Solubility Parameters of Permanent Gases

Marcus, Yizhak

doi:https://doi.org/10.1155/2016/4701919

Journal of Chemistry

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Review Article | Open Access

Volume 2016 | Article ID 4701919 | https://doi.org/10.1155/2016/4701919

Solubility Parameters of Permanent Gases

Yizhak Marcus¹

Academic Editor: Tomokazu Yoshimura

Received14 Aug 2016

Accepted09 Oct 2016

Published08 Dec 2016

Abstract

The solubility parameters, , of nonreactive permanent gases at their boiling points (<290 K) 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 are also tabulated. The trends noted in the 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 values are shown to correlate linearly with the depths of the potential wells (attractive interaction energies, ) for binary collisions of the gaseous molecules and with the surface tensions, , of the liquefied gases.

1. 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 F₂, Cl₂, the hydrogen halides, NO₂, 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, , 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). are also considered to be “corresponding states” as is indicated by the Trouton constant (the molar entropy of vaporization at ) being the same, , 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 of the solute gas (subscript ) in the liquid solvent (subscript ) is as follows:where is the molar volume and the two ’s are the total (Hildebrand) solubility parameters. The ideal solubility at the temperature , , is given by where is the molar enthalpy of vaporization of the liquefied solute gas at its normal boiling point . 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, , 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, , which is related to the mole fraction solubility in the solvent, , as follows:where 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 is a reference value from which the temperature dependence of 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.

1.2. Hildebrand Solubility Parameters

The values of the total (Hildebrand) solubility parameter of the gases dealt with here, , are obtained as the square roots of the cohesive energy densities, . 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 , that is, at 101.325 kPa, as follows:

2. 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 are the normal boiling points of the liquefied gases, , their molar enthalpies of vaporization , and their molar volumes 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 : /cm³ 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 [8–11].

Following are details of the data used and the results of the application of (2), yielding /MPa^1/2 values.

2.1. 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^1/2cm^−3/2 (i.e., 1.02 MPa^1/2). However the text above the table states that 0.6 cal^1/2cm^−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 = 4.22 K and = 0.1250 g cm⁻³. They also presented four reports for at 4.207 K that average at J mol⁻¹, from which the solubility parameter = MPa^1/2 is derived and represents the selected value.

2.1.2. Neon

The value tabulated by Clever et al. [20], obtained as described for He, is 4.9 cal^1/2 cm^−3/2 (i.e., 10.02 MPa^1/2). The value = 9.49 MPa^1/2 is derived from the [22] data reported by Yosim and Owens [21]. Linford and Thornhill [24] reported the energy of vaporization as (presumably ) = 0.37 kcal mol⁻¹ and with the density from Gladun [25], 0.06093 mol cm⁻³, the value = 8.98 MPa^1/2 is derived. Leonhard and Deiters [26] reported the densities and the molar enthalpy of the gas and liquid at 5 K intervals between 25 and 40 K. The difference in the latter yields values, so the expression shown in Table 3 results, from which follows the value = 10.01 MPa^1/2. The value = 10.01 MPa^1/2 from [26], agreeing with that of [20], is adopted as the selected value for Ne.

2.1.3. Argon

The value tabulated by Clever et al. [20], obtained as described for He, is 7.0 cal^1/2 cm^−3/2 (i.e., 14.32 MPa^1/2). The value = 14.19 MPa^1/2 is derived from the data of [22] reported by Yosim and Owens [21]. Much lower values were reported by Prausnitz and Shair [27] at an unspecified temperature, 5.33 (cal/cm³)^1/2 (i.e., 10.90 MPa^1/2), that was quoted by LaPack et al. [28]. Chen et al. [29] presented the molar volumes and the molar enthalpies of vaporization or Ar at 17 temperatures between the triple and boiling points, from which the expression for the solubility parameter shown in Table 3 results and = 14.07 MPa^1/2. Linford and Thornhill [24] reported the energy of vaporization as = 1.385 kcal mol⁻¹ and with the molar volume from Terry et al. [30], = 28.713 cm³ mol⁻¹, the value = 14.21 MPa^1/2 is derived. The average of the four agreeing values, MPa^1/2, is adopted as the representative value for .

2.1.4. Krypton

The value tabulated by Clever et al. [20], obtained as described for He, is 7.5 cal^1/2 cm^−3/2 (i.e., 15.34 MPa^1/2). The value = 15.21 MPa^1/2 is derived from the data of [22] reported by Yosim and Owens [21]. Much lower values were reported by Prausnitz and Shair [27] at an unspecified temperature, 6.4 (cal/cm³)^1/2 (i.e., 13.09 MPa^1/2). Chen et al. [29] presented the molar volumes and the molar enthalpies of vaporization of Kr at 19 temperatures between the triple and boiling points, from which the expression for the solubility parameter shown in Table 3 results and = 15.18 MPa^1/2. Linford and Thornhill [24] reported the energy of vaporization as = 2.00 kcal mol⁻¹ and with the molar volume from Terry et al. [30], = 34.731 cm³ mol⁻¹, the value = 14.57 MPa^1/2 is derived. The average of the three agreeing values, MPa^1/2, is adopted as the representative value for .

2.1.5. Xenon

The 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 = 16.19 MPa^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 = 15.79 MPa^1/2. Linford and Thornhill [24] reported the energy of vaporization as = 2.69 kcal mol⁻¹ and with the molar volume from Terry et al. [30], = 44.68 cm³ mol⁻¹ (interpolated), the value = 14.87 MPa^1/2 is derived. The average of the three largest values, MPa^1/2, is adopted as the representative value for .

2.1.6. Radon

Prausnitz and Shair [27] reported a low value (compared with the other noble gases) at an unspecified temperature, 6.83 (cal/cm³)^1/2 (i.e., 13.97 MPa^1/2). A value better compatible with the other noble gases was reported by Lewis et al. [31], cal^1/2cm^−3/2 (i.e., MPa^1/2) at an unspecified temperature, derived from the solubility of Rn in fluorocarbon solvents. The molar enthalpy of vaporization = 16.36 kJ mol⁻¹ and the liquid density ρ = 4329 kg m⁻³ reported recently by Mick et al. [32], at the boiling point of ²²²Rn, 210.5 K, were obtained from Monte Carlo simulations, leading to = 16.88 MPa^1/2. Mick et al. quoted experimental values obtained more than 100 years ago for the enthalpy of vaporization, /kJ mol⁻¹ = 16.59 and 16.78, but not highly accurate liquid densities. With the density from the simulation, these two enthalpy values yield /kJ mol⁻¹ = 17.01 and 17.12 MPa^1/2. The average of the four agreeing values, , is selected here as representative.

