Qualitative PVT Behavior of Pure Substances

A qualitative observation of PVT behavior of pure substances indicates continuity in 

These mathematical conditions at the critical point may be applied to various equations of state to determine their parameters in terms of the critical constants. The equations themselves may then be written in terms of the critical constants which are characteristic of each substance. The temperature, pressure, and volume may be replaced in the equation of state by the reduced properties, dehned as 

An equation of state written in terms of the reduced properties is a generalized equation that could be applied to any substance. It follows that, if two substances are at the same reduced temperature and pressure, they would have the same reduced volume. This is the concept of the principle of corresponding states, which may be used to correlate PVT properties of similar components. 

An equation of state based on the principle of corresponding states as described above takes the form 

Once this function is determined, it could be applied to any substance, provided its critical constants Pc, T, and V are known. One way of applying this principle is to choose a reference substance for which accurate PVT data are available. The properties of other substances are then related to it, based on the assumption of comparable reduced properties. This straightforward application of the principle is valid for components having similar chemical structure. In order to broaden its applicability to disparate substances, additional characterizing parameters have been introduced, such as shape factors, the acentric factor, and the critical compressibility factor. Another difficulty that must be overcome before the principle of corresponding states can successfully be applied to real fluids is the handling of mixtures. The problem concerns the definitions of Pq P( and Vc for a mixture. It is evident that mixing rules of some sort need to be formulated. One method that is commonly used follows the Kay s rules (Kay, 1936), which define mixture pseudocritical constants in terms of constituent component critical constants  

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