$($Batch reactor $)$ A batch reactor is a reactor of volume V where there areno in and out flow rates. Reactants are loaded instantaneously and thenallowed to react over a time T $,$ called the residence time. Then the contentsare expelled instantaneously. Fermentation reactors and even sacularstomachs of some animals can be modeled as batch reactors. If a chemicalis loaded in a batch reactor and it degrades with rate r$($C$)=$ kC$,$ given inmass per unit time, per unit volume, what is the residence time requiredfor $90$ percent of the chemical to degrade?