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 de Zaragoza, 50009-Zaragoza, Spain

Received April 19, 1989

MARIA ASUNCION GALLARDO, MARIA DEL CARMEN LOPEZ, JOSE SANTIAGO URIETA, and CELSO GUTIERREZ LOSA. Can. J. Chem. 68, 435 (1990).

Solubility measurements of He, Ne, Ar, Kr, Xe, Hz, DZ, N2, CH4, C2H4, C2H6, CF4, SF6, and C 0 2 in 2,6-dimethylcyclo- hexanone at temperatures 273.15 to 303.15 K and at a gas partial pressure of 101.33 kPa are reported. Standard changes in Gibbs energy, enthalpy, and entropy for the dissolution process at 298.15 K are also presented. Results for both solubility and thermodynamic functions are compared with those for cyclohexanone and 2-methylcyclohexanone. The scaled particle theory is used to obtain the effective Lennard-Jones (6,12) pair potential parameters for 2,6-dimethylcyclohexanone and, from these, the values it predicts for the solubility of the studied gases in the solvent are obtained.

Key words: gas solubility, Henry coefficient, 2,6-dimethylcyclohexanone, thermodynamic functions of solution, non-polar gases.

MARIA ASUNCION GALLARDO, MARIA DEL CARMEN LOPEZ, JOSE SANTIAGO URIETA et CELSO GUTIERREZ LOSA. Can. J. Chem. 68, 435 (1990).

Operant i des tempkratures allant de 273,15 i 303,15 K et i une pression partielle de gaz de 101,33 kPa, on a mesurt les solubilitCs du He, du Ne, du Ar, du Kr, du Xe, du Hz, du D2, du N2, du CH4, du C2H4, du C2H6, du CF4, du SF6 et du C 0 2 dans la 2,6-dimtthylcyclohexanone. On en a tirC les changements standard de 1'Cnergie de Gibbs, de l'enthalpie et de 1'en:ropie du processus de dissolution i 298,15 K. On a compart les rksultats obtenus tant pour les solubilitts que pour les fonctions thermodynamiques avec celles rapporttes anterieurement pour la cyclohexanone et la 2-mCthylcyclohexanone. On a fait appel ii la thCorie de la particule scalaire pour dCterminer les parametres effectifs de Lennard-Jones (6,12) pour le potentiel de paire de la 2,6-dimtthylcyclohexanone et, i partir de ceux-ci, les valeurs qu'elles permettent de prCdire pour la solubiliti des gaz Ctudits dans ces solvants.

Mots clks : solubilitC des gaz, coefficient de Henry, 2,6-dimCthylcyclohexanone, fonctions thermodynamiques de solution, gaz non-polaires.

[Traduit par la revue]

Introduction solution vessel was to within 20.05 K. Precision in the mole fraction

This paper is a continuation of our work on the solubility of non-polar gases (1-8) to study the influence exerted by the presence of different features in the solvent molecule. In this particular case we were interested in seeing how the solubility changes with the introduction of methyl groups as substituents in the solvent cyclohexanone. Previously, the solubility of fourteen non-polar gases in cyclohexanone and 2-methylcyclo- hexanone was measured and published in this journal (4, 7). Here w e present the solubility of the same fourteen gases in 2,6-dimethylcyclohexanone. This solvent was chosen because it not only has one more methyl substituent but its relative position in the cycle is the same as that of the methyl group in 2-methylcyclohexanone. Therefore the molecule is "symmetrical" and both methyl groups are equivalent (the product used was a mixture of cis-trans stereoisomers). The values of the thermodynamic functions for the solution process are also reported and compared with those for the other cyclohexanones. Finally, using the scaled particle theory for solubility of gases (9, 10) the effective Lennard-Jones (6,12) pair potential parameters for the solvent will be calculated and our experimental results will be compared with the values predicted by that theory.