2.1.7. Hydrogen

Yosim and Owens [21] quoted data from Stull and Sinke [33] leading to = 5.08 MPa^1/2. Linford and Thornhill [24] reported the energy of vaporization as = 0.175 kcal mol⁻¹ and with the molar volume from Van Itterbeek et al. [34] interpolated to , = 28.375 cm³mol⁻¹, the value = 5.08 MPa^1/2 is derived. The reference data by Leachman et al. [35] showed liquid density and gas and liquid molar enthalpy values at temperatures between 14 and 21 K that yield the expression shown in Table 3 and = 5.08 MPa^1/2. Sistla et al. [36] quote Hansen [2] and report = 5.1 MPa^1/2 at 298 K and 1 atm for the dispersion partial solubility parameter. The well agreeing value from three authors, = 5.08 MPa^1/2, is the selected value.

2.1.8. Nitrogen

Gjaldbaek and Hildebrand [37] assigned to nitrogen the value = 5.3 cal^1/2cm^−3/2 (10.84 MPa^1/2) in order to fit its solubility in several solvents at 298 K. Yosim and Owens [21] quoted data from Rossini et al. [9] leading to = 11.96 MPa^1/2. Linford and Thornhill [24] reported the energy of vaporization as = 1.18 kcal mol⁻¹ and with the molar volume from Terry et al. [30] 34.91 cm³mol⁻¹ the value = 11.89 MPa^1/2 is derived. Jordan et al. [38] reported the molar enthalpy of vaporization from the Handbook [7], 5569 J mol⁻¹, and the density ρ = 0.8801 g cm⁻³ at = 77.35 K, yielding = 11.92. The experimental latent heat of vaporization (at an unspecified temperature, presumably ) of 201.2 J g⁻¹ yields with ρ = 0.8801 g cm⁻³ the value = 12.02. Sistla et al. [36] quote Hansen [2] and report = 11.9 MPa^1/2 at 298 K and 1 atm for the dispersion partial solubility parameter. The mean value from the five mutually agreeing reports, = 11.95, is selected here.

2.1.9. Oxygen

Suyama and Oishi [39] quoted earlier-published molar enthalpies of vaporization at the boiling point that agree with their own value, 6822.7 J mol⁻¹. This value is somewhat larger than that used by Yosim and Owens [21] from Kelley and King [40], 6812 J mol⁻¹. These two values with the molar volume interpolated in Terry et al. [30] data, 28.135 cm³mol⁻¹, yield the solubility parameters MPa^1/2 = 14.69 and 14.68, respectively. A much lower value, at an unspecified temperature, was reported by Prausnitz and Shair [27], = 4.0 (cal/cc)^1/2, 8.18 MPa^1/2, quoted by LaPack et al. [28]. A value was also derived from the molar energy of vaporization at the boiling point reported by Linford and Thornhill [24], 1.45 kcal mol⁻¹, yielding MPa^1/2 = 14.69. Molecular dynamics simulations by Zasetsky and Svishchev [41] yielded /J mol⁻¹ = 6934, 6232, and 5083 at /K = 84, 100, and 120, respectively. These yield with the density data the following solubility parameter values: MPa^1/2 = 15.11, 13.56, and 11.13 at these three temperatures, interpolating to MPa^1/2 = 14.55 and yielding the data shown in Table 3. Sistla et al. [36] quote Hansen [2] and report = 11.9 MPa^1/2 at 298 K and 1 atm for the dispersion partial solubility parameter. From the four agreeing values at the boiling point, the average MPa^1/2 = is taken as selected.

2.1.10. Boron Trifluoride

No data regarding the molar enthalpy of vaporization of liquid BF₃ were found, except for the entry in the Handbook [7] that was not traced to a definite reference, of /J mol⁻¹ = 19330. The boiling point was given there as −101°C, that is, 172.2 K. The density of liquid BF₃ was obtained from Fischer and Weidemann [42] as ρ(/°C)/g cm⁻³ = ], that is, 1.5757 g cm⁻³ at . These data yield MPa^1/2 = 20.39, but there is no corroboration of this value from any other source.

2.1.11. Boron Trichloride

The vapor pressure of liquefied BCl₃ was reported by Fetisov et al. [43] as , from which by the Clausius-Clapeyron expression J mol⁻¹, at = 12.65°C [7] = 285.8 K. ( = 12.1°C was given in [43] and = 23.77 kJ mol⁻¹ was given in [7]). The density of liquefied BCl₃ was reported by Ward [44] from −44 to +5°C, being linear with the temperature and a brief extrapolation to = 12.65°C yields ρ(/°C)/g cm⁻³ = 1.3472 (extrapolation to 11.0°C yields ρ/g cm⁻³ = 1.3493, in agreement with the value reported by Briscoe et al. [45]). These data yield MPa^1/2 = 16.07.

2.1.12. Carbon Monoxide

Prausnitz and Shair [27] reported = 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 data of Kelley and King [40], from which the value 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 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 , = 35.53 cm³mol⁻¹ and the value 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 cm³ mol⁻¹, from which 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 = 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 (298 K) MPa^1/2 = 12.50. The average of the four agreeing values, MPa^1/2 = 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 = 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 = 216.59 K and = 298.15 K, from which /MPa^1/2 = 19.10 and (298.15 K)/MPa^1/2 = 6.78 result, a wide span of values. Politzer et al. [49] predicted from ab initio computations for CO₂ the heats of formation at 298.15 K as /kcal mol⁻¹ = −92.3 for the gas and −96.6 for the liquid, yielding /J mol⁻¹ = 17991 for the difference, that is, for vaporization of the liquid. With the density at = 1.17846 g cm⁻³ this yields /MPa^1/2 = 20.82. Prausnitz and Shair [27] quote Hansen [2] and report = 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 (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 and that /MPa^1/2 = 19.10 may be selected here.

2.1.14. Phosgene

The normal boiling point of COCl₂ was established as 280.66 K 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 /K = 282.95 at which the pressure equals 0.101325 MPa (i.e., 1 atm). The molar enthalpy of vaporization at the boiling point was reported as /cal mol⁻¹ = , that is, 24401 J mol⁻¹ [50]. 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 ρ/g cm³ = 1.42014 − 0.0023120(/°C) − 0.000002872(/°C)², that is, /g cm³ = 1.40146 and /cm³ mol⁻¹ = 70.59. A slightly smaller value, 70.13 cm³ mol⁻¹ results from the interpolated liquid density data in [51]. The solubility parameter resulting from the more recent is MPa^1/2 = 18.13 and the temperature dependence is shown in Table 3.

