$5.$ The PonchonSavarit method differs from McCabeThiele by taking into account both $\_\_\_\_\_\_$ and $\_\_\_\_$ balances, which allows for the determination of the optimal number of stages and feed location for a given separation, especially when handling $\_\_\_\_\_\_$ mixtures.

$6.$ The Fenske equation provides a way to calculate the minimum number of theoretical stages required at $\_\_\_\_\_\_$ reflux for a given separation, focusing on the components with the highest and lowest $\_\_\_\_$ in a $\_\_\_\_\_\_$ mixture.

$7.$ Differential distillation operates without $\_\_\_\_\_\_,$ leading to a continuously changing composition of the $\_\_\_\_$ over time, making it suitable for the separation of components with significantly different $\_\_\_\_\_\_.$

$8.$ In flash distillation, a feed is partially vaporized in a single step, achieving separation based on differences in $\_\_\_\_\_\_,$ without the need for multiple $\_\_\_\_$ stages or the continuous addition of $\_\_\_\_\_\_.$