Experimental In refs. 2, 11 details of the apparatus and the procedure have been

given. The experimental technique is based on the determination of the volume of gas which dissolves in a known mass of solvent at a constant temperature and pressure. The total pressure is chosen to be such that the partial pressure of gas is about 101.33 kPa. The solute mole fraction in the liquid phase, x2 , was derived by assuming the gas phase to be ideal. The temperature of the air thermostatic bath holding the apparatus was controlled to within +- 0.2 K. Temperature control in the

x2 is estimated to be 20.7% with the exception of gases with low solubility (He and Ne) for which it is approximately 22.0%. The non-ideality of the gas phase was not considered due to the lack of the necessary data to get the gas virial coefficients for the solvent and the mixture. However, empirical approaches (12, 13) were used to estimate the critical data for the solvent and the necessary parameters, and from these the mentioned virial coefficients in the case of the most soluble gases, to give an idea of the error introduced by considering ideal gas phase behaviour. In the least favourable instances, Xe, C2H4, C2H6, and SF6, such estimations led to mole fractions about 1 % , 1 % , 1.5%, and 2.3%, respectively, higher than when ideality is assumed.

For COz dry gas was used (the procedure was slightly different, see ref. 2) and the number of moles in the solution vessel at constant pressure and temperature was determined by taking into account the non-ideality of COz by means of its second virial coefficient. The solute mole fraction in the liquid phase is obtained by subtracting the number of moles of COz in the gas phase above the liquid from the number of moles of gas in the solution vessel. The volume of this gas phase is so small that any corrections to account for its non-ideality are certainly smaller than the experimental error.

All the gases were from Sociedad Espafiola del Oxigeno, except Ne and CF4, which were from Baker. Their mole-percentage purities were: He 99.995, Ne 99.9, Ar 99.9990, Kr 99.95, Xe 99.995, HZ 99.99, D2 99.4, N2 99.998, CH4 99.95, C2H4 99.90, CzH6 99 .O, CF4 99, SF6 99.5, and COz 99.998.

The solvent was 2,6-dimethylcyclohexanone (mixture of cis-trans stereoisomers) and was aFluka product. Its purity was checked by GLC to be 98.2%. The main impurities were identified as cyclohexanone, 2-methylcyclohexanone, and some other methylated and dimethylated cyclohexanones, all of which are products that have similar gas solubilities to that of 2,6-dimethylcyclohexanone (4,7). The refractive index was also measured (nD(293. 15 K) = 1.44686) but no literature values were found for it. The vapour pressures and the densities of 2,6-dimethylcyclohexanone were determined in the working tempera- ture range and fitted by least squares to equations

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436 CAN. J. CHEM. VOL. 68, 1990

TABLE 1. Experimental solubility of gases ( X 2 X lo4) in 2,6-dimethyl-cyclohexanone at 101.33 kPa partial pressure of gas between 273.15 and 303.15 K, values of the coefficients A; in eq. [3] and

standard deviations as defined by eq. [4]

Gas 273.15 283.15 293.15 298.15 303.15 Ao A I u

and

[2] p/g cmP3 = -8.313 X 10-4(t/T) + 0.9290 respectively.

Results and discussion Experimental equilibrium mole fraction of gas, x2, in

2,6-dimethylcyclohexanone at temperatures between 273.15 and 303.15 K and at a gas partial pressure of 101.33 kPa are displayed in Table 1. These x2 (101.33 kPa, T) data were fitted by a least-squares method to an equation of the form

[3] - 1 n x 2 = A o + A l X T-'

Table 1 contains the coefficients A; for the different gases. The standard deviation, u, defined as

is also included in Table 1. The standard changes in partial molar Gibbs energy, AG:,~,

partial molar enthalpy, partial molar entropy, AS:,2, and Hildebrand entropy, ASH, for the dissolution process were calculated using equations (14-16):

d In x2(sat) [6] AH& = RT [ d l n T 1

d In x2(sat) [7] = R [ d l n T

+ In x2 l where R is the gas constant, T is the absolute temperature, and x2(sat) is the mole fraction of the gas in the liquid phase in equilibrium with the gas at a partial pressure of 101.33 kPa. In the derivations of eqs. [5]-[8] both ideal behaviour of the gas and validity of the laws for dilute solutions are assumed (14-16).