2.1.15. Nitrogen Trifluoride

There are conflicting reports regarding the boiling point of liquid NF₃: the older value is −119°C by Ruff et al. [53] and a more recent one is 144.2 K by Sladkov and Novikova [54], confirmed as −128.75°C [7], that is, = 144.40 K, that is taken to be the valid one. Also, the reported values differ: 2400 cal mol⁻¹, that is, 10042 J mol⁻¹ [53] and 11600 J mol⁻¹ [54] or 11560 J mol⁻¹ [7], and again the latter value is used. The molar volume at the boiling point is listed as = 46.1 cm³ mol⁻¹ [54], so that /MPa^1/2 = 15.0.

2.1.16. Nitrous Oxide

Yosim and Owens [21] used the data of Kelley and King [40] for N₂O, from which the value MPa^1/2 = 20.41 is derived. Atake and Chihara [55] reported /J mol⁻¹ = 16544 and with the density data of Leadbetter et al. [56] yielding = 35.64 cm³ mol⁻¹ this produced /MPa^1/2 = 20.52. Sistla et al. [36] quote Hansen [2] and report = 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 (298 K) MPa^1/2 = 20.81. The average of these agreeing values, , is selected here.

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 /MPa^1/2 = 23.24 is derived. There seems to be no more modern value for this quantity in the literature.

2.1.18. Silicon Tetrafluoride

The liquid range of SiF₄ (also called tetrafluorosilane) is quite narrow and its normal boiling point has been reported differently by various authors: 177.5 ≤ /K ≤ 187.2 [58], and its triple point, /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 = 177.83 K, below of 186.35 K, but discuss properties of the liquid!). The density of liquid SiF₄ was reported by Pace and Mosser [59] as ρ/g cm⁻³ = 2.479 − 0.004566 at 186 ≤ /K ≤ 195, extrapolating to 1.624 g cm⁻³ at = 187.2 K and a molar volume = 64.08 cm³ mol⁻¹. The solubility parameter of SiF₄ is therefore /MPa^1/2 = 14.91.

2.1.19. Sulfur Tetrafluoride

The data needed for obtaining the solubility parameter of SF₄ at its boiling point are all available from Brown and Robinson [68]. The boiling point is −40.4°C, that is, = 232.75 K, the molar enthalpy of vaporization is 6320 cal mol⁻¹, that is, 26443 J mol⁻¹, and the density of the liquid follows ρ/g cm⁻³ = 2.5471 − 0.00314 (at ), assumed to be valid up to , yielding ρ()/g cm⁻³ = 1.8164. Hence, /MPa^1/2 = 20.31. A somewhat larger value of = 236 K was reported later by Streng [69] with ρ()/g cm⁻³ = 1.8061, but with no other latent heat of vaporization. The resulting /MPa^1/2 = 20.22 does not differ much from the value selected here.

2.1.20. Sulfur Hexafluoride

Since SF₆ 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 = 223.56 K 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 SF₆ was 75.3 cm³ mol⁻¹. The value (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 = 17375 J mol⁻¹ and the molar volume is = 79.16 cm³ mol⁻¹ at 224 K, yielding (224 K)/MPa^1/2 = 14.82. However, a considerably larger = 5.6 kcal mol⁻¹ was quoted from Lange’s Handbook of Chemistry for SF₆ by Anderson et al. [72], that is, 23430 J mol⁻¹. This value is near the molar enthalpy of sublimation 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 (224 K)/MPa^1/2 = 14.82 as representative.

2.1.21. Diborane

The molar enthalpy of vaporization of B₂H₆ at the boiling point = 180.32 K was reported by Clarke et al. [74] as /cal mol⁻¹ = 3412 in the text and as 3422 as the average of four runs in a table, that is, J mol⁻¹. The density was reported by Laubengayer et al. [75] as ρ/g cm⁻³ = 0.3140 − 0.001296(/°C), being accordingly 0.4343 at , yielding a molar volume of 63.71 cm³ mol⁻¹ and a solubility parameter of /MPa^1/2 = 14.17. A subsequent study by Wirth and Palmer [76] reported = 180.63 K and /cal mol⁻¹ = 3413, that is, 14280 J mol⁻¹. The molar volume at the boiling point = 180.66 K was quoted by Jhon et al. [77] from the Landoldt-Börnstein compilation as 63.36 cm³ mol⁻¹. This pair of values yields /MPa^1/2 = 14.20. The average between the two values, 14.185, is selected here.

2.1.22. Silane

The boiling point and molar heat of vaporization of liquid SiH₄ 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 = 55.04 cm³ mol⁻¹ and from molecular dynamics simulations of the density reported by Sakiyama et al. [80] interpolated to the boiling point as = 57.27 cm³ mol⁻¹, but the experimental value is preferred. The resulting solubility parameter is /MPa^1/2 = 14.22.

2.1.23. Germane

The boiling point and molar heat of vaporization of liquid GeH₄ were quoted in [78] from secondary sources as 184 K and 3.65 kcal mol⁻¹, that is, 15270 J mol⁻¹, reported by Devyatykh et al. [81] as −88.51°C and 3608 cal mol⁻¹, that is, 15096 J mol⁻¹, and listed in [7] as −88.1°C, that is, 185.05 K and 14.06 kJ mol⁻¹. The molar volume at the boiling point was reported in [79] from experimental density measurements as = 55.91 cm³ mol⁻¹. Hence /MPa^1/2 = 14.97 results from the more recent data.

2.1.24. Stannane

There are only the older data for liquid SnH₄; 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 = 63.18 cm³ mol⁻¹. Hence /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 PH₃ 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, = 185.40 K, which is taken as the valid value. The molar enthalpy of vaporization at the boiling point is reported as = 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 H₂S an experimental value in accord with other reports, so that it is unclear why for PH₃ such a low value is reported.) The mean of the earlier reported values, namely, /J mol⁻¹ = 16160, is taken as valid. The density of PH₃ at the boiling point is interpolated in the data of [83] as ρ() = 0.7653 g cm⁻³ yielding = 44.43 cm³ mol⁻¹. A somewhat larger value, = 45.72 cm³ mol⁻¹ was reported in [79]. The solubility parameters /MPa^1/2 = 18.13 and 17.88 result from these two molar volume values, and the mean, 18.00, is selected here.

