilibria 193 (2002) Conclusion A new apparatus for the measurement of gas solubilities in liquids has been assembled. The experimental technique is based in the saturation method and the measurements are performed at constant volume. Solubilities, expressed as Henry s law coefficients, were measured between 257 and 333 K with a precision of 0.6% and an estimated accuracy of 1%. From Henry s law coefficient and its variation with temperature, partial molar functions of solvation such as the standard Gibbs energy, the enthalpy and entropy have been calculated. With the existing equilibrium cell, the present apparatus covers a solubility range between 0.35 and mol dm 3. These limits can however be easily expanded by replacing the liquid and gas bulbs by others of appropriate volumes. As secondary data, apparent molar volumes of xenon in n-hexane were determined in the shorter temperature range from 277 to 325 K. The reported values show an imprecision, as characterised by the AAD from an appropriate smoothing function, of 11%. List of symbols B ij second virial coefficient f i fugacity of compound i H ij Henry s law coefficient of solute i in solvent j n P i molar quantity of species i in phase P p pressure R universal gas constant T thermodynamic temperature V volume x i mole fraction of i in the liquid phase y i mole fraction of i in the vapour phase Z ij compressibility factor for a mixture of i and j Fugacity coefficient of i φ i Subscripts and superscripts 1 pure solvent property 2 pure solute property at infinite dilution standard state c critical point property g property of the gaseous phase l property of the liquid phase sat vapour liquid saturation vap vapour phase References [1] C. Lynch III, J. Baum, R. Tenbrinck, Anesthesiology 92 (2000) [2] G.L. Pollack, J. Chem. Phys. 75 (1981) [3] G.L. Pollack, Science 251 (1991)

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