The values obtained for the thermodynamic functions of the solution of the studied gases in 2,6-dimethylcyclohexanone at 298.15 K are given in Table 2.

When comparing the solubility of the studied gases in 2,6-dimethylcyclohexanone, 2-methylcyclohexanone (7), and cyclohexanone (4), it is seen that the solubility of any of the studied gases is always higher in 2,6-dimethylcyclohexanone than in 2-methylcyclohexanone and higher in this solvent than in cyclohexanone in the temperature range studied (as an example, the solubility of He, Ar, Kr, and Xe in the three cycloketones as a function of 1/T is plotted in Fig. 1). The only exception is C 0 2 . For this gas the solubility in 2,6-dimethyl- cyclohexanone only becomes higher than in 2-methylcyclo- hexanone above a certain temperature in between 273.15 and 298.15 K.

Consequently with the solubility sequence, the more methyl groups the cyclohexanone has, the lower the partial molar Gibbs energy for the dissolution process becomes.

As far as the sequence of increasing solubility of gases in 2,6-dimethylcyclohexanone is concerned, it is found to be basically the same as for cyclohexanone and 2-methylcyclo- hexanone though there are some interchanges in the positions of some of the most soluble gases depending on the temperature, examples of which are SF6 and Kr, Xe and C2H4, and C2H6 and C 0 2 .

Table 2 shows the variation of the standard partial molar enthalpy of solution, AH,^,^, (this thermodynamic function is directly related via eq. [6] to the variation of solubility with temperature) with the solubility of gases. As in the case of other solvents (15), there is a tendency of the temperature coefficient of solubility to decrease with increasing solubility of the gas, e.g. the more soluble the gas, the smaller its standard partial molar enthalpy of solution. He, Ne, Hz, and D2 show increasing solubilities with temperature and positive values for AH&, while the most soluble gases (Xe, C2H4, C2H6, and COz) have very negative values for AH&, and solubility decreases with temperature.

That the standard partial molar enthalpy AH^,^ decreases with the increase of solubility of gas holds for the three different solvents considered here (see Fig. 1). Moreover, according to

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GALLARDO ET AL.

TABLE 2. EX rimental and calculated (SPT) values for partial molar Gibbs energy, AG:,~, partial molar enthalpy, AH,^,^, and partial molar g. entropy, and experimental partial molar Hildebrand entropy for the solution of gases in 2,6-dimethylcyclohexanone at 298.15 K and 101.33 kPa partial pressure of gas*

AH& (kJ mol-I) (kJ K-I mol-l) AG:.~

X2 x lo4 (kJ mol-I) Calcd Calcd ASH

Gas Fitted Calcd Exp Calcd Exp l I = 1.48 x l1 = 0 Exp II = 1.48 x l1 = 0 ( ~ J K - ' mol-')