2.1.26. Arsine

Durrant et al. [83] report the boiling point of liquid AsH₃ as 214.5 K in agreement with some earlier data but somewhat lower than a much older value, 218.2, quoted also in [78] and larger than the value 211.1 K (from −62.1°C) reported in [81]. Sherman and Giauque [85] report = 210.68 K, listed as −62.5°C in [7], that is, 210.65 K, and a mean = 3988 cal mol⁻¹, that is, 16686 J mol⁻¹. The molar enthalpy of vaporization at the boiling point is reported as = 4.34 kcal mol⁻¹ in [83], that is, 18160 J mol⁻¹, as 4.27 kcal mol⁻¹ in [78], that is, 17870 J mol⁻¹, as 4.100 kcal mol⁻¹ in [81], that is, 17150 J mol⁻¹. Again, a lower value, 16690 J mol⁻¹, is listed in [7], but the average of the former three values, 17730 J mol⁻¹, is taken here as valid. The density of AsH₃ at the boiling point is interpolated in the data of [83] as ρ() = 1.6320 g cm⁻³ yielding = 47.76 cm³ mol⁻¹. A very similar value, 47.82 cm³ mol⁻¹, was reported in [79]. The resulting solubility parameter is /MPa^1/2 = 18.27.

2.1.27. Stibine

Durrant et al. [83] report the boiling point of liquid SbH₃ as −17.0°C, that is, 256.2 K, in agreement with 256 K in [78]. The molar enthalpy of vaporization at the boiling point is reported as = 5.067 kcal mol⁻¹ in [83], that is, 21200 J mol⁻¹, and as 4.9 to 5.0 kcal mol⁻¹ in [78], that is, 20700 J mol⁻¹, and is listed as 21300 J mol⁻¹ in [7]; the latter is taken as valid. The density of AsH₃ at the boiling point is interpolated in the data of [83] as ρ() = 2.2039 g cm⁻³ yielding = 56.62 cm³ mol⁻¹. A larger value, 57.83 cm³ mol⁻¹, was reported in [79]. The resulting solubility parameters are /MPa^1/2 = 18.40 and 18.20, their mean, 18.30, being selected here.

2.1.28. Hydrogen Sulfide

The molar enthalpy of vaporization of H₂S was reported by Cubitt et al. [86] from experimental data as = 18701 J mol⁻¹ and the molar volume as V = 35.83 cm³mol⁻¹ (interpolated) at the boiling point = 212.85 K. The value /MPa^1/2 = 21.74 results from these values. The temperature dependence of is shown in Table 3. A less precise value of = 18.36 kJ mol⁻¹ and a density of ρ = 934 kg m⁻³ were reported as experimental values at 220.2 K from an undisclosed source by Kristóf and Liszi [87]. The value (220.2 K)/MPa^1/2 = 21.28 is derived from these data. = 18.67 kJ mol⁻¹ at the boiling point was reported by Ludwig [84] as the experimental value. A value = 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 /MPa^1/2 = 21.69. Sistla et al. [36] quote Hansen [2] and report = 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 (298 K)/MPa^1/2 = 20.71. The average of the values resulting from [86, 89], /MPa^1/2 = 20.72, nearly coincides with the latter value (for 298 K).

2.1.29. Hydrogen Selenide

The boiling point of H₂Se was reported as −41.5°C by Robinson and Scott [91], 231 K in [78], taken from secondary sources, and as −41.25°C in [7], that is, 231.90 K. The very early = 4740 cal mol⁻¹ by Forcrand and Fonzes-Diacon [92] at the boiling point −42°C, that is, 19830 J mol⁻¹, is confirmed by the value 19790 J mol⁻¹, derived from the Trouton constant of 20.4 cal K⁻¹ mol⁻¹ reported in [91], leading to 4.78 kcal mol⁻¹ in [78], that is, 20000 J mol⁻¹. The ρ() = 2.004 g cm⁻³ [91] yields = 40.42 cm³ mol⁻¹. The density data of [79] yield the reported = 41.21 cm³ mol⁻¹; hence, the solubility parameter /MPa^1/2 = 20.97 results from the means of the and values.

2.1.30. Hydrogen Telluride

Robinson and Scott [91] reported boiling points of −4 and −5°C, definitely lower than previous reports leading to 272 K in [78] and −2°C in [7]. For the present purpose = 270 K is used. Trouton’s constant 16.7 cal K⁻¹ mol⁻¹ reported in [91] yields = 18870 J mol, much lower than 23430 J mol⁻¹ (from 5.6 kcal mol⁻¹) from [78], but confirmed by 19.2 kJ mol⁻¹ listed in [7]. The mean, 19040 J mol⁻¹, of the better agreeing values is used here. The density at the boiling point is 2.650 g cm⁻³ according to [91], yielding = 48.9 cm³mol⁻¹, much lower than 55.14 cm³ mol⁻¹ resulting from the density data in [79]. The minimal value of /MPa^1/2 from these data is 17.5 and the maximal value is 20.8. The value 18.4 MPa^1/2 from the old data of [91] may represent the true value, but the trend with the molar mass of the gaseous substances points to the maximal value 20.8 MPa^1/2 as possibly better.

2.1.31. Methane

Yosim and Owens [21] used the data of Kelley and King [40], from which the value MPa^1/2 = 13.83 is derived. Prausnitz and Shair [27] reported = 5.68 (cal/cc)^1/2, that is, 11.62 MPa^1/2 (reported as 11.6 in [28]), a low value compared to other reports. Linford and Thornhill [24] reported the energy of vaporization as = 1.73 kcal mol⁻¹ and with the molar volume from Terry et al. [30], = 38.1 cm³mol⁻¹, the value = 12.87 MPa^1/2 is derived. Jorgensen et al. [93] quoted experimental data at the boiling point from compilations: /kcal mol⁻¹ = 1.96 and V/Å³ molecule⁻¹ = 62.8, from which /MPa^1/2 = 13.86 is calculated. Daura et al. [94] quoted experimental data at the boiling point from compilations: /kJ mol⁻¹ = 8.19 and density ρ/kg m⁻³ = 424, from which /MPa^1/2 = 13.87 is calculated. Prausnitz and Shair [27] quote Hansen [2] and report = 14.0 MPa^1/2 at 298 K and 1 atm for the dispersion partial solubility parameter, which for methane is the total solubility parameter. The mean of the agreeing values, /MPa^1/2 = 13.87 is selected here.

2.1.32. Fluoromethane

Oi et al. [95] provided the coefficients of the vapor pressure expression for CH₃F, from which = 15764 J mol⁻¹ is derived. Fonseca and Lobo [96] provided the molar volume of CH₃F at 161.39 K and at 195.48 K, from which () = 38.61 cm³ mol⁻¹ is interpolated. The resulting solubility parameter is /MPa^1/2 = 19.14.

2.1.33. Difluoromethane

Potter et al. [97] provided the needed data for the calculation of the solubility parameter: /bar, /g cm⁻³, and /kJ mol⁻¹, from the former of which = 221.6 K is interpolated for p/bar = 1.01325 (= 1 atm for the normal boiling point). The resulting values ρ()/g cm⁻³ = 1.268 and /kJ mol⁻¹ = 19.97 yield /MPa^1/2 = 21.02 for CH₂F₂. The temperature dependence of is shown in Table 3.

