Using the Clapeyron equation to obtain hydration number

1 Using the Clapeyron equation to obtain hydration number 

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 method considers the equilibrium of gas and n mol of liquid water (or ice) with hydrates on either side of the ice point  

Equation 4.14 for Lw-H-V equilibrium may be subtracted from Equation 4.15 for I-H-V equilibrium at quadruple point Qi (approximately 273 K), with the result of the number of moles of liquid water converted to ice  

Because the enthalpy of fusion (AHf) of water is well known, AH3, the difference in the AH values of Equations 4.14 and 4.15, may be divided by the heat of fusion of ice (AHf) to obtain n, the number of moles of water (or ice) converted to hydrates. 

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