Integrated form of van’t Hoff Isochore

In a recent paper [3] we described how adsorption equilibrium constants for a range of paraffinic and olefinic species could be estimated using the following integrated form of van t Hoffs isochore equation,... 

The isochore, Equation (4.81), was derived from the integrated form of the Gibbs-Helmholtz equation. It is readily shown that the van t Hoff isochore can be rewritten in a slightly different form, as ... 

This is the well-known equation for the reaction isochore discovered by van t Hoff. The equation tells us qualitatively that the equilibrium constant increases with the temperature for endothermic reactions (0<0), and diminishes with the temperature for exothermic reactions (Q>0). In other words (since the products of the reaction are in the numerator of the constant), an increase in the temperature favours the production of the substances which are formed with absorption of heat. We can test the equation quantitatively if we assume the heat of reaction to be constant and integrate for a small range of temperature. This assumption is justified by experience, as the quantity... 

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