A single equation of state (EOS) such as the Peng-Robinson (PR) EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state, including estimation of pure component properties and computation of the vapor-liquid equilibrium (VLE) diagram for binary mixtures. We perform high-pressure chemical-equilibrium calculations. Finally, we solve an adiabatic flash distillation problem for a multi- component mixture. All these computations are available in electronic format in the form of MATLAB[R] programs upon request from the authors or from the File Exchange Center. These problems can serve as teaching material for a chemical engineering thermodynamics undergraduate level course.