A single equation of state (EOS) such as the Peng-Robinson EOS can accurately describe both the liquid and vapor phase. We present several applications of this equation of state including adiabatic flash calculation, determination of the solubility of methanol in natural gas, and the calculation of high-pressure chemical equilibrium. The problems serve as teaching material to senior students at the National Institute of Applied Sciences and Technology in Tunis. All these computations are available in the form of notebooks upon request from author or from the Wolfram Research Information Center. (Contains 3 figures.)