Using the Noninteracting Cluster Theory to Predict the Properties of Real Vapor

We examine the nonideal behavior of real vapor in the context of the theory of nonin-teracting molecular clusters. The vapor is treated as a perfect mixture of clusters, which in equilibrium attain a distribution in size determined by formation energies G i , where G i is the energy required to form a cluster of i molecules from i molecules in bulk saturated liquid. A theory for the G i gives an equation of state that captures the nonideal behavior of the vapor; conversely, equation of state data provide a validation of the theory. In this paper, we compare the predictions of this equation of state to experimental data. Utilizing the G i proposed by Dillmann and Meier and based on Fisher's droplet model, we compute the vapor compressibility along the saturation curve for several nonpolar substances and obtain excellent agreement with experiment. We also compute the third virial coeecient for these substances and observe correct qualitative behavior; in the case of benzene and n-octane, for which some data is available, we nd rough agreement with experiment. The conventional kinetic theory of homogeneous nucleation, which is based on the assumption of noninteracting clusters, demonstrates that the cluster series equation of state can be continued past the saturation point to describe metastable vapor, a claim that no non-virial equation of state can make a priori. Furthermore, the noninteracting cluster theory readily accommodates results of more detailed calculations of molecular clusters (e.g., results of Monte Carlo or molecular dynamics studies). These considerations and the success of the simple Fisher-Dillmann-Meier model in predicting the behavior of nonideal vapor suggest possible avenues of investigation in equation of state research.