Solubility Parameters of Permanent Gases

The solubility parameters, δH(Tb), of nonreactive permanent gases at their boiling points Tb (<290K) are calculated from individually discussed values of their molar enthalpies of vaporization and densities obtained from the literature. These values are tabulated and where available the coefficients of the temperature dependence expression δH(T) are also tabulated. The trends noted in the δH(Tb) values are dealt with and the values are compared with those reported in the literature and derived from the solubilities of the gases in various solvents. The δH(Tb) values are shown to correlate linearly with the depths of the potential wells (attractive interaction energies, ε/kB) for binary collisions of the gaseous molecules and with the surface tensions, σ(Tb), of the liquefied gases.


Introduction
The solubility of gases in liquid solvents is an important issue in many fields of chemistry and chemical engineering, from processing to environmental elimination.In this review the solubility of permanent, nonreactive gases is dealt with, in terms of their solubility parameters at the normal boiling points of the liquefied gases and their temperature dependence.Permanent gases are those substances that are gaseous at ambient conditions, that is, at atmospheric pressure and ≤290 K. Nonreactive gases include those that dissolve in their molecular (atomic for noble gases) form in the solvents without causing chemical changes in them.This limit excludes gases like F 2 , Cl 2 , the hydrogen halides, NO 2 , and a few others.Still, this review is not exhaustive but attempts to include practically all the inorganic gases and most of the organic ones up to butane.The normal boiling points,  b , of the liquefied gases are selected because the required data mainly pertain to these conditions (at which the vapor pressures of the saturated liquefied gases reach 101.325 kPa or one atm). b are also considered to be "corresponding states" as is indicated by the Trouton constant (the molar entropy of vaporization at  b ) being the same, Δ V ( b ) = 10.5, for ordinary (nonassociating) liquids.
1.1.Gas Solubility from Regular Solution Theory.The gases dealt with here are generally non-or only mildly polar and their solubilities can be described by means of the regular solution theory of Hildebrand [1].This states that the mole fraction solubility  G of the solute gas (subscript G) in the liquid solvent (subscript S) is as follows: where  G is the molar volume and the two  H 's are the total (Hildebrand) solubility parameters.The ideal solubility at the temperature ,  G id , is given by where Δ V  G ( b ) is the molar enthalpy of vaporization of the liquefied solute gas at its normal boiling point  b .In the cases of polar solutes or solvents or those prone to hydrogen bonding the partial (Hansen) solubility parameters [2] of such solvents should be used instead for the prediction of the gas solubilities, but this needs not concern much the present review.The solubility parameters of liquid solvents,  HS , are available in compilations for molecular [3,4] and ionic [5,6] solvents.
The solubility of a gas in a liquid is often expressed as the Henry constant,  G(S) , which is related to the mole fraction solubility in the solvent,  G(S) , as follows: where  G is the partial pressure of the gas that is at equilibrium with its saturated solution.Hence, the larger the measured Henry constant, the smaller the actual (mole fraction) solubility.The solubility of a permanent gas is generally not needed at its normal boiling point, but  HG ( b ) is a reference value from which the temperature dependence of  HG can be used to obtain the value at the desired temperature.Such temperature dependence data, unfortunately, are available for only a minority of gaseous solutes.

Hildebrand Solubility
Parameters.The values of the total (Hildebrand) solubility parameter of the gases dealt with here,  HG , are obtained as the square roots of the cohesive energy densities,  G .The latter are obtained from the molar enthalpies of vaporization and the molar volumes, assuming the liquefied gas vaporizes without association or dissociation to an ideal gas at  b , that is, at 101.325 kPa, as follows:

The Required Data
In the following the subscript G is dropped, because only the solute gases are being dealt with.The required data for obtaining the solubility parameters  H are the normal boiling points of the liquefied gases,  b , their molar enthalpies of vaporization Δ V ( b ), and their molar volumes ( b ) at the boiling point.The molar volumes  are obtained from the ratios of the molar masses  and the densities :  = /.The molar volume is also the reciprocal of the concentration : /cm 3 mol −1 = 1000/(/mol dm −3 ).The molar masses and boiling points are taken from the Handbook [7].The other quantities are obtained from the literature, from primary sources as noted below when readily available or else from secondary sources (compilations) such as [8][9][10][11].
Following are details of the data used and the results of the application of (2), yielding  H ( b )/MPa 1/2 values.

