We investigated the mathematical structure of Gibbsian multicomponent thermodynamics with instabilities. We analyzed the construction of such thermodynamics from a pressure law using ideal gases as the low density limit. The fluid mixtures were allowed to have mechanically and chemically unstable states that were excluded in previous work on supercritical fluids, and the Soave-Redlich-Kwong cubic equation of state was specifically considered. We also investigated the mathematical structure of extended thermodynamics in the presence of cohesive forces—capillary effects—for a simplified diffuse interface fluid model. The thermodynamic formalism was validated by comparison with experimental data for mixtures of ethane and nitrogen. Very good agreement with experimental data was obtained for specific heats, multiphase equilibrium, and critical points, and we also analyzed the structure of strained jets of ethane.