2.1.34. Trifluoromethane

Potter et al. [97] provided the needed data for the calculation of the solubility parameter: /bar, /g cm⁻³, and /kJ mol⁻¹, from the former of which = 191.1 K is interpolated. The resulting values ρ()/g cm⁻³ = 1.467, and /kJ mol⁻¹ = 16.14 yield /MPa^1/2 = 17.46 for CHF₃. The temperature dependence of is shown in Table 3.

2.1.35. Tetrafluoromethane

Gilmour et al. [98] reported the values of = 145.1 K, /kcal mol⁻¹ = 3.01 (= 12.59 kJ mol⁻¹), and /cm³ mol⁻¹ = 54.9, from which = 14.40 MPa^1/2 results. Linford and Thornhill [24] reported the energy of vaporization as = 2.72 kcal mol⁻¹ at = 145.2 K and with the molar volume from Terry et al. [30], = 54.4 cm³ mol⁻¹, the value = 14.46 MPa^1/2 is derived. The values resulting from the Potter et al. [97] data are ρ()/g cm⁻³ = 1.563 and /kJ mol⁻¹ = 11.72, yielding /MPa^1/2 = 14.66. The most recent report is of Monte Carlo computer simulation results by Watkins and Jorgensen [99] that compare well with the experimental values for the enthalpy of vaporization and the density, yielding /MPa^1/2 = 14.48 The mean of the three closely agreeing reported values, 14.43 MPa^1/2, is taken to represent the solubility parameter of CF₄. The temperature dependence of is shown in Table 3.

2.1.36. Chloromethane

Meyer et al. [100] reported the coefficients of the Antoine vapor pressure expression [missing the minus sign between and for ], from which was obtained /kJ mol⁻¹ = 22803 over the range , that is, up to the boiling point of −24.14°C, that is, 249.0 K. Kumagai and Iwasaki [101] reported the specific volumes of CH₃Cl at the saturated vapor pressures at four temperatures above −20°C, extrapolating to 0.988 cm³ g⁻¹ at and a molar volume of 49.40 cm³ mol⁻¹. The value /MPa^1/2 = 20.38 results from these data. Freitas et al. [102] quoted /kJ mol⁻¹ = 21.5 and the density ρ/g cm⁻³ = 0.985 from a secondary source, taking = 239.39 K. The resulting solubility parameter is /MPa^1/2 = 19.47. The mean of the two values, 19.9 MPa^1/2, is taken for the solubility parameter for CH₃Cl.

2.1.37. Bromomethane

The boiling point = 276.70 K of CH₃Br and its molar enthalpy of vaporization at this temperature = 5.76 kcal mol⁻¹ (= 24.10 kJ mol⁻¹) were reported by Kudchadker et al. [103]. The specific volumes at −20, 0, 20, and 40°C and saturation pressures were reported by Kumagai and Iwasaki [101], yielding a linear relationship. From which the density ρ()/g cm⁻³ = 1.7196 and the molar volume /cm³ mol⁻¹ = 55.21 could be derived. The resulting solubility parameter is /MPa^1/2 = 19.87.

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 /MPa^1/2 = 24.06. These are the only data found for this gaseous substance in the neat liquid form; hence the value of must be considered as tentative.

2.1.39. Methylthiol

The molar enthalpy of vaporization of CH₃SH was reported by Russell et al. [105] as 5872 cal mol⁻¹, that is, 24568 J mol⁻¹, at the normal boiling point = 279.12 K. The density was reported by Kaminski et al. [106] presumably at (for which the above-noted reference is appropriate) as 0.888 g cm⁻³. Hence, the solubility parameter is /MPa^1/2 = 20.26.

2.1.40. Acetylene

This substance sublimes and has no definite liquid phase at ambient pressures, hence no boiling point. The triple point was reported as 192.4 K by Tan et al. [107] and the molar volume at 191.9 K was reported as 42.06 cm⁻³ mol⁻¹ from molecular dynamics computation by Klein and McDonald [108]. These authors also deduced the molar enthalpy of vaporization over the temperature range of 191 to 223 K from vapor pressure data of Kordes [109] as 16.6 kJ mol⁻¹, who also reported the density at 191.5 K as 0.613 g cm⁻³, that is, = 42.48 cm³ mol⁻¹. The resulting solubility parameter of HC≡CH is thus = 18.89 MPa^1/2. According to Vitovec and Fried [65], quoting from a secondary source, under pressure (48 atm) at 25°C the enthalpy of vaporization of the saturated acetylene is 3.737 kcal mol⁻¹ and the molar volume is 69.14 cm³ mol⁻¹, yielding (298 K) = 6.75 cal^1/2 cm^−3/2, that is, 13.81 MPa^1/2. The solubility of acetylene in benzene, toluene, and p-xylene at 25°C [65] and application of the regular solution expression yielded the mean value 6.86 cal^1/2 cm^−3/2, that is, 14.03 MPa^1/2, for (HCCH), in fair agreement with their value from the enthalpy of vaporization. Sistla et al. [36] quote from Hansen [2] values for the dispersion, polar, and hydrogen bonding partial solubility parameters of 14.4, 4.2, and 11.9 MPa^1/2, respectively, adding up to the total (298 K, 1 atm) = 19.15 MPa^1/2, an unlikely value in view of the nonexistence of liquid acetylene at 298 K and 1 atm.

2.1.41. Ethylene

Prausnitz and Shair [27] reported = 6.6 (cal/cc)^1/2, that is, 13.5 MPa^1/2, a low value compared to other reports. Michels and Wassenaar [110] reported an expression for the temperature dependence of the vapor pressure, leading to = 14.641 kJ mol⁻¹ (148 ≤ /K ≤ 281). Yosim and Owens [21] used the density and data from a secondary source, from which the value MPa^1/2 = 15.64 is derived. Calado et al. [111] reported liquid molar volumes and enthalpies of vaporization over the temperature range , from which the values at the boiling point of C₂H₄ = 169.5 K of /cm³ mol⁻¹ = 49.48 and /J mol⁻¹ = 13447 are deduced, yielding /MPa^1/2 = 15.60. The temperature dependence of is shown in Table 3. Sistla et al. [36] quote from Hansen [2] values for the dispersion, polar, and hydrogen bonding partial solubility parameters of 15.0, 2.7, and 2.7 MPa^1/2, respectively, adding up to the total (298 K, 1 atm) = 15.48 MPa^1/2. The value from Calado et al. [111] is selected here as valid.