Specific Data for Each Gas
2.1.1.Helium.The earliest report of the solubility parameter of helium is that of Clever et al. [20], derived from its solubility in hydrocarbons and fluorocarbons, and is tabulated at the normal boiling point as 0.5 cal 1/2 cm −3/2 (i.e., 1.02 MPa 1/2 ).However the text above the table states that 0.6 cal 1/2 cm −3/2 (i.e., 1.23 MPa 1/2 ) is "more compatible with the solubility parameter at the gas b.p.".The subsequent report by Yosim and Owens [21] evaluated the molar enthalpy of vaporization, using the scaled particle theory, but reported also its experimental value and the density at the boiling point [22], from which the value 1.20 MPa 1/2 is derivable.The most recent report is by Donnelly and Barenghi [23], who presented density and vapor pressure data at 0.05 K intervals around the boiling point that interpolate to  b = 4.22 K and ( b ) = 0.1250 g cm −3 .They also presented four reports for Δ V  at 4.207 K that average at 83.04 ± 0.37 J mol −1 , from which the solubility parameter  H ( b ) = 1.22 ± 0.01 MPa 1/2 is derived and represents the selected value.

Xenon.
The  H ( b ) value tabulated by Clever et al. [20], obtained as described for He, is 8.0 cal 1/2 cm −3/2 (i.e., 16.36 MPa 1/2 ).The value  H ( b ) = 16.19MPa 1/2 is derived from the data of [22] reported by Yosim and Owens [21].Chen et al. [29] presented the molar volumes and the molar enthalpies of vaporization of Xe at 17 temperatures between the triple and boiling points, from which the expression for the solubility parameter shown in Table 3 results and  H ( b ) = 15.79MPa 1/2 .Linford and Thornhill [24] reported the energy of vaporization as Δ V ( b ) = 2.69 kcal mol −1 and with the molar volume from Terry et al. [30], ( b ) = 44.68cm 3 mol −1 (interpolated), the value  H ( b ) = 14.87 MPa 1/2 is derived.The average of the three largest values, 16.1 ± 0.3 MPa 1/2 , is adopted as the representative value for  H ( b ).

