It is essential for reliable process simulation and optimization software to have extremely robust subroutines for thermophysical property evaluation and vapor-liquid equilibrium (flash) calculations. However, in the course of obtaining such values or solving such a problem, it is possible that the thermodynamic model will be queried for liquid or vapor properties of a mixture at conditions far from the physical solution or where one phase physically does not exist. Under these conditions, and in the common situation where both phases are described by the same equation of state (EOS), the model may return a liquid-like density for the vapor phase or vice-versa. It is well known that this behavior can cause a flash calculation algorithm to converge to the trivial solution of the equations (indistinguishable liquid and vapor phases) or simply fail. To mitigate this behavior, a number of articles have suggested methods for evaluating and post-processing the density calculated by the EOS to promote convergence of the flash calculations to physical solutions through creatively-defined extrapolations. In keeping with the efforts of the other articles in this series, this paper describes new nonsmooth algorithms for robustly evaluating appropriate density values for mixtures at conditions where use of the EOS alone yields unreasonable results. Unlike many such proposals in the literature, this new approach requires only a simple evaluation procedure and may be augmented with accurate sensitivity analysis through the use of nonsmooth operators and automatic generalized derivative computation. Applications of this new strategy are highlighted for commonly studied equations of state in hydrocarbon systems.