2.1.42. Ethane

Prausnitz and Shair [27] reported = 6.6 (cal/cc)^1/2, that is, 13.5 MPa^1/2, repeated in [28], a low value compared to other reports. Yosim and Owens [21] used the density and data from a secondary source, from which the value MPa^1/2 = 14.56 is derived. Bradford and Thodos [66] reported expressions and parameters from which the solubility parameter was supposed to be calculated, but the resulting value (7.9 MPa^1/2) is too small. Gilmour et al. [98] reported density and data from an undisclosed source, from which the value MPa^1/2 = 15.5 is deduced. Linford and Thornhill [24] reported the energy of vaporization as = 3.15 kcal mol⁻¹ and with the density of ρ() = 0.5481 g cm⁻³ extrapolated from the data of Chui and Canfield [112], the value = 15.50 MPa^1/2 is derived. Jorgensen et al. [93] reported the molecular volume in Å³ molecule⁻¹ of ethane at its boiling point, from which the molar volume 55.1 cm³ mol⁻¹ is obtained, that with the = 3.52 kcal mol⁻¹ that they report yields MPa^1/2 = 15.48. Daura et al. [94] report = 14.70 kJ mol⁻¹ and the density ρ() = 0.546 kg m⁻³, from which MPa^1/2 = 15.48 results. Sistla et al. [36] quote Hansen [2] and report = 15.6 MPa^1/2 at 298 K and 1 atm for the dispersion partial solubility parameter, which for ethane is the total solubility parameter. The value = 15.50 MPa^1/2 is selected here.

2.1.43. Chloroethane

The boiling point of C₂H₅Cl is somewhat below ambient, 12.26°C = 285.4 K, and the coefficients of the Antoine vapor pressure expression [missing the minus sign between and for ] were reported by Meyer et al. [100], from which /kJ mol⁻¹ = 26.615 was obtained over the range . A somewhat smaller /kJ mol⁻¹ = 24.73 was quoted by Smith [113] from a secondary source. The molar volume was estimated by Taft et al. [114] (for an unspecified temperature, presumably 25°C) as = 71.5 cm³mol⁻¹, whereas the Handbook [7] specifies the density as ρ(25°C) = 0.8902 g cm⁻³, from which the molar volume is (25°C) = 69.1 cm³ mol⁻¹. Averaging the and values, the tentative solubility parameter is 18.2 MPa^1/2 near the boiling point.

2.1.44. Hexafluoroethane

Gilmour et al. [98] provided the molar enthalpy of vaporization (from vapor pressure measurements) and the molar volume of C₂F₆ at the boiling point 194.9 K, yielding the value = 13.00 MPa^1/2 and reported /cal^1/2 cm^−3/2 = 6.4, that is, 13.1 MPa^1/2 (with the error of inverting the signs on the units). Subsequently Watkins and Jorgensen [99] quoted literature values of the molar enthalpy of vaporization and the density of C₂F₆ at the boiling point 195.05 K, yielding the value = 12.94 MPa^1/2. Sharafi and Boushehri [115] reported the following values: = 194.95 K, ρ() 1605 kg m⁻³, and K, from which = 13.00 MPa^1/2 is derived. The mean, 12.98 MPa^1/2, is selected here.

2.1.45. Ethylene Oxide

Maass and Boomer [116] measured the vapor pressure and density of c-C₂H₄O over a considerable temperature range and reported the molar enthalpy of vaporization at the boiling point, −10.73°C (283.88 K), as /kcal K⁻¹ mol⁻¹ = 6.00, that is, 25104 J mol⁻¹. At this temperature (interpolated) the density is 0.8823 g cm⁻³ and the molar volume is 49.93 cm³ mol⁻¹. The resulting solubility parameter is = 21.34 MPa^1/2. Giauque and Gordon [117] obtained /kcal mol⁻¹ = 6.101 calorimetrically (6.082 from the vapor pressures), that is, 25527 J mol⁻¹. Olson [118] reported the density at three temperatures: 0, 25, and 50°C, interpolated to ρ() = 0.88266 g cm⁻³ and = 49.91 cm³ mol⁻¹. These two data yield = 21.55 MPa^1/2. Eckl et al. [119] recently reported the density and molar enthalpy of vaporization at 235, 270, 305, and 340 K, from which the interpolated values for = 283.5 K are /kJ mol⁻¹ = 25659 and ρ()/mol L⁻¹ = 20.07, that is, = 49.83 cm³mol⁻¹, resulting in = 21.62 MPa^1/2 and the temperature dependence is shown in Table 3. The mean of the latter two mutually agreeing estimates is selected here, 21.59 MPa^1/2.

2.1.46. Dimethyl Ether

Maass and Boomer [116] measured the vapor pressure and density of (CH₃)₂O over a considerable temperature range and reported the molar enthalpy of vaporization at the boiling point, −24.9°C (248.25 K), as /kcal K⁻¹ mol⁻¹ = 5.31, that is, 22220 J mol⁻¹. At this temperature the (interpolated) density is 0.7345 g cm⁻³ and the molar volume is 62.72 cm³mol⁻¹. The resulting solubility parameter is = 17.93 MPa^1/2. Kennedy et al. [120] measured the vapor pressure and reported the molar enthalpy of vaporization at the boiling point as /cal K⁻¹ mol⁻¹ = 5141.0, that is, 21510 J mol⁻¹. Staveley and Tupman [121] reported the molar entropy of vaporization at the temperature at which the vapor pressure is 760 mmHg, that is, the boiling point, = 248.4 K. /cal K^-1mol⁻¹ = 20.73. Hence, the molar enthalpy of vaporization is /kJ mol⁻¹ = = 21680, near that reported in [120] and quoted by Briggs et al. [122], who reported the boiling point as −24.8°C. The mean of the latter two values and the Maass and Boomer [116] molar volume yield the solubility parameter = 17.65 MPa^1/2, selected here instead of the slightly larger earlier value.

2.1.47. Propene

Powell and Giauque [123] reported vapor pressure data for C₃H₆ from which they derived the molar enthalpy of vaporization 4402 cal mol⁻¹, that is, 18418 J mol⁻¹, and reported the boiling point as 225.35 K. Jorgensen et al. [124] adopted this value for /cal K⁻¹ mol⁻¹ at = 225.5 K. The densities for propene under pressure were reported by Parrish [125] between 5 and 25°C that were extrapolated to 225.5 K as ρ()/g cm⁻³ = 0.60049 yielding = 70.08 cm³ mol⁻¹. The resulting solubility parameter is = 15.36 MPa^1/2.