Boron Trifluoride.
No data regarding the molar enthalpy of vaporization of liquid BF 3 were found, except for the entry in the Handbook [7] that was not traced to a definite reference, of Δ V /J mol −1 = 19330.The boiling point was given there as −101 ∘ C, that is, 172.2 K.The density of liquid BF 3 was obtained from Fischer and Weidemann [42] as (/ ∘ C)/g cm −3 = 1.68[1 − 0.0023( + 128)], that is, 1.5757 g cm −3 at  b .These data yield  H ( b ) MPa 1/2 = 20.39,but there is no corroboration of this value from any other source.
2.1.12.Carbon Monoxide.Prausnitz and Shair [27] reported  H = 3.13 (cal/cc) 1/2 , that is, 6.40 MPa 1/2 , a very low value compared to other reports.Yosim and Owens [21] used the Δ V  data of Kelley and King [40], from which the value  H ( b ) MPa 1/2 = 12.37 is derived.Goodwin [46] presented enthalpy of vaporization and density data from the melting to the boiling points that yield the expression shown in Table 3 and  H ( b ) MPa 1/2 = 12.29.Linford and Thornhill [24] reported 1.28 kcal mol −1 for the molar energy of vaporization at the boiling point, yielding with the molar volume data of Terry et al. [30], interpolated to  b ,  = 35.53cm 3 mol −1 and the value  H ( b ) MPa 1/2 = 12.27.Barreiros et al. [47] reported the molar enthalpy of vaporization and the molar volume at 80 to 125 K, and at the boiling point 5991 kJ mol −1 and 35.373 cm 3 mol −1 , from which  H ( b ) MPa 1/2 = 12.26 is derived.The temperature dependence at temperatures above those in Goodwin's paper [46] is shown in Table 3. Prausnitz and Shair [27] quote Hansen [2] and report  d = 11.5 MPa 1/2 at 298 K and 1 atm for the dispersion partial solubility parameter, but the total, Hildebrand solubility parameter included a contribution from the polar interactions of these gas molecules, adding up to  H (298 K) MPa 1/2 = 12.50.The average of the four agreeing values,  H ( b ) MPa 1/2 = 12.30 ± 0.05 is taken as selected.
2.1.13.Carbon Dioxide.Carbon dioxide sublimes from the solid to the gas without passing at ambient pressures through a liquid phase.Prausnitz and Shair [27] reported  H = 6.0 (cal/cc) 1/2 , that is, 12.37 MPa 1/2 , quoted as 12.3 MPa 1/2 by LaPack et al. [28], at an unspecified temperature, a value comparable to some other reports.Span and Wagner [48] reported data over a wide temperature range for both the molar enthalpy and the density of the condensed and gaseous phases, from which the expression shown in Table 3 is derived for temperatures between the triple point  t = 216.59K and  = 298.15K, from which  H ( t )/MPa 1/2 = 19.10 and  H (298.15 K)/MPa 1/2 = 6.78 result, a wide span of values.Politzer et al. [49] predicted from ab initio computations for CO 2 the heats of formation at 298.15 K as Δ f /kcal mol −1 = −92.3for the gas and −96.6 for the liquid, yielding Δ V /J mol −1 = 17991 for the difference, that is, for vaporization of the liquid.With the density at  t = 1.17846 g cm −3 this yields  H ( t )/MPa 1/2 = 20.82.Prausnitz and Shair [27] quote Hansen [2] and report  d = 15.7 MPa 1/2 at 298 K and 1 atm for the dispersion partial solubility parameter, but the total, Hildebrand solubility parameter included a contribution from the polar interactions and hydrogen bonding of this gas molecules, adding up to  H (298 K) MPa 1/2 = 17.85.This value is incompatible with that resulting from the Span and Wagner data.It appears that the compilation of Span and Wagner [48] results in the most reliable values of  H () and that  H ( t )/MPa 1/2 = 19.10 may be selected here.
2.1.14.Phosgene.The normal boiling point of COCl 2 was established as 280.66K by Giauque and Jones [50] and was listed in the Handbook [7] as 8 ∘ C, that is, 281.2 K, and the most recently reported vapor pressure data of Huang et al. [51] lead to  b /K = 282.95at which the pressure equals 0.101325 MPa (i.e., 1 atm).The molar enthalpy of vaporization at the boiling point was reported as The more recent value [51] is larger, 25565 J mol −1 , derived from the vapor pressure curve.The density of liquid phosgene was reported by Davies [52] as /g cm 3 = 1.42014 − 0.0023120(/ ∘ C) − 0.000002872(/ ∘ C) 2 , that is, ( b )/g cm 3 = 1.40146 and ( b )/cm 3 mol −1 = 70.59.A slightly smaller value, 70.13 cm 3 mol −1 results from the interpolated liquid density data in [51].The solubility parameter resulting from the more recent Δ V  is  H ( b ) MPa 1/2 = 18.13 and the temperature dependence is shown in Table 3.

Nitrous Oxide. Yosim and Owens
2.1.17.Nitrogen Monoxide.Monomeric nitrogen oxide, NO, has received very little attention in the literature regarding its molar enthalpy of vaporization.A very early "calculated" value of 3412 cal mol −1 due to Bingham [57], that is, 14276 J mol −1 , differs from the value 3293 cal mol −1 , that is, 13778 J mol −1 of Kelley and King [40] quoted by Yosim and Owens [21].From the latter, with the supplied density of 1.269 g cm −3 at the boiling point of 121.4 K, the solubility parameter  H ( b )/MPa 1/2 = 23.24 is derived.There seems to be no more modern value for this quantity in the literature.

Silicon Tetrafluoride.
The liquid range of SiF 4 (also called tetrafluorosilane) is quite narrow and its normal boiling point has been reported differently by various authors: 177.5 ≤  b /K ≤ 187.2 [58], and its triple point,  t /K = 186.35[59]; hence, the lower values appear not to be valid.The higher values, 187 [60] and 187.2 [7], appear to be more nearly correct.The molar enthalpy of vaporization was reported by Lyman and Noda [61] as 15.802 kJ mol −1 (but they report  b = 177.83K, below  t of 186.35 K, but discuss properties of the liquid!).The density of liquid SiF 4 was reported by Pace and Mosser [59] as /g cm −3 = 2.479 − 0.004566 at 186 ≤ /K ≤ 195, extrapolating to 1.624 g cm −3 at  b = 187.2K and a molar volume ( b ) = 64.08 cm 3 mol −1 .The solubility parameter of SiF 4 is therefore  H ( b )/MPa 1/2 = 14.91.

