Solubility of non-polar gases in cyclohexanone between and K at kpa partial pressure of gas

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Solubility of non-polar gases in cyclohexanone between 273.15 and 303.15 K at 101.

1 Solubility of non-polar gases in cyclohexanone between and K at kpa partial pressure of gas MAR~ASUNCI~N GALLARDO, JOS~ MAR~A MELENDO, JOS~ SANTIAGO URIETA, AND CELSO GUTIERREZ LOSA Departatnento de Quimica Fisica, Facultad de Ciencias, Universidad de Zaragoza, Zaragoza, Spain Received September 18, 1986' MAR~A ASUNCI~N GALLARDO, JOS~ MAR~A MELENDO, JOS~ SANTIAGO URIETA, and CELSO GUTIERREZ LOSA. Can. J. Chem. 65, 2198 (1987). Solubility measurements of several non-polar gases (He, Ne, Ar, Kr, Xe, H2, D2, N2, 02, C2H4, C2H6, CF4, SF6, and C02) in cyclohexanone at to K and a partial pressure of gas of kpa, are reported. Gibbs energy, enthalpy, and entropy of solution at K and kpa partial pressure of gas were evaluated. Effective hard-sphere diameter temperature dependence has been studied and its effect on the calculated SPT (Scaled Particle Theory) solubilities, and enthalpies and entropies of solution was also examined. MAR~A ASUNC~~N GALLARDO, JOS~ MAR~A MELENDO, JOS~ SANTIAGO URIETA et CELSO GUTIERREZ LOSA. Can. J. Chem. 65,2198 (1987). Operant a des temperatures allant de 273,15 a 303,15 K et a des pressions partielles de gaz de 101,32 kpa, on a mesurt les solubilitts de plusieurs gaz non polaires (He, Ne, Ar, Kr, Xe, H2, D2, N2, O?, C2H4, C2H6, CF4, SF6 et C02) dans la cyclohexanone. On a Cvalut l'energie libre de Gibbs, I'enthalpie ainsi que l'entropie de solution ,15 K et une pression partielle de gaz de 101,32 kpa. On a ttudic la relation entre le diamktre effectif des sphkres solides et la temperature et on a aussi ttudic son effet sur les solubilitts calculces sur la base de la thcorie de la particule graduee; de plus, on a aussi examine les enthalpies et les entropies de solution. [Traduit par la revue] Introduction Apart from their practical usefulness, solubility measurements of non-polar gases in liquids are of great interest in the theoretical study of liquids. In spite of the various approaches proposed up to now, no general method exists for rigorous gas solubility predictions. While it is true that some successful calculations of solubility and of thermodynamic properties for simple systems, using either perturbation or variation methods, were performed (1-8) when more complex molecules are involved, a strict explanation of solubility at molecular level is unattainable, specially when anisotropy effects are important. While lacking the strictness of the above-mentioned methods, Pierotti's "Scaled Particle Theory" (SPT) (1963) (9) shows an outstanding consistency and was extensively used for estimating molecular pair-potential parameters of liquids from gas solubility data. The main simplifications introduced into the original cavity theory for solutions are as follows: (a) solutions are made up of "hard-sphere" molecules; (b) the radial distribution function is independent of temperature and therefore G; = E;; and (c) solvent molecules are uniformly distributed around each solute molecule, that is to say, the radial distribution function, g(u,r), is unity. In the first steps of the development of the cavity theory the effect of temperature on the "effective hard-sphere diameter" of solvent molecules was ignored. However, more recent works (10-15) have revealed that a hard-sphere temperature dependence must be taken into account if an adequate theoretical explanation of solubility results is to be given. In 1981, Cosgrove analysed in depth the effect of the effective hardsphere diameter temperature dependence on solution enthalpies of rare gases in some non-polar organic solvents (benzene, cyclohexane, tetrachloromethane, and n-hexane) and in water, too (15). In the present paper, the effect of temperature on effective hard-sphere diameter, al, is studied for a polar molecule, cyclohexanone (1.1. = 9.34 x m C), and solubility data of fourteen gases in this solvent, between and K and at a gas pressure of kpa, are given. Experimental The equipment used for solubility measurements and the associated experimental technique were similar to those described in previous papers (16, 17). The purity of the gases (all from Sociedad Espaiiola de Oxigeno except Ne and CF4 which were from Baker) was He %, Ne 99.9%, Ar %, Kr 99.95%, Xe %, H %, DZ 99.4%, Nz %, O %, C2H %, C2H6 99.0%, CF4 99%, SF, 99.5%, and COz %. Cyclohexanone (Carlo Erba: 299%) was used as solvent; its purity was checked by GLC and by refractive index measurement (experimental value, n~ ( K) = ; literature, (18)). Vapour pressure data of the solvent were taken from the literature (18). The uncertainty on about the reported solubilities is estimated in +0.7%, or less, except for gases with low solubilities (He and Ne) for which it is approximately + 2.0%. Results In Table 1, the experimental results for the solubilities of He, Ar, Kr, Xe, H2, D2, N2, 02, C2H4, C2H6, CF4, SF6, and C02 in cyclohexanone in terms of the equilibrium mole fraction, x2, are given at temperatures ranging from to K, and at kpa partial pressure of gas. The results were fitted by least squares to an equation of the form: In Table 1 the values of a and b for each system are set out together with the standard deviations u = { 5 (In x2,1 + aln Ti + bi2l(n - 2) i= l.. Table 2 shows the values of partial molar Gibbs energy, AGE,2, partial molar enthalpy, AH:,2, partial molar entropy, 'Revision received April 3, and partial molar Hildebrand entropy, AS:, for the Prinlcd in Canada 1 ImprimC au Canada

