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**Course Syllabus**

A graduate-level course. This course emphasizes a microscopic approach to phase tansitions, in general, and phase equilibrium, in particular. Being able to calculate the phase equilibrium of non-ideal mixtures and to use this information to design separation processes.

Thermodynamics from a chemical engineering viewpoint. Review of basic laws and their application: First Law as it applies to non-flow and steady-flow processes, pressure-volume-temperature behavior of fluids and heat effects, the Second Law and its applications, thermodynamic properties of pure fluids and fluid mixtures.

Thermodynamic properties from volumetric data. Interpretation, construction, and thermodynamics of one, two, three to n-component phase diagrams with examples of their use in chemical engineering.

Classical thermodynamics of phase and chemical equilibrium. Chemical potentials in gas and liquid mixtures. The Gibbs-Duhem equation. Total and partial molar properties of mixtures. Classical thermodynamic and statistical mechanical basis of activity and fugacity coefficients.

Experimental measurements in thermodynamics. Formulation of the general conditions for equilibrium in multi-component multi-phase systems. Phase equilibrium in two-component systems (vapor-liquid, liquid-liquid, liquid-solid phase equilibrium). Phase equilibrium in three-and other multi-component systems, diagrams. Miscibility, solubility, retrograde condensation, high-pressure equilibrium and supercritical phenomena. Hill Thermodynamics of small systems (Hill Nanothermodynamics).

Introduction to statistical thermodynamics. Intermolecular forces (hard-sphere, Mie, Yukawas, polarities, 3-body), extended corresponding states, Molecular-based study of dense fluids. Statistical-mechanical equations of state: Perturbation and variational approaches for dense fluids and mixtures. Theories of solution:conformal solutions and flucctuations. Radial distribution and direct correlation functions approximations and mixing rules (van der Waals, HSE, DEX, etc.), associating solutions. Theory and calculation of infinite dilution chemical potential. Statistical mechanical description of supercritical fluid extraction and retrograde condensation.

Advanced chemical engineering applications: Pseudoization techniques and heavy /C7+ fraction characterization. Phase equilibrium computational algorithms of continuous mixtures, continuous mixture Gibbs free energy minimization and phase rule. Phase equilibrium calculations of highly polar systems, polymer solutions, colloidal and micellar solutions. Partitioning of monodispersed / polydispersed polymers and in aqueous two-phase systems. Phase equilibrium of mixtures consisting of molecules with large size and shape differences. The role of three-body forces and mixing rules on the phase behavior of mixtures around the critical region. Theory and calculation of surface and interfacial tensions. Use of velocity of sound and molar refraction in predicting PVT relations of dense fluids. Predicting activity and osmotic coefficients of electrolyte solutions. Phase behavior prediction of complex fluids with minimum characterization data.