He 1.143 1.63 22.50 21.62 8.61 8.62 4.45 -0.047 -0.044 -0.058 0.029 Ne 1.60 4.84 21.67 18.92 6.82 6.25 1.68 -0.050 -0.043 -0.058 0.023 Ar 11.94 22.6 16.68 15.10 -0.37 3.85 -2.41 -0.057 -0.038 -0.059 -0.001 Kr 36.0 46.1 13.94 13.34 -4.68 2.77 -4.28 -0.062 -0.035 -0.059 -0.016 Xe 152 103 10.38 11.35 -9.32 1.62 -6.37 -0.066 -0.033 -0.060 -0.031 H2 3.40 3.47 19.80 19.74 4.50 7.23 2.47 -0.051 -0.042 -0.058 0.015 D2 3.52 3.72 19.71 19.57 4.55 7.06 2.29 -0.051 -0.042 -0.058 0.015 N2 6.07 8.04 18.36 17.67 1.64 7.18 0.04 -0.056 -0.035 -0.059 0.005 CH, 26.1 35.5 14.74 13.68 -3.34 3.50 -3.65 -0.061 -0.035 -0.059 -0.01 1 C2H4 147.9 121 10.45 10.93 -10.76 1.53 -6.84 -0.071 -0.032 -0.060 -0.036 C2H6 170 123 10.10 10.90 -10.99 2.48 -6.98 -0.071 -0.028 -0.060 -0.037 cF4 7.44 7.70 17.86 17.77 -0.21 10.30 -0.21 -0.061 -0.025 -0.060 -0.001 SF6 35.1 26.1 14.02 14.75 -6.08 10.55 -3.52 -0.067 -0.014 -0.061 -0.020

i C02 167 64.4 10.14 12.51 -12.57 2.71 -5.21 -0.076 -0.033 -0.059 -0.042

' *Theoretical values of AH:,, and AS;., were calculated uslng both 1 , = 1.48 X K-' and 1 , = 0). Column 2 shows the fitted values of x2 at 298.15 K

1 from our experimental fitting coeffic~ents in Table I . Column 3 contains the values of x2 at 298.15 K calculated via SFT

I FIG. 1. The lines in the plot represent the fitting of experimental gas

/ solubility data to eq. [3] for different solvents: - cyclohexanone (4), I -_ - 2-methyl-cyclohexanone (7), - - - 2,6-dimethylcyclohexanone.

2,6-dimethylcyclohexanone of the gases studied follows the same pattern and has values similar to other organic solvents' but no tendencies are detected when comparing the values for a given gas in the three cyclohexanones (4, 7).

The scaled particle theory (SPT) allows an evaluation of effective Lennard-Jones pair potential parameters for the solvent from a knowledge of both gas solubility data and the corresponding parameters for gases (9, lo), and it has also been used to predict Henry coefficients of gases in different solvents (1-4, 6, 7, 9 , 10, 17, 19, 20, and references therein) and the thermodynamic magnitudes associated with the solution process. The theory stipulates that dissolution takes place in two steps: (a) creation in the solvent of a cavity of the right size to accommodate the solute molecule, and (b) insertion of the solute molecule into the cavity, then the solute interacts with the solvent. The partial molar Gibbs energy for the cavity formation is calculated using the SPT expressions derived by Reiss et al. for hard spheres (10, 21). The calculation of the partial molar Gibbs energy coming from the interaction involves more approximations (10) and it is usually made on the basis of an effective Lennard-Jones (6,12) potential corrected with a term for dipole- induced dipole interactions. Objections can be made to the use of the induction contribution term obtained by this model, since pair additivity is assumed in deriving it. An option to avoid this would be the use of just a Lennard-Jones (6,12) pair potential, thus the effective parameters would include all the induction effects in them. In this work the Lennard-Jones pair potential parameters presented are those obtained when the first option is adopted to allow comparisons with other solvents, the parameters of which were obtained in the same way.

The properties of gases required for the calculations were

the solubility sequence, for any given gas, AH,^,^ at 298.15 K is 'see, for example, the review on thermodynamic functions for always lower in 2,6-dimethyl~y~lohexanone than in 2-methyl- dissolution of gases in organic solvents by Wilhelm and Battino,

1 cyclohexanone and is lower in this Solvent than in cyclohexa- ref, 14. Due to the hydrophobic effect for water the experimental none; the only exception is C 0 2 . values of are much more negative than for any other solvent

The standard partial molar entropy for dissolution in (16-18).

