disparaître tous les cristaux, un abaissement léger suffit parfois pour les faire apparaitre de nouveau. Ainsi je les ai vus se former à 3°, 4°, 5°.
M.M. Cailletet et Wroblewski font mention d'un fait analogue. D'après ces savants une simple compression suffit pour reproduire les hydrates (dont ils se sont occupés) peu de temps après qu'ils ont disparu. M. Cailletet suppose que dans ce cas, un cristal infiniment petit est resté dans le tube. Dans le cas de l'hydrate de SO2, cependant, il me semble que cette supposition est inadmissible, parce qu'un cristal de l'hydrate, quelque petit qu'il soit, aurait déjà provoqué une cristallisation dès 7o (voir page 39).
Ne peut‐on pas supposer: que peu de temps après la dissociation de l'hydrate solide, quelques agrégats de molécules liquides présentent encore un arrangement favorable à la recomposition, mais qu'ils perdent plus tard?2
Whether this “memory” effect is related to the “crystal memory” effect later observed for some high‐pressure polymorphs of ice by Bridgman [48] who noticed it both in the freezing of pressurized liquid water and in the transformation of one solid polymorph to another is still in doubt. The origin of the memory effect in hydrate phase formation continues to be a source of interest over a hundred years after it was first discovered, see Chapter 13.
Later in 1884, Henri Louis Le Châtelier [49] used the then well‐known Clausius–Clapeyron equation for the variation of vapor pressure or dissociation pressure of the hydrates with temperature,
(2.1)
where q represents the quantity of heat absorbed during hydrate dissociation and ΔV is the corresponding change of volume during the transformation. He predicted that an abrupt change in slope should occur when q was changed because, for example, one of the bodies (phases) in the transformation passed through its temperature of fusion. To illustrate this point, Le Châtelier chose chlorine hydrate and measured the pressures of its dissociation into liquid water and gas, and into ice and gas. The change in slope was in the direction anticipated and the two values of q derived from Eq. (2.1) differed by less than 20% from the value expected for the heat of fusion of the amount of water in Cl2·10H2O, 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.
