a$)$ A reactor is designed to destroy pathogens in water by using chlorine. For a volumetric flow

rate of $4500\frac{L}{m}in,$ a minimum contact time of $40$ minutes is required to reduce the

pathogen concentration from $100$ pathogens$/$L to below $1$ pathogen$/$L through a first order

decay process. Note that the respective PFR and CMFR model is given as

$k\frac{V}{Q}$ and $C_{\text{o}\text{u}\text{t}}=\frac{C_{in}}{1+k\frac{V}{Q}}.$

$($i$)$ Determine the first$-$order decay rate constant, $k,$ if the reactor is a PFR$.$

$($ii$)$ Calculate the minimal size of the reactor required for a PFR$.$

$($iii$)$ Solve the size of a CMFR required to reach the same outlet concentration.

$($iv$)$ Recommend the most suitable type of reactor, if it was known that the reactor would

receive variable inlet concentrations and it was pertinent that the discharge could

never be greater than $1$ pathogen$/$L$.$ Give reasons for your recommendations.

b$)$ The BOD concentration in a river just downstream of a sewage treatment plant's effluent

pipe is $75m\frac{g}{L}.$ If the BOD is destroyed through a first$-$order reaction with rate constant

equal to $0\mathrm{.}05/$day$,$ solve the BOD concentration $50km$ downstream. Note that the velocity

of the river is $15k\frac{m}{?}$ day.