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43 8 CAN. 1. CHEM. VOL. 68, 1990

TABLE 3. Effective Lennard-Jones (6,12) pair potential parameters is represented for the three cyclohexanones using the parameters for the solvents: effective hard sphere diameter at 298.15 K U I , and estimated from our gas solubility data.

energy parameter E /k The value obtained for the linear coefficient of the effective hard sphere diameter at 298.15 K of 2,6-dimethylcyclohexa-

Compound u~ l0l0 (,) ( € 1 1 ~ ) (K) none, l1 = ( l / a l ) ( aa l / aT)p , was l1 = -1.58 X lop4 K-'

Cyclohexanone* 5.651 584 2-Methylcyclohexanonet 5.988 627 2,6-Dimethylcyclohexanone 6.292 665

*From ref. 3, 4. ?From ref. 7.

t 3 0 0

0

- Y - - Y \ 3 -

- 300

from the solubility data of rare gases at different temperatures (23), and l1 = - 1.48 X lop4 K-' from enthalpy solution data (24). The agreement between both methods is ordinary (4, 7, 24).

Once the parameters for the solvent were known, calculations were made to obtain the theoretical values of the thermodyna- mic functions in the solution process. The results obtained are shown in Table 2. The agreement between the calculated and experimental values for AG:,2 and x2 follows the same pattern as for other solvents (1-4, 6, 7, 17, 20, 25) and can be consi- dered satisfactory if one takes into account the simplifications in the theory. The same result as in literature is found for enthalpies and entropies of solution (4, 7 , 24): the introduction of temperature dependence in the effective hard-sphere diameter of the solute (1, + 0) leads to AH,^,^ and AS:,2 values that agree with the experimental values for gases closest to being hard- spheres (polarizability approaching zero): He and Ne. The use of l1 = 0 leads to values for AH,^,^ and AS:,2 more in agreement with the experimental ones for gases such as Ar, Kr, CH4, or CF4.

Acknowledgement This project was financially supported by the Comision

Asesora de Investigaci6n Cientifica y Tkcnica (Project number 1788/82), to which the authors are very grateful.

1. F. GIBANEL, J. S. URIETA, and C. GUTIERREZ LOSA. J. Chim. Phys. 78, 171 (1981).

2. M. A. GALLARM), J. S. URIETA, and C. GUTIERREZ LOSA. J. Chim. Phys. 80, 621 (1983).

3. J. M. MELENM), M. A. GALLARW, J. S. URIETA, and C. - 600 GUTIERREZ LOSA. Acta Cient. Compostelana, XXII, 269 (1985).

4. M. A. GALLARDO, J. M. MELENDO, J. S. URIETA, and C. GUTIERREZ LOSA. Can. J. Chem. 65, 2198 (1987).

5.0 5. M. C. LOPEZ, M. A. GALLARDO, J. S. URIETA, and C. GUTIERREZ LOSA. J. Chem. Eng. Data, 32,472 (1987).

FIG. 2. Lennard-Jones (6,12) pair potential as a function of the interparticle distance for cyclohexanone (c6), 2-methylcyclohexanone (2mc6), and 2,6-dimethylcyclohexanone (2,6dmc6) with the para- meters u , and e l /k obtained from gas solubility data (refs. 4 and 7, and present work).

taken from the literature (22); the dipole moment of 2,6- dimethylcyclohexanone was estimated to be 3.13 D from dielectric permittivity measurements. The values found for the effective Lennard-Jones (6,12) pair potential parameters for 2,6-dimethylcyclohexanone are shown in Table 3. These values can be considered an average of the cis and trans stereoisomers since the product used in the experimental measurements was a mixture of the two. There is a clear increase in the distance parameter in the order cyclohexanone, 2-methylcyclohexanone, 2,6-dimethylcyclohexanone, as would be expected (given the increasing size of the molecule) since the distance parameter is, in a way, a measure of the diameter of the molecule.

The energy parameter also increases in the same sequence, meaning a deeper potential well as the cyclohexanone becomes more methylated. In Fig. 2, the Lennard-Jones (6,12) potential

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