distillation separate components in chemical engineering processes? Explain the principles behind distillation, including vapor$-$liquid equilibrium, boiling point differences, and fractionation. Discuss the role of trays or packing in a distillation column and how they enhance separation efficiency. Analyze factors influencing the selection of optimal operating conditions for a distillation process, such as temperature, pressure, and reflux ratio. Additionally, describe common applications of distillation in industry and its importance in producing pure substances."