hydrates [74]. Starting with initial success with acetylene, he also found that ethylene, carbon dioxide, and SO2 could perform that function.
In the new century, de Forcrand initiated a new approach to the determination of hydrate compositions in recognition of the fact that direct determinations were difficult and prone to errors. He generalized Trouton's rule, proposed in 1887, that the entropy of vaporization for various kinds of liquids at their boiling points is almost the same value, about 85–88 J K−1 mol−1 [75]. The entropy of vaporization is defined as the ratio between the enthalpy of vaporization and the boiling temperature. de Forcrand calculated compositions for all of the known hydrates, first improving doubtful data when necessary. The results of his calculations are shown in Table 2.2 [28], of which about half of the entries appear to support Villard's rule. Except for outliers Ar and Br2, for the other entries, both the heats of dissociation to form ice Q(ice) and water Q(water), and the hydration number generally increased with molecular weight to give up to eight waters/guest.
Further progress in determining hydrate compositions virtually ground to a halt, as neither direct, nor indirect, methods were able to give a convincing explanation of the apparent complexity of the variable hydrate compositions. For instance, de Forcrand, from previously obtained data, calculated the composition of the chloroform–H2S hydrate to be CHCl3·2H2S·19H2O. This composition was explained by de Forcrand in terms of the formula (CH3Cl·7H2O) + 2(H2S·6H2O); thus, two hydrates present in a 1 : 2 ratio. This formula was then taken to be common to all sulfhydrated hydrates (binary hydrates with H2S). The composition found that for chloroform hydrate, CHCl3·18H2O in 1885 by Chancel and Parmentier [61] was ascribed to the presence of a large excess of water, although CHCl3·17H2O is the true formula.
More complexities arose from de Forcrand's efforts to investigate hydrate formation by the noble gases [76], in particular argon hydrate after it having been reported by Villard [28, 77]. He was able to make krypton hydrate, and from the dissociation behavior and heats of formation, he arrived at a composition of Kr·5.08H2O, and a redetermination of the value for Ar hydrate led to a composition of Ar·5.5H2O. Eventually, he was able to form Xe hydrate and determined its composition to be Xe·6.6H2O [78]. Rounding off, Ar and Kr then have a hydration number of 5 or 6; however, xenon's value then would be 6 or 7, which again led to speculation why these rather similar noble gases would have different hydration numbers. There were further efforts made to confirm or refute Villard's rule, but without much success either way. The formation of hydrates of noble gas indicated that the chemists of the day realized that the water–gas interactions in hydrates were not chemical in nature.
Table 2.2 De Forcrand's hydrate compositions obtained using calorimetric data [1, 28].
| Guest | Tboiling (K) | Tdissoc. (K) | Q(ice) (cal) | Q(water) (cal) | Calculated formula | Probable formula |
|---|---|---|---|---|---|---|
| Ar | 86 | 229.2 | 13.30 | 6.87 | Ar + 4.5H2O | 4/5H2O |
| CH4 | 109 | 244 | 16.35 | 7.32 | CH4 + 6.31H2O | 6H2O |
| CO2 | 194.8 | 251.8 | 16.16 | 7.55 | CO2 + 6.02H2O | 6H2O |
| N2O | 185 | 253.7 | 16.29 | 7.61 | N2O + 6.06H2O | 6H2O |
| C2H2 | 188 | 257.6 | 15.92 | 7.73 | C2H2 + 5.73H2O | 6H2O |
| C2H6 | 188 | 257.2 | 17.71 | 7.71 | C2H6 + 6.99H2O | 7H2O |
| C2H4 | 169 | 259.6 | 18.34 | 7.76 | C2H4 + 7.37H2O | 7H2O |
| PH3 | 188 | 266.6 | 16.44 | 8.00 | PH3 + 5.90H2O | 6H2O |
| H2S | 211 | 273.35 | 16.34 | 8.20 | H2S + 5.69H2O | 6H2O |
| C2H5F | 241 | 276.7 | 20.12 | 8.30 | C2H5F + 8.27H2O | 8H2O |
| SO2 | 263 | 280 | 19.83 | 8.40 | SO2 + 8.06H2O | 8H2O |
| CH3Cl | 250 | 280.5 | 18.83 | 8.41 | CH3Cl + 7.28H2O | 7H2O |
| H2Se | 231 | 281 | 16.82 | 8.43 | H2Se + 5.87H2O | 6H2O |
| Cl2 | 238.4 | 282.6 | 18.36 | 8.48 | Cl2 + 7H2O | 7H2O |
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