Villard’s Rule

Historically, two periods occurred for the determination of the number of hydrate water molecules per guest molecule. In the first century (1778-1900) after the discovery of hydrates, the hydration number was determined directly. That is, the amounts of hydrated water and guest molecules were each measured via various methods. The encountered experimental difficulties stemmed from two facts (1) the water phase could not be completely converted to hydrate without some occlusion and (2) the reproducible measurement of the inclusion of guest molecules was hindered by hydrate metastability. As a result, the hydrate numbers differed widely for each substance, with a general reduction in the ratio of water molecules per guest molecule as the methods became refined with time. After an extensive review of experiments of the period, Villard (1895) proposed Villard s Rule to summarize the work of that first century of hydrate research ... 

While the above estimate may seem antiquated, Villard s Rule is a good rule of thumb in many cases. Note that if a guest fills all of both cavities in si and sll, the hydration number would be 5.75 and 5.67, respectively, so a value of 6 allows for the possibility of empty cages, and is frequently taken as a good approximation to the hydration number for methane hydrates. However, Villard s Rule is not a good approximation for components that only fill the large cavity of either si (e.g., ethane) or sll (e.g., propane). 

After 1900 the direct determination of hydrate number was abandoned in favor of the second, indirect method. The indirect method is still in use today and is based on calculation of the enthalpies of formation of hydrate from gas and water, and from gas and ice. This method was originally proposed by de Forcrand (1902) who used the Clapeyron equation to obtain the heat of dissociation from three-phase, pressure-temperature data, as in the below paragraph. With this more accurate method many exceptions were found to Villard s Rule. The historical summary provided in Chapter 1 indicates that while the number of hydrated water molecules was commonly thought to be an integer, frequently that integer... 

The de Forcrand method has been found to be much more accurate than Villard s Rule. One reason for its accuracy is related to the determination of AHf and AH2 from three-phase (Lw-H-V or I-H-V) equilibrium measurements of pressure and temperature via the Clapeyron equation ... 

To prevent water occlusion. Without agitation, Villard (1896) showed, for example, that nitrous oxide hydrate formation was continuous for a period longer than 15 days under a pressure of 2 MPa. Villard also determined that in previous research the ratio of water to guest molecules had been analyzed as greater than G 6H20 (Villard s Rule) due to either occlusion of water within the hydrate mass, or due to the loss of the guest component. 

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