$(10$ points$)$ A water tower containing $4,000m^3$ of water has been taken out of service for

installation of a chlorine monitor. The concentration of chlorine in the water tower was $2\mathrm{.}0m\frac{g}{L}$

when the tower was taken out of service. If the chlorine decays by first$-$order kinetics with a rate

constant $k=1\mathrm{.}0d^{-1}($Grayman and Clark, $1993),$ what is the chlorine concentration when the tank

is put back in service $8$ hours later? What mass of chlorine $($in kg $)$ must be added to the tank to

raise the chlorine level back to $2\mathrm{.}0m\frac{g}{L}?$ Although it is not completely mixed, you may assume

the tank is a completely mixed batch reactor.