$4)$ Using a color indicator which shows when the concentration of A falls below $0\mathrm{.}1$mol $/$ liter, the following scheme is devised to explore the kinetics of the decomposition of A$.$ A feed of $0\mathrm{.}6$mol$$A $/$ liter is introduced into the first of the two mixed flow reactor in series each having a volume of $400$ ml$,$ the colour change occurs in the ist reactor for a steady$-$state feed rate of $50$cm$^3/$ min. Find the rate equation for the decomposition of A from this information.