2 GALLARDO ET AL TABLE 1. Solubility of gases (x2 X lo4) in cyclohexanone, at kpa partial pressure of gas between and K, coefficients of the equation -In x2 = a In T + b, and standard deviations as defined in the text TIK a x 104 Gas " a b (st. dev.) He Ne Ar Kr Xe H Dz N CzH C2H CF SF, COz "From ref. 19. TABLE 2. Gibbs energies, enthalpies, entropies of solution, and SPT calculated enthalpies and entropies in cyclohexanone at K and kpa partial pressure of gas, both when 1 I = 0, and li = 1.87 x K-I AHnq.2 AHnq.2 As:,2 As:,Z A~2.2 AH:., AS:,Z AS: (11 = 0) (11 f 0) (11 = ) (11 f 0) Gases kl mol-' kl mol-i kl K-I mol-i kj K-' mol-i kj mol-i kl mol-' kj K-I mol-' kl K-I mol-i solution process calculated from our experimental results, and using the adequate relations (20). Discussion The scaled particle theory formalism of gas solubility has been explained so many times that we consider unnecessary to do it again; we will just summarize the pertinent equations instead. The changes in Gibbs energy and enthalpy for the solution process are given by equations (9, 12): where R is the gas constant, T is the absolute temperature, KH = p2/x2 is the Henry's law constant, p2 is the partial pressure of the gas, x2 is the gas mole fraction in the solution, uy is the molar volume of the solvent, a, is the thermal expansion coefficient of the solvent; the subscripts 1 and 2 refer to the solvent and the solute, respectively, and c and i refer to cavity formation and interaction steps, respectively. In the present paper we are interested in the temperature dependence of the effective hard-sphere diameter. It can be seen (Fig. 1) that Henry's law constant decreases regularly with the polarizability of the rare gases; from this plot, the extrapolated value of In KH to zero polarizability leads to the solubility of a hard sphere of nm diameter. This diameter is obtained from the extrapolation to zero polarizability of the plot of diameter of the rare gases against the corresponding polarizabilities. Introducing such a value in eq. [2] with a2 = 0, the effective hard-sphere diameter of the solvent, al, can be calculated (9). As solubility data of rare gases were available for several temperatures, we were able to evaluate the linear coefficient of expansion of al, at K and kpa, namely: li = (1/al)(dal/aT), = X lop4 K-' The necessary data used in the calculations are given in Table 3.

