The Clausius-Clapeyron Equation and Hydrate Equilibrium

In the most common thermodynamic case, the Clapeyron equation is used with pure components to obtain the heat of vaporization from pure component two-phase (vapor pressure) data. The Clapeyron equation is one of the primary successes of thermodynamics, because it enables the calculation of AH, which is difficult to measure, from easily available properties of pressure and temperature. 

In hydrate equilibrium, it may seem slightly unusual to apply it to binary systems (water and one guest component) of three-phase (Lw-H-V or I-H-V) equilibrium to obtain the heats of dissociation. As van der Waals and Platteeuw (1959b) point out, however, the application of the Clapeyron equation is thermodynamically correct, as long as the system is univariant, as is the case for simple hydrates. 

If the volume of hydrate approximates that of water (or ice) in the hydrate formation reaction (Lw + V H), then to a good approximation, A V Vg (= zRT// , where z is compressibility). The substitution of this expression for AV 

Accuracy of the Clausius-Clapeyron Equation for Hydrate Heat of Dissociation to Vapor and Water 

Semilogarithmic plots of formation pressure versus reciprocal absolute temperature yield straight lines, over limited temperature ranges, for hydrate formation from either liquid water, or ice. From Equation 4.13 such linear plots either indicate (1) relatively constant values of the three factors (a) heat of formation, AH, (b) compressibility factor, z, (c) stoichiometry ratios of water to guest or (2) cancellation of curvilinear behavior in these three factors. 

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