Sulfur Tetrafluoride.
The data needed for obtaining the solubility parameter of SF 4 at its boiling point are all available from Brown and Robinson [68].The boiling point is −40.4 ∘ C, that is,  b = 232.75K, the molar enthalpy of vaporization is 6320 cal mol −1 , that is, 26443 J mol −1 , and the density of the liquid follows /g cm −3 = 2.5471 − 0.00314 (at 170 ≤ /K ≤ 200), assumed to be valid up to  b , yielding ( b )/g cm −3 = 1.8164.Hence,  H ( b )/MPa 1/2 = 20.31.A somewhat larger value of  b = 236 K was reported later by Streng [69] with ( b )/g cm −3 = 1.8061, but with no other latent heat of vaporization.The resulting  H ( b )/MPa 1/2 = 20.22 does not differ much from the value selected here.

Sulfur Hexafluoride.
Since SF 6 sublimes and does not form a liquid on heating the solid; it is difficult to specify a temperature at which the solubility parameter should be obtained.The triple point has been reported as  t = 223.56K by Funke et al. [70], but the molar enthalpy of vaporization and the density have been reported at other temperatures.Linford and Thornhill [24] reported the molar energy of vaporization as 4.08 kcal mol −1 , that is, 17071 J mol −1 , at an unspecified temperature.A so-called "boiling temperature" of 204 K was reported by Gorbachev [71] at which the molar volume of SF 6 was 75.3 cm 3 mol −1 .The value  H (204 K)/MPa 1/2 = 14.29 results from this pair of data.Funke et al. [70] reported vapor pressures and liquid densities over the temperature range 224 to 314 K. From these data the molar enthalpy of vaporization is Δ V  = 17375 J mol −1 and the molar volume is  = 79.16cm 3 mol −1 at 224 K, yielding  H (224 K)/MPa 1/2 = 14.82.However, a considerably larger Δ V  = 5.6 kcal mol −1 was quoted from Lange's Handbook of Chemistry for SF 6 by Anderson et al. [72], that is, 23430 J mol −1 .This value is near the molar enthalpy of sublimation Δ subl  = 23218 J mol −1 at 186 K reported by Ohta et al. [73].However, no density data at this temperature, lower than the triple point, are available.A tentative value, based on the data in [70], is suggested here  H (224 K)/MPa 1/2 = 14.82 as representative.
2.1.22.Silane.The boiling point and molar heat of vaporization of liquid SiH 4 were quoted by Taft and Sisler [78] from secondary sources as 161 K and 2.98 kcal mol −1 , that is, 12470 J mol −1 , and listed in [7] as −111.9∘ C, that is, 161.3 K and 12.1 kJ mol −1 .The molar volume at the boiling point was reported by Zorin et al. [79] from experimental density measurements as ( b ) = 55.04 cm 3 mol −1 and from molecular dynamics simulations of the density reported by Sakiyama et al. [80] interpolated to the boiling point as ( b ) = 57.27cm 3 mol −1 , but the experimental value is preferred.The resulting solubility parameter is  H ( b )/MPa 1/2 = 14.22.

Stannane.
There are only the older data for liquid SnH 4 ; the boiling point and molar heat of vaporization were reported by Paneth et al. [82] as −52 ∘ C and 4.55 kcal mol −1 and were quoted in [78] from secondary sources as 221 K and 4.5 kcal mol −1 , that is, 18800 J mol −1 .The molar volume at the boiling point was reported in [79] from experimental density measurements as ( b ) = 63.18cm 3 mol −1 .Hence  H ( b )/MPa 1/2 = 16.40 results.