3 2200 CAN. J. CHEM. VOL. 65, 1987 FIG. 1. Experimental In KH versus a2 for the rare gases in cyclohexanone at different temperatures. TABLE 3. Parameters and properties used in calculations 1030 a2a lolo 02n e2/ka Gases rn rn K He Ne Ar Kr Xe Hz D N CzH CzH CF SF Hard sphere lo4 ap lop3 den~ity'~' lo9 alc ellkc Liquid C m K-' kg m-3 m K c6hl "Reference 2 1. breference 22. 'Reference u2. 10'01rn FIG. 2. Difference between experimental and calculated (SPT) values of the partial molar enthalpy of solution, -(AHK3- AH:,'^^), of gases dissolved in cyclohexanone at K, versus the effective hard sphere diameter of solutes: 0, values calculated with 1, f 0; 0, values calculated with li = 0. Recently, Cosgrove and Walkley have proposed a method for calculating 1, from enthalpy of solution data (15). If the enthalpies of solution of rare gases in a given solvent are available, the enthalpy of solution of a hard sphere (a2 = nm), AH2,0, can be obtained fromextrapolation of AH:,^ vs. a2 to zero polarizability; then 1, can be calculated by means of eq. [3] and also the corresponding expression for H, which depends on the linear coefficient of expansion of a,. The value of AH2,0 found for cyclohexanone was kj mol-l. Likewise, the value of 1, obtained for cyclohexanone at K and kpa was X lop4 K-l, in good agreement with that calculated from In KH at several temperatures. In order to study the effect of the effective hard-sphere diameter temperature dependence, solubility and thermodynamic functions associated to the solution process were calculated by means of the scaled particle theory either assuming a constant a, (11 = 0) or admitting its temperature dependence (1 + 0). Table 2 contains also the theoretical values for AH^,^ and AS:,2, both when 1, = 0 or 1, + 0. In Figs. 2 and 3 the differences between experimental and calculated values are plotted against the effective hard-sphere diameter of the solute. The following observations are worth making: (i) for He and Ne (that is to say, the gases with the shallowest energy well)

4 GALLARDO ET AL FIG. 3. Difference between experimental and calculated (SPT) values of the partial molar entropy of solution, -(ASK3 - As:,'sd), of gases dissolved in cyclohexanone at K, versus the effective hard sphere diameter of solutes: 0, values calculated with li # 0; a, values calculated with 1 I = 0. experimental and calculated AH:,, and AS:, are in good agreement when ll = X K-' is used; with ll = 0 the calculated values differ greatly from the experimental ones; (ii) for gases whose potential energy curves are similar in depth to that of Kr, only the values of AH:, and AS:, obtained with 1, = 0 agree with the experimental ones. Cosgrove and Walkley found similar concordance pattern for the calculated enthalpies of solution for other solvents (15). When the values of solution enthalpy obtained from eq. [3] (Table 2) are compared with those deduced from the slope of the plot of the theoretical In KH against In T, one can observe that the two ways only agree when Gi is temperature independent. This is because the theory assumes the entropy of interaction to be equal to zero. However, the predicted values of In KH are better if Gi is assumed to be temperature dependent in eq. [2]. Figure 4 shows the plot of In KH against In T for the rare gases with Gi = constant. Following Cosgrove and Walkley (15), we have checked the thermodynamic consistency of equations [2] and [3] for a hypothetical solute of hard-sphere molecules for which Gi = Hi = 0. The diameters used were the hard-sphere effective diameters for the rare gases (see Table 3). Enthalpy of solution at K was calculated from [3], either with 1, = 0 or with ll = 1.87 X K-'. Once the values of In KH were obtained from eq. [2] at and K, the enthalpy of solution was calculated by means of: both supposing a, = constant = a (298.15), AHP(ln KH), and a = a (T), AH1(ln KH). The results obtained (Table 4) show FIG. 4. In KH of inert gases in cyclohexanone as a function of In T: the unbroken line are experimental values; the broken lines are calculated (SPT) values using Gi temperature independent, --- with li = X lop4~-' and --- with li = 0. TABLE 4. Enthalpies of solution of rare gases as hard spheres (G, = Hi = 0) AH^ AH' AHP (In KH) AH' (In KH) - - Gases kj mol-' kj mol-' kj mol-' kj mol-i that [2] and [3] lead to similar values when the same criterion about hard-sphere temperature dependence is used in both cases (either with 1, = 0 or with ll + 0). This confirms that the disagreement between the values for AH;,, calculated using both ways should be ascribed to the interaction term, Gi. Acknowledgements Authors are grateful for financial assistance of Comision Asesora de Investigacibn Cientifica y TCcnica (Madrid) (Proyecto ). One of the authors (M.A.G.) thanks P.F.P.I. (Plan de Formacibn del Personal Investigador) for a grant. 1. R. 0. NEFF and D. A. Mc. QUARRIE. J. Chem. Phys. 77, 413 (1973). 2. S. GOLDMAN. J. Phys. Chem. 81, 608 (1977).

Solubility of nonpolar gases in 2,6-dimethylcyclohexanone

Solubility of nonpolar gases in 2,6-dimethylcyclohexanone MARIA ASUNCION GALLARDO, MARIA DEL CARMEN LOPEZ, JOSE SANTIAGO URIETA, AND CELSO GUTIERREZ LOSA Quimica Fisica, Facultad de Ciencias, Universidad