the presence of impurities affect the efficiency of distillation processes in chemical engineering? Discuss the theoretical principles underlying the separation of binary and ternary mixtures, considering factors like vapor$-$liquid equilibrium, relative volatility, and tray efficiencies. Elaborate on the design considerations for efficient separation columns, including the selection of packing materials, column diameter, and operating conditions. Analyze the impact of varying pressure and temperature on separation performance, referencing thermodynamic principles such as Raoult's law and Dalton's law.