A $12,000$ m$3$ well$-$mixed stabilization pond is used to treat municipal wastewater before discharge into a receiving river. The inflow to the pond has a flow rate of Q $=500$ m$3/$day and BOD$5$ concentration of Cin $=200$ mg$/$L$.$ The pond allows time for the decay of BOD with a first$-$order rate constant equal to $0\mathrm{.}2/$day before discharge.

$1)$ What is the BOD concentration at the outflow of the pond, in units of mg$/$L$?$ Answer this question by establishing and solving the mass balance equation for this problem.

$2)$ Now, if three $400$ m$3$ of well$-$mixed ponds are used in series instead of a single $1200$ m$3$ pond as above, what would be the BOD concentration at the final outflow of the pond being discharged to the same receiving river? Note: the same kinetics apply, k $=0\mathrm{.}2$ d$-1$ in all three ponds. Ponds in series mean: the outflow from Pond $1$ enters into Pond $2$ as influent, etc.

$3)$ Compare the final effluent values in $1)$ and $2).$ Incorporate this comparison in your discussion of the reactor performance between the two ideal reactors, i$.$e$.,$ PFR vs$.$ CSTR$.$