2.1.25.
Phosphine.The paper by Durrant et al. [83] reports all the required data for the group V hydrides.For PH 3 the boiling points −87.4,−85, and −86.2 ∘ C were quoted in [83] from previous publications, 187 K is listed in [78], −87.9 ∘ C is reported by Devyatykh et al. [81], and −87.75 ∘ C is listed in [7], that is,  b = 185.40K, which is taken as the valid value.The molar enthalpy of vaporization at the boiling point is reported as Δ V ( b ) = 3.85 kcal mol −1 in [83], that is, 16110 J mol −1 , as 3.79 kcal mol −1 in [55], that is, 15860 J mol −1 , as 3.949 kcal mol −1 in [81], that is, 16520 J mol −1 .However, considerably lower values were reported more recently: 14600 J mol −1 in [7] and 13440 J mol −1 in [84] as the measured value.(Note that Ludwig [84] reports for H 2 S an experimental Δ V  value in accord with other reports, so that it is unclear why for PH 3 such a low value is reported.)The mean of the earlier reported values, namely, Δ V ( b )/J mol −1 = 16160, is taken as valid.The density of PH 3 at the boiling point is interpolated in the data of [83] as ( b ) = 0.7653 g cm −3  yielding ( b ) = 44.43cm 3 mol −1 .A somewhat larger value, ( b ) = 45.72 cm 3 mol −1 was reported in [79].The solubility parameters  H ( b )/MPa 1/2 = 18.13 and 17.88 result from these two molar volume values, and the mean, 18.00, is selected here.
2.1.28.Hydrogen Sulfide.The molar enthalpy of vaporization of H 2 S was reported by Cubitt et al. [86] from experimental data as Δ V  = 18701 J mol −1 and the molar volume as V = 35.83cm 3 mol −1 (interpolated) at the boiling point  b = 212.85K.The value  H ( b )/MPa 1/2 = 21.74 results from these values.The temperature dependence of  H is shown in Table 3.A less precise value of Δ V  = 18.36 kJ mol −1 and a density of  = 934 kg m −3 were reported as experimental values at 220.2 K from an undisclosed source by Kristóf and Liszi [87].The value  H (220.2 K)/MPa 1/2 = 21.28 is derived from these data.Δ V  = 18.67 kJ mol −1 at the boiling point was reported by Ludwig [84] as the experimental value.A value Δ V  = 4.46 kcal mol −1 , that is, 18661 J mol −1 at the boiling point, was reported by Riahi and Rowley [88] as well as by Orabi and Lamoureux [89], attributed to Clarke and Glew [90], and the density 949 kg m −3 and a density of 940 kg m −3 result from the data of [79].These values yield  H ( b )/MPa 1/2 = 21.69.Sistla et al. [36] quote Hansen [2] and report  d = 17.0 MPa 1/2 at 298 K and 1 atm for the dispersion partial solubility parameter, but the total, Hildebrand solubility parameter included a contribution from the polar interactions of these gas molecules, adding up to  H (298 K)/MPa 1/2 = 20.71.The average of the values resulting from [86,89],  H ( b )/MPa 1/2 = 20.72,nearly coincides with the latter value (for 298 K).

Methane. Yosim and Owens
2.1.32.Fluoromethane.Oi et al. [95] provided the coefficients of the vapor pressure expression log(/torr) =  − /( + / ∘ C) for CH 3 F, from which Δ V ( b ) = 15764 J mol −1 is derived.Fonseca and Lobo [96] provided the molar volume of CH 3 F at 161.39 K and at 195.48        2.1.38.Formaldehyde.The boiling point of liquid HCHO was reported as −21.5 ∘ C by Mali and Ghosh [104], that is, 252 K.The density at −20 ∘ C of 0.815 g cm −3 is available in [7].The latent heat of evaporation was reported as 5600 cal mol −1 in [104].The resulting solubility parameter is  H ( b )/MPa 1/2 = 24.06.These are the only data found for this gaseous substance in the neat liquid form; hence the value of  H must be considered as tentative.
As the temperature is increased, the molar enthalpy of vaporization Δ V () diminishes towards its disappearance at the critical point.Over a temperature range near the normal boiling point  b the function Δ V () is linear with the temperature.Also, as the temperature is increased, the density () diminishes and the molar volume () increases, both linearly over a temperature range near the normal boiling point  b .Therefore, the solubility parameter  H () = [(Δ V () − )/()] 0.5 necessarily diminishes as the temperature is increased.For several of the gaseous solutes for which there are data over a sufficient temperature range (excluding the noble gases) the decrease in  H () is linear with  with a slope of −0.06 ± 0.02 K −1 as is seen in Table 3.This slope may be used for the approximate estimation from the  H ( b ) values in Tables 1 and 2 of the applicable solubility parameter of the solute gases at the temperatures at which their solubility is needed.

