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by sudden détente of pressure to produce a crystal nucleus, and then increase of pressures to above the value at which the wall of the containing vessel becomes coated with hydrate crystals. With a subsequent reduction of pressure below the value of bulk hydrate formation, which did not depend on the relative amount of water and carbon dioxide present, the hydrate disappeared. To determine the composition, Wróblewski [45] volumetrically measured the quantity of CO₂ gas which combined with a small weighed amount of water. Accounting for non‐ideality corrections for the gas, he found the stoichiometry of CO₂·8.01H₂O as the average of 19 analyses at 16 atm and 0 °C, with a standard deviation in the hydration number of ±0.54. A further study [46] involved the role played by the abrupt fall of pressure during détente and crystallization. He promoted the principle that hydrates can only form when the concentration of dissolved gas in the aqueous solution matches its concentration in the hydrate. This condition is not normally met with carbon dioxide which becomes a liquid at a pressure well below that at which its concentration in liquid water becomes equal to its hydrate composition. He believed, however, that the cooling produced by détente could produce the requisite increase in solubility. The principle of equal concentrations was not generally true for the other known hydrates, in particular for the case of methane hydrate. That it had credibility reflects the rather poor understanding of phase equilibria at the time. Wróblewski recognized that the cooling normally produced ice as well as hydrate and insisted that all of the water would be converted to hydrate only if the relative amount of water was very small and its surface area very large.

By 1880, eight gas hydrates were known, usually observed as octahedral crystals formed at relatively low gas pressures. These had melting points above 0 °C and compositions close to eight waters per molecule of gas. The researchers involved were often on the track of other projects, so that hydrate discoveries were incidental and sustained efforts to study gas hydrates as a distinct class of materials were not made. However, after 1880, there were important changes as the tools to work at higher pressures became available, along with more reliable methods of hydrate synthesis and characterization. The laws of chemical thermodynamics were also being established and used during this time, which put the analysis of hydrate formation on a sound conceptual framework. There were concerted efforts to understand the gas hydrates as a distinct class of materials as several researchers used physical chemistry techniques to study gas hydrates for their doctoral dissertations.

2.3 The Phase Rule

      Early studies on gas hydrates had shown that the equilibrium pressure of formation of the hydrate from (or decomposition of the hydrate into) liquid water and gas depended only on temperature (i.e. the equilibrium is univariant), and this equilibrium pressure increased with increase of temperature for chlorine [43], phosphine [42], hydrogen sulfide [42], and carbon dioxide hydrates [44]. This behavior was similar to that observed when a solid decomposed into a solid and a gas and was known as Debray's law after the recent observations of the dissociation pressures of calcium carbonate and a variety of stoichiometric salt hydrates.

The proper definition of the phase relationship possible in gas–water systems capable of hydrate formation is due to H.W. Bakhuis Roozeboom (Figure 2.3), working at Leiden. In a 70‐page long memoire [47] published in 1884, Roozeboom gave the results of his careful studies of the gas hydrates of sulfur dioxide, chlorine, bromine, and hydrogen chloride; work which constituted the subject of his doctoral thesis. He confirmed the applicability of Debray's Law and showed that the aqueous solution which coexists with the hydrate at different temperatures has the same vapor tension (i.e. vapor pressure) as the hydrate and that its concentration increases with temperature as the pressure is increased. He disproved Wróblewski's contention that the equilibrium solution must have the same composition as the hydrate. He distinguished between the critical decomposition in an open vessel, where the dissociation pressure is one atmosphere, and the critical decomposition temperature in a closed vessel where the gas liquefies. Neither of these temperatures was a critical temperature in the absolute sense of a temperature above which gas hydrate can never exist. Roozeboom called the highest temperature at which SO₂ hydrate can exist in a closed tube a “point de discontinuité” since the hydrate at least could continue to exist (see point Q_2, Figure 2.3) in equilibrium with liquid water and liquefied gas at a higher temperature with the application of increased external pressure. In this assertion, he disagreed with Cailletet. He confirmed the observations of Cailletet and Bordet [42] and Wróblewski that, although gas hydrates were normally difficult to crystallize from solution under gas pressures well in excess of those required for hydrate stability (which with today's understanding is related to the kinetic barrier to hydrate nucleation), this difficulty was not encountered for solutions in which hydrate had been present previously.

      Figure 2.3 Pioneers of clathrate science in the late 1800s and early 1900s. From left to right, Hendrik Willem Bakhuis Roozeboom, Robert Hippolyte de Forcrand, and Paul Ulrich Villard. Sources: Original photograph by Albert Greiner, reproduced with permission from the Allard Pierson Museum, University of Amsterdam, Reproduced with permission from Université de Montpellier, Reproduced courtesy of the Archives de l'Académie des Sciences, 23, Quai de Conti, 75006 Paris, France.

      Lorsqu'on fait passer un courant rapide de SO₂, dans une solution, où une élévation de la température jusqu'a 8° ou 9° a fait 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 7^o (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)

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