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 t heory of noninteracting molecular clusters. The vapor is treated as a perfect mixture of clusters, which in equilibrium attain a distributio n in size determined by formation energies Delta G(i), where Delta G(i ) is the energy required to form a cluster of i molecules from i molec ules in bulk saturated liquid. A theory for the Delta G(i) gives an eq uation of state that captures the nonideal behavior of the vapor; conv ersely, equation of state data provide a validation of the theory. In this paper, we compare the predictions of this equation of state to ex perimental data. Utilizing the Delta G(i) proposed by Dillmann and Mei er and based on Fisher's droplet model, we compute the vapor compressi bility along the saturation curve for several nonpolar substances and obtain excellent agreement with experiment. We also compute the third virial coefficient for these substances and observe correct qualitativ e behavior; in the case of benzene and n-octane, for which some data a re available, we find rough agreement with experiment. The conventiona l kinetic theory of homogeneous nucleation, which is based on the assu mption of noninteracting clusters, demonstrates that the cluster serie s equation of state can be continued past the saturation point to desc ribe metastable vapor, a claim that no nonvirial equation of state can make a priori. furthermore, the noninteracting cluster theory readily accommodates results of more detailed calculations of molecular clust ers (e.g., results of Monte Carlo or molecular dynamics studies). Thes e considerations and the success of the simple Fisher-Dillmann-Meier m odel in predicting the behavior of nonideal vapor suggest possible ave nues of investigation in equation of state research.