A $1000$ L CMFR operating at steady state is treating a waste stream containing $500m\frac{g}{L}$ of a contaminant at a volumetric flow rate of $20\frac{L}{m}in.$ The contaminant decays according to a first order reaction with a $k=0\mathrm{.}05mi{n}^{-1}.$ The concentration of contaminant exiting the reactor is $47\mathrm{.}5m\frac{g}{L}.$ You run a pulse tracer experiment to check the behaviour of the reactor and the resulting RTD is shown below:

Time

You give your pulse tracer experiment data to your colleague and ask them to describe the reactor behaviour using the $N-$tanks$-$in$-$series model. Their calculations are messy and either $2$ tanks or $20$ tanks best models the reactor. Perform the necessary calculations to determine which number of tanks is the best model for the reactor behaviour.

$($a$)$ The actual reactor conversion of the contaminant is $1\%$

$($b$)$ For $N=2$ tanks the predicted conversion of the contaminant is

$($c$)$ For $N=20$ tanks the predicted conversion of the contaminant is $\%.$

$($d$)$ tanks$-$in$-$series is the best model for the behaviour of this reactor.