2.1.48. Cyclopropane

Ruehrwein and Powell [126] measured the vapor pressures of c-C₃H₆ and derived the molar enthalpy of vaporization /cal mol⁻¹ = 4793, that is, 20054 J mol⁻¹, at the boiling point = 240.30 K. Lin et al. [127] reported the molar enthalpy of vaporization at temperatures ≥ 20°C, obtained from the vapor pressures, extrapolating to /cal g⁻¹ = 119.03, that is, 20956 J mol⁻¹. Calado et al. [111] reported a vapor pressure expression from which /kcal mol⁻¹ = 22200 J mol⁻¹ is calculated for 170 ≤ T/K ≤ 225. Helgeson et al. [128] reported /kcal mol⁻¹ = 4.79, that is, 20041 J mol⁻¹. The agreement between these values is only fair, and their mean, 20810 J mol⁻¹, is adopted here. The densities reported by Lin et al. [127] at temperatures ≥ 20° extrapolate to 0.7119 g cm⁻³ at , Helgeson et al. [128] reported 0.705 g cm⁻³ at , and Costa Gomes et al. [129] report data up to 175 K that extrapolate to 689.4 kg m⁻³ at . Again, the mean of these three values is adopted here, 0.7021 g cm⁻³. The resulting solubility parameter is = 17.7 MPa^1/2.

2.1.49. Propane

Linford and Thornhill [24] reported the energy of vaporization as = 4.03 kcal mol⁻¹, that is, 16845 J mol⁻¹, and with the molar volume /Å³ molecule⁻¹ = 126.0, that is, 75.88 cm³mol⁻¹, from Jorgensen et al. [93], the value = 14.90 MPa^1/2 is derived. The latter authors provided /kcal mol⁻¹ = 4.49, that is, 18686 J mol⁻¹ at the boiling point = 231.88 K, so that the same value = 14.90 MPa^1/2 is derived. Bradford and Thodos [66] reported the parameters of the following expression:where = 2.362 (cal/cm³)^1/2 is the solubility parameter at the critical point, , , and is the reduced temperature, the critical temperature being K according to Goodwin [130]. The value = 14.67 MPa^1/2 results. Gilmour et al. [98] reported the values (230 K)/kcal mol⁻¹ = 4.48 and (230 K)/cm³mol⁻¹ = 75.3, from which = 14.94 MPa^1/2 is derived. Helpenstill and van Winkle [67] reported /(cal/cm³)^1/2 = 6.92 at 0°C and 6.54 at 25°C, that is, (273 K)/MPa^1/2 = 14.15 and (298 K)/MPa^1/2 = 13.38, the latter value being near that of LaPack et al. [28] at an unspecified temperature (presumably 25°C) of 13.6 MPa^1/2. Daura et al. [94] reported data obtained from their GROMOSC96 model, /kcal mol⁻¹ = 14.79 and ρ(T) = 493 kg m⁻³ at K, from which (298 K)/MPa^1/2 = 12.30. The value at the boiling point, = 14.90 MPa^1/2, is selected here. Then temperature dependence of is shown in Table 3.

2.1.50. Octafluoropropane

Gilmour et al. [98] reported data for C₃F₈ at several temperatures from 230 to 237 K, from which the values at = 236.5 K are readily derived, = 4.70 kcal mol⁻¹ (= 19.79 kJ mol⁻¹), = 116.8 cm³ mol⁻¹, and /MPa^1/2 = 12.28. The computer simulations of Watkins and Jorgensen [99] agree with experimental values, yielding = 4.73 kcal mol⁻¹ (= 19.66 kJ mol⁻¹), = 117.1 cm³mol⁻¹, and /MPa^1/2 = 12.26. Sharafi and Boushehri [115] reported the following values: = 236.65 K, ρ() 1603 kg m⁻³, and , from which = 12.24 MPa^1/2 is derived. The mean value /MPa^1/2 = 12.26 is selected here. Then temperature dependence of is shown in Table 3.

2.1.51. Ethyl Methyl Ether

The molar enthalpy of vaporization of CH₃OC₂H₅ at its boiling point of 7.35°C ( K) was reported by Ambrose et al. [131] as 25.1 kJ mol⁻¹. A slightly lower value, 5.91 kcal mol⁻¹, that is, 24.73 kJ mol⁻¹, was reported by Maass and Boomer [116]. These authors quoted Aronovich et al. [132] for the density ρ() = 0.7205 g cm⁻³, so that the solubility parameters resulting from the above two values of are /MPa^1/2 = 16.52 and 16.38. The mean, 16.45, is selected here as representative.

2.1.52. 1-Butene

Helpenstill and van Winkle [67] reported /(cal/cm³)^1/2 = 7.24 at 0°C and 6.90 at 25°C and /(cal/cm³)^1/2 = 1.43 at 0°C and 1.32 at 25°C, where pertains to the dispersion aspect and to the polarity aspects ( for the saturated hydrocarbons). The total solubility parameter for 1-C₄H₈ is , that is, 15.10 MPa^1/2 at at 0°C and 14.37 MPa^1/2 at 25°C. Jorgensen et al. [93] reported (298 K)/kcal mol⁻¹ = 4.87 and V(298 K)/Å³ molecule⁻¹ = 158.2, that is, 95.27 cm³ mol⁻¹, resulting in (298 K)/MPa^1/2 = 13.81. Spyriouni et al. [133] reported results from molecular dynamics simulations over the temperature range 290 to 390 K, extrapolating to = 267.5 K as /J mol⁻¹ = 20480 and ρ()/g cm⁻³ = 0.5738, resulting in = 13.66 MPa^1/2 and the temperature dependence is shown in Table 3. The Handbook [7] reports = 266.9 K and /kJ mol⁻¹ = 22.07 and with the extrapolated molar volumes from [67] = 89.07 cm³ mol⁻¹ the resulting solubility parameter is ( = 266.9 K)/MPa^1/2 = 14.93, being selected here.

2.1.53. Cyclobutane

Only scant relevant data are available for c-C₄O₈, namely, from Helgeson et al. [128] /kcal mol⁻¹ = 5.78 and ρ()/g cm⁻³ = 0.732, the boiling point being [7] −12.6°C, that is, = 260.6 K. The resulting = 16.95 MPa^1/2. /kJ mol⁻¹ = 24.19 in the Handbook [7] yields practically the same solubility parameter. The density in the Handbook pertaining to 25°C, ρ(298)/g cm⁻³ = 0.6890, and the molar volume (182.34 K) = 69.62 cm³ mol⁻¹ from Martins et al. [134] are irrelevant here.

2.1.54. Octafluorocyclobutane

The computer simulations of Watkins and Jorgensen [99] do not agree very well with experimental values (translated from the engineering values of Martin [135] in psi and ft³/lb), = 4.69 kcal mol⁻¹ (= 19.62 kJ mol⁻¹) and ρ() = 1.753 g cm⁻³, and there is also a misprint in their : −40.20 instead of −4.20°C, the correct value being = 267.3 K. The experimental data yield = 13.67 MPa^1/2, whereas the computed data yield 14.14 MPa^1/2, the former value being preferred.

