Capillary condensation and the Kelvin equation

As already indicated in Section 3.1, the study of mesoporous solids is closely bound up with the concept of capillary condensation and its quantitative expression in the Kelvin equation. This equation is, indeed, the basis of virtually all the various procedures for the calculation of pore size 

As with all thermodynamic relations, the Kelvin equation may be arrived at along several paths. Since the occurrence of capillary condensation is intimately, bound up with the curvature of a liquid meniscus, it is helpful to start out from the Young-Laplace equation, the relationship between the pressures on opposite sides of a liquid-vapour interface. 

Picture a small element of a curved interface between a liquid a and a vapour p, having two radii of curvature r, and (Fig. 3.6). These radii are defined by taking two planes at right angles to one another, each of them 

Substitution for dx iand dy in Equation (3.3) gives the Young-Laplace equation  

Let us now consider the process of capillary condensation. For the pure liquid (a) in equilibrium with its vapour fi), the condition for mechanical equilibrium is given by Equation (3.6) and that for physicochemical equilibrium by 

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