Trends in the Solubility Parameters.
The following trends may be seen in the data of Tables 1 and 2, remembering that the normal boiling points may be considered as "corresponding temperatures" for the comparison of thermophysical data. H ( b ) of the noble gases and of the hydrides of group IV and V elements increase with increasing molar masses of the gases.The opposite appears to be the case for homologous organic compounds.Polarity adds to the value arising from dispersion forces only, as, among others, Sistla et al. [36] pointed out.  4 for 298 K.
Lawson [62] reported values of  H (298 K)/(cal cm −3 ) 1/2 for eight gases, obtained indirectly from their solubilities and are shown in Table 4. LaPack et al. [28] quoted previously reported values, as shown in Table 4. Sistla et al. [36] quoted the partial solubility parameters given by Hansen [2] for 298 K and the total (Hildebrand) solubility parameters shown in Table 4.
It should be remembered that at ambient conditions that pertain to Table 4 the solutes are gases.If the critical temperature is  c > 298 K they are liquid only under considerable pressure.Still, it has been tempting to take (1) to be valid at ambient conditions for these gaseous solutes, so that solubility parameters might be evaluated from the solubility data.In some cases the authors find lower solubility parameters of the solutes than from the relevant thermodynamic data at the boiling points of the liquefied gaseous solutes, for example, by Clever et al. [20] for noble gases and by Prausnitz and Shair [27] for these and other gases.In another case, in acetylene according to Vitovec and Fried [65], the nonideality of the gas had to be taken into account to obtain agreement between the solubility and thermodynamic values.Linford and Thornhill [24] related the solubilities of a variety of solvents in many solvents to the cohesive energy of the solute gases but did not use the solubility parameters.Lawson [62] used the solubility parameters of solute gases listed in Table 4 to calculate their solubilities in hydrocarbons and perfluorohydrocarbons.Lewis et al. [31] fitted the solubility of radon in selected perfluorocarbon solvents at 278 to 313 K by assigning it the value 8.42 cal 1/2 cm −3/2 (17.22 MPa 1/2 ).
Vetere [63] used solubility data of ten gases, H 2 , O 2 , N 2 , CH 4 , C 2 H 4 , C 2 H 6 , C 3 H 8 , CO, CO 2 , and H 2 S, in a variety of polar and nonpolar solvents and the NRTL (nonrandom twoliquid) model to obtain the (absolute) values of  HS −  HG .From these, with known values of the solvent  HS values, those for the solute gases could be estimated.The presented  HS −  HG data pertained to a variety of temperatures for each solute gas, and it is difficult to obtain values for a definite temperature for all the solvents employed for a given gas.The mean values pertaining to 303 ± 5 K are listed in Table 4. Shamsipur et al. [139] dealt with the solubilities of gases in various solvents and reported " H " values for the alkanes C  H 2+2 (1 ≤  ≤ 8).When these are related to their known Hildebrand solubility parameters as solvents, the relationship  H /MPa 1/2 = 7.65" H " 0.2 results.When this relationship is applied to " H " = 0.1402 for Ne this yields  H = 10.8MPa 1/2 .Note that for He the resulting value is too large, 10.6 MPa 1/2 , so the approximate agreement for Ne should not be taken as valid.
As is seen in Table 4, the agreement between the entries for a given gas by diverse authors at a given temperature near ambient is rather poor.This arises from the means used by the authors to calculate the values from solubilities, via (1) or equivalent expressions or based on other premises.
On the other hand, the miscibility of the liquefied gases among themselves should be directly related to their solubility parameters according to (1).Some data on the miscibility of gases were presented by Streng [69].

Correlations.
The cohesive energies of permanent gases at their boiling points should be related to the attractive interactions of the particles.These, in turn, are related to the depths, , of the potential wells arising from the energetics of the collisions of the particles in the gas phase.A common measure of the energetics is the 12-6 Lennard-Jones relationship: where  is the distance apart of the two colliding particles,  is the distance of their centers at contact, and , reported in units of the Boltzmann constant in Kelvins, that is, (/ B )/K, is the minimum of the interaction potential energy .Indeed, the cohesive energy densities, [ H ( b )] 2 , are linearly related to the (/ B ) values of the gases for which values were found, see Figure 1.It should be noted that the (/ B ) reported by various authors, like De Ligny and Van der Veen [14], Teplyakov and Meares [13], Leites [12], and Churakov and Gottschalk [15], with a correlation coefficient 0.9194 is found.Another conceivable correlation of the solubility parameters of the liquefied gases would be with their surface tensions, .Data for the latter quantities are not plentiful but were found for a representative group of the gases treated here.Indeed, for the 17 liquefied gases for which surface tension data were found [16][17][18][19]140] there is a linear relationship between the surface tension and the solubility parameter at the boiling point as follows: with a correlation coefficient of 0.9797; see Figure 2. The value [18] for dimethyl ether is an outlier.
Koenhen and Smolders [141] reported the relationship between the dispersion solubility parameter and the index of Figure 2: The surface tension of liquefied gases at their boiling points, /mN m −2 , plotted against their solubility parameters,  H / MPa 1/2 .The symbols are for the surface tension from [16,17] e, from [18] , and [19] , and for the outlier (CH 3 ) 2 O,  [18].refraction,  D , for many substances that are liquid at ambient temperatures, but not for those that are gases.The expression  H / (cal cm −3 ) 1/2 = 9.55 D − 5.55 at an unspecified temperature (presumably 298 K) was found and may be applicable also for gaseous solutes.

