Aerobacter aerogenes is cultivated in a $3$m$3$ bioreactor with a diameter of $1\mathrm{.}5$ m$.$ A pre$-$aerated fresh nutrient medium containing dissolved oxygen at a concentration of $0\mathrm{.}01$ moles$/$m$3$ enters the bioreactor at a flow rate of $1\mathrm{.}8$ m$3/$h$.$ Under steady$-$state conditions, the bioreactor operates at a $5$ kg$/$m$3$ cell concentration. a$.$ Determine the KLa required to ensure a dissolved oxygen concentration of $0\mathrm{.}05$ mole$/$m$3$ in the bioreactor. b$.$ What minimum KLa is required if the bioreactor's critical oxygen concentration is $0\mathrm{.}01$ mole$/$m$3?$ DATA: Specific oxygen uptake rate $=20$ moles O$2/$kg cells$$h$.$

Show all the steps and calculations clearly, the ansers should match these:Start by writing mass balance for oxygen in the bioreactor. $$ Estimate C$*$ using Henry$$s law and then kLa. Answers: $($a$)$ kLa $=0\mathrm{.}136$ s$-1,($b$)($kLa$)$min $=0\mathrm{.}113$ s$-1.$