"How does the application of mass balance principles contribute to the design and optimization of chemical processes? Explain how the conservation of mass principle is utilized to analyze and predict the flow of materials within a system, considering various unit operations and reactors. Discuss the importance of understanding material balances in addressing environmental concerns and ensuring process safety. Additionally, explore how deviations from ideal behavior, such as non$-$ideal flow patterns or reaction kinetics, are accounted for in mass balance calculations. Provide examples illustrating the practical significance of mass balance theory in real$-$world chemical engineering applications."