the composition of the hydrate as estimated by Faraday. Le Châtelier was thus the first to relate the Clausius–Clapeyron equation to gas hydrate compositions, although the later extensive use of the Clausius–Clapeyron equation as an indirect method of analysis by de Forcrand and Villard was hardly anticipated.
Le Châtelier's results were presented to the Académie des Sciences in Paris at the séance of 15 December 1884. On 14 February 1885, Roozeboom submitted to the Recueil an account [50] of his own more accurate measurements of the dissociation pressures of sulfur dioxide, chlorine, and bromine hydrates below 0 °C. For all three hydrates, the dissociation pressure was higher in the presence of ice than in the presence of supercooled aqueous solution at the same temperature. Roozeboom neither made an attempt to use the Clausius–Clapyeron equation (2.1) to calculate heats of dissociation from his data, nor to check their consistency with the hydrate compositions which he had previously determined by direct analysis viz., SO2·7H2O, Cl2·8H2O, and Br2·10H2O. The dissociation pressure diagrams which incorporated the new results for the first time showed clearly the pressure–temperature fields of hydrate stability under all conditions except those of very low temperature or high pressure. The diagram shown in Figure 2.4 for SO2 hydrate has a general form which is typical of the great majority of gas hydrates which have since been studied [51].
By this time, the thermodynamics of equilibria in heterogeneous systems had been established by J. Willard Gibbs, then working as an unpaid professor of mathematical physics at Yale University. In the 300 pages of the article On the Equilibrium of Heterogeneous Substances [52], Gibbs laid down the formal basis of classical thermodynamics as derived from its first two laws. One of the immediate and most important consequences was the now well‐known Gibbs phase rule, according to which the number of variables which can be independently adjusted in a system in equilibrium is given by C − P + 2, where C is the number of independent chemical components and P is the number of coexisting phases.
Figure 2.4 The phase diagram of SO2 and water mixture showing the stability region of the hydrate phase. The h, I, and g represent the hydrate phase, ice, and the gas‐phase SO2, respectively. The ℓ1 represents liquid water and ℓ2 liquid SO2. The two quadruple points are shown by Q1 and Q2. Source: Davidson [47], reproduced with permission from Springer.
In general, an appreciation of Gibbs' work by European scientists only followed its translation into German by Wilhelm Ostwald in 1892 and into French by Le Châtelier in 1899. However, in 1886, Johannes D. van der Waals brought the Gibbs phase rule to the attention of Roozeboom, who adopted it with great enthusiasm. Roozeboom devoted his future work almost exclusively to the application of the phase rule to heterogeneous equilibria in a wide variety of chemical systems where he did more than anyone else to prove its validity. In 1887, he published [53] Sur le Différentes Formes de l'Équilibre Chimique Hétérogène, in which he systematically classified chemical and physical processes according to the number and nature of the components and phases present, and Sur les Points Triples et Multiples [54], a treatment of the invariant points at which equilibrium lines meet in the phase diagram.
Through the phase rule, it now became clear why Debray's law of univariant equilibrium would apply to gas hydrates and other two‐component equilibria between three phases. Examples of univariant equilibria cited by Roozeboom included the hydrate‐ice‐gas (h‐I‐g), hydrate‐(liquid‐rich‐in‐water)‐gas (h‐ℓ1‐g), hydrate‐(liquid‐rich‐in‐water)‐(liquid‐rich‐in‐hydrate‐former) (h‐ℓ1‐ℓ2), and hydrate‐ice‐(liquid‐rich‐in‐water) (h‐I‐ℓ1) systems. These lines are all shown in Figure 2.4. Only one point on the (h‐I‐ℓ1) equilibrium line was known, in particular, at the quadruple point with the gas phase for SO2 (point Q1 of Figure 2.4), Cl2 and Br2 hydrates, but Roozeboom easily predicted that the equilibrium temperature along this line should fall with increase in pressure. According to the phase rule, the univariant behavior of the three component CHCl3–H2S hydrate and similar double hydrates studied by de Forcrand (see below) was simply ascribed to the coexistence of hydrate with aqueous liquid, organic liquid, and gaseous phases. Finally, the nature of Le Châtelier's recent results [55] of a study of the effect of added HCl or NaCl on the equilibrium vapor pressure of Cl2 hydrate was accounted for by the presence of a third component whose concentration affected the dissociation pressure unless it was present in sufficient quantity to form a separate phase, such as solid NaCl.
In his last publication specifically devoted to gas hydrates [56] Roozeboom remarked that:
Il s'agit donc seulement, … pour chaque hydrate nouveau, de la détermination des valeurs numériques correspondant à l'équilibre; mais les lois générales ne sont plus inconnues.3
2.4 de Forcrand and Villard – Career Gas Hydrate Researchers
After submitting a thesis entitled Recherches sur les hydrates Sulfhydrés to the Faculté des Sciences de Paris in 1882 [57], Robert Hippolyte de Forcrand (Figure 2.3) spent the next 43 years contributing prolifically to gas hydrate research. Nominally, de Forcrand worked in the organic chemistry laboratory of le Collège de France in Paris under the direction of Marcellin Berthelot, although most of his work was performed in Lyon under A. Loir.
Some 30 years previous, Loir [58] had formed a solid compound from chloroform, hydrogen sulfide, and water at room temperature. Similar compounds were formed when methyl chloride, 1,1‐dichloroethane, ethyl chloride, methyl bromide, or methyl iodide were used instead of chloroform, or hydrogen selenide was used instead of hydrogen sulfide. Since Loir had only measured the relative proportions of chloroform and hydrogen sulfide, the composition of these compound hydrates remained essentially unknown. Since de Forcrand found that the pressure–temperature stability conditions for the compound hydrates (double hydrates, in today's parlance) were more convenient to work with than those of the single component hydrates, he chose the former for analysis.
The term hydrate sulfhydré was coined by de Forcrand to distinguish the compound hydrate of volatile organic liquids with hydrogen sulfide from the simple gas hydrate of hydrogen sulfide itself. Since there is no simple English equivalent of this term, it is best rendered as the awkward “double hydrate with hydrogen sulfide.” de Forcrand pointed out [59] that the compound hydrates appeared to be similar to the double hydrate of phosphine and carbon disulfide, newly formed under pressure by Cailletet and Bordet [42].
Using the production of crystals when hydrogen sulfide was bubbled through an organic liquid layer underlying a layer of water at a temperature near 0 °C as the criterion of hydrate formation, de Forcrand identified double hydrates of the 33 organic compounds, mainly halogenated hydrocarbons, listed in Table 2.1. No doubt, these organic compounds, many of them synthesized by de Forcrand himself, varied greatly in purity and the boiling points (b.p.) given are mid‐points of the observed ranges of the boiling point. Similarly, a number of organic liquids were found to form “hydrates selenhydrés,” double hydrates with hydrogen selenide gas substituted for hydrogen sulfide, such as Loir had found [58] for chloroform. Hydrogen selenide was also found [59] by de Forcrand to form a hydrate by itself, although apparently not soon enough for inclusion in his thesis.
Double hydrates with hydrogen sulfide were formed only by the organic halides which boiled below about 110 °C, a result now known to be due to a rough