$9.$ Explain how the Fenske equation determines the minimum number of theoretical stages in a distillation column.

$10.$ What is the purpose of the Underwood equations in the context of distillation?

$11.$ How does the Gilliland correlation help in estimating the number of stages in a distillation column?

$12.$ Describe the process and advantages of differential distillation over other types of distillation.