2.1.55. n-Butane

Yosim and Owens [21] reported data from secondary sources /cal mol⁻¹ = 5352 and ρ()/g cm⁻³ = 0.601 at = 272.7 K, from which /MPa^1/2 = 14.43 is derived. Bradford and Thodos [66] reported the parameters of the expression (5), where = 2.259 (cal/cm³)^1/2, , , and , K from Kratzke et al. [136], with the value = 14.24 MPa^1/2 resulting. Gilmour et al. [98] reported /kcal mol⁻¹ = 5.35 and /cm³mol⁻¹ = 96.4 from which /MPa^1/2 = 14.45 is derived. Helpenstill and van Winkle [67] reported /(cal/cm³)^1/2 = 7.25 at 0°C, and 6.954 at 25°C, and 6.77 at 45°C, extrapolating to /MPa^1/2 = 14.82. Das et al. [137] reported the molar enthalpies and volumes of liquid and gaseous butane over the temperatures from to , from which the expression in Table 3 is derived and /MPa^1/2 = 14.43 as from the previous authors. An appreciably smaller value, /MPa^1/2 = 13.9, at an unspecified temperature (presumably 298 K) was reported by LaPack et al. [28]. This value is near that, 13.75, derived from the (298) and ρ(298) obtained from GROMOSC96 model of Daura et al. [94]. The mean of the mutually agreeing values, /MPa^1/2 = 14.47, is selected here.

2.1.56. n-Decafluorobutane

Brown and Mears [138] provided the required data for -C₄F₁₀: = –2.00°C ( = 271.15 K), /kcal mol⁻¹ = 5.480 (= 22.93 kJ mol⁻¹), and the density interpolated in the reported data ρ()/g cm⁻³ = 1.5925, yielding /MPa^1/2 = 11.76. The data provided by Gilmour et al. [98] lead to a similar value, /MPa^1/2 = 11.78, whereas the simulation of Watkins and Jorgensen [99] yielded a slightly lower value, /MPa^1/2 = 11.69. The mean of the two agreeing values is selected here, 11.77 MPas^1/2.

2.1.57. Isobutane

Gilmour et al. [98] reported 2-methylpropane (isobutane) /kcal mol⁻¹ = 5.09 and /cm³ mol⁻¹ = 97.8 at = 261.4 K, from which /MPa^1/2 = 13.98 is derived. Jorgensen et al. [93] reported similar values for (298)/kcal mol⁻¹ = 4.57 and /Å³ molecule⁻¹ = 175.1 from secondary sources as the previous authors resulting in (298)/MPa^1/2 = 12.56. Daura et al. [94] reported data obtained from their GROMOSC96 model, /kcal mol⁻¹ = 19.54 and ρ(T) = 551 kg m⁻³ at K, from which (298 K)/MPa^1/2 = 12.83 results. The value at the boiling point, /MPa^1/2 = 13.98, is selected here.

2.2. Results

The resulting selected values are shown in Table 1 for inorganic liquefied gases and in Table 2 for organic ones (carbon compounds).

As the temperature is increased, the molar enthalpy of vaporization diminishes towards its disappearance at the critical point. Over a temperature range near the normal boiling point the function 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 . Therefore, the solubility parameter 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 is linear with with a slope of − K⁻¹ as is seen in Table 3. This slope may be used for the approximate estimation from the values in Tables 1 and 2 of the applicable solubility parameter of the solute gases at the temperatures at which their solubility is needed.

3. Discussion

3.1. 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. 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. Meyer 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 CH₃Cl and C₂H₅Cl, 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 /(cal cm⁻³)^1/2 of the noble gases helium to xenon to one decimal digit that correspond well to the selected values in Table 1. 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 (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 /(cal cm⁻³)^1/2 for Ar, Kr, Rn, N₂, O₂, CO, CO₂, CH₄, C₂H₄, and C₂H₆, suggested to be valid over a range of temperatures much larger than the boiling points. As expected, these values are smaller than . Similarly, Blanks and Prausnitz [64] reported values of (298 K)/(cal cm⁻³)^1/2 from undisclosed sources for CH₄, C₂H₄, C₂H₆, C₃H₆, C₃H₉, and C₄H₁₀, shown in Table 4. Bradford and Thodos [66] provided the parameters for equation (5) for CH₄, C₂H₆, C₃H₈, and C₄H₁₀, from which solubility parameters at any temperature may be evaluated. The values at 298 K are shown in Table 4, except for methane, for which K. Gilmour et al. [98] reported /(cal cm⁻³)^1/2 values for CF₄, C₂F₆, CH₄, C₂H₆, C₃H₈, and C₄H₁₀ 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 C₃H₈, and C₄H₁₀ are only the dispersion ones, equaling /(cal cm⁻³)^1/2 and shown in Table 4 for 298 K.

Lawson [62] reported values of (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 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, H₂, O₂, N₂, CH₄, C₂H₄, C₂H₆, C₃H₈, CO, CO₂, and H₂S, in a variety of polar and nonpolar solvents and the NRTL (nonrandom two-liquid) model to obtain the (absolute) values of . From these, with known values of the solvent values, those for the solute gases could be estimated. The presented 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 K are listed in Table 4. Shamsipur et al. [139] dealt with the solubilities of gases in various solvents and reported “” values for the alkanes (). When these are related to their known Hildebrand solubility parameters as solvents, the relationship /MPa^1/2 = 7.65 results. When this relationship is applied to “” = 0.1402 for Ne this yields = 10.8 MPa^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].

3.3. 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, ()/K, is the minimum of the interaction potential energy . Indeed, the cohesive energy densities, []², are linearly related to the () values of the gases for which values were found, see Figure 1. It should be noted that the () reported by various authors, like De Ligny and Van der Veen [14], Teplyakov and Meares [13], Leites [12], and Churakov and Gottschalk [15], among others, vary considerably as the figure shows. Still, a correlationwith 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 [16–19, 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 refraction, , for many substances that are liquid at ambient temperatures, but not for those that are gases. The expressionat an unspecified temperature (presumably 298 K) was found and may be applicable also for gaseous solutes.

4. Conclusions

The solubility parameters, , of nonreactive permanent gases at their boiling points (<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 are also tabulated. The values of representative inorganic gases increase with their molar masses but those of organic solutes (hydrocarbon) tend to diminish with increasing molar masses. The 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 values correlate linearly with the attractive interaction energies of binary collisions of the gas molecules, the depths of the potential wells and with the surface tensions, , of the liquefied gases.

Competing Interests

The author declares that there are no competing interests regarding the publication of this paper.

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