Conclusions
The solubility parameters,  H ( b ), of nonreactive permanent gases at their boiling points  b (<290 K) including most inorganic gases (excluding reactive ones such as halogens and hydrogen halides) and organic ones up to butane are presented.They have been calculated from individually discussed values of their molar enthalpies of vaporization and densities obtained from the literature.Where available, the coefficients of the temperature dependence expression  H () are also tabulated.The  H ( b ) values of representative inorganic gases increase with their molar masses but those of organic solutes (hydrocarbon) tend to diminish with increasing molar masses.The  H values generally diminish with increasing temperatures.Values of the solubility parameters reported in the literature that were derived from the solubilities of the gases in various solvents are inconsistent among various authors.The  H ( b ) values correlate linearly with the attractive interaction energies of binary collisions of the gas molecules, the depths of the potential wells / B and with the surface tensions, ( b ), of the liquefied gases.

2. 1 .
43. Chloroethane.The boiling point of C 2 H 5 Cl is somewhat below ambient, 12.26 ∘ C = 285.4K, and the coefficients of the Antoine vapor pressure expression [missing the minus sign between  and /( + ) for log ] were reported by Meyer et al.

Table 2 :
Selected solubility parameters of liquefied organic gases at their boiling points.
[67]r et al. [100]calculated the contribution of the dispersion, polarity, and orientation to the cohesive energy, the dispersion part being 73 and 80% of the total for CH 3 Cl and C 2 H 5 Cl, respectively, but did not obtain the solubility parameters.3.2.Solubility Parameters Derived from Solubilities.In view of the concern with the solubility of gases in a variety of solvents, many authors have presented values of the solubility parameters of gases.Clever et al.[20]reported values of  H ( b )/(cal cm −3 ) 1/2 of the noble gases helium to xenon to one decimal digit that correspond well to the selected values in Table1.These values, however, are larger (except for helium) than those derived from the relative solubilities in cyclohexane and perfluorocyclohexane. Vitovec and Fried[65]derived a value for  H (298 K)/(cal cm −3 ) 1/2 = 6.75 for acetylene, that is, as expected, smaller than the value at the triple point, 191.5 K, but agrees with the mean value derived from the solubility in benzene, toluene, and p-xylene, 6.86 (cal cm −3 ) 1/2 .Prausnitz and Shair[27]reported values of  H /(cal cm −3 ) 1/2 for Ar, Kr, Rn, N 2 , O 2 , CO, CO 2 , CH 4 , C 2 H 4 , and C 2 H 6 , suggested to be valid over a range of temperatures much larger than the boiling points.As expected, these values are smaller than  H ( b ).Similarly, Blanks and Prausnitz[64]reported values of  H (298 K)/(cal cm −3 ) 1/2 from undisclosed sources for CH 4 , C 2 H 4 , C 2 H 6 , C 3 H 6 , C 3 H 9 , and C 4 H 10 , shown in Table4.Bradford and Thodos[66]provided the parameters for equation(5)for CH 4 , C 2 H 6 , C 3 H 8 , and C 4 H 10 , from which solubility parameters at any temperature may be evaluated.The values at 298 K are shown in Table4, except for methane, for which  c < 298 K. Gilmour et al.[98]reported  H ( b )/(cal cm −3 ) 1/2 values for CF 4 , C 2 F 6 , CH 4 , C 2 H 6 , C 3 H 8 , and C 4 H 10 that agree well with the values in Table 2. Helpenstill and van Winkle[67]reported the dispersion and polarity partial solubility parameters of hydrocarbons, which in the cases of C 3 H 8 , and C 4 H 10 are only the dispersion ones, equaling  H /(cal cm −3 ) 1/2 and shown in Table

Table 4 :
Literature values of solubility parameters of gases near ambient temperatures.