A single completely mixed rectangular reactor is used to treat troublesome waste

Question

A single completely mixed rectangular reactor is used to treat troublesome waste. The tank is 180 cubic meters and has a detention time of 24 hours. The influent concentration is 3.0 moles/liter and the waste can be reduced by 90% when we assume first-order kinetics. What would the effluent concentration and percent reduction be if we fit the reactor with five baffles? These baffles would divide the tank into six equally sized compartments. Also, what would the percent reduction be if the influent concentration to the baffled reactor were doubled?

Explanation / Answer

for a first order CSTRs and 5 reactors in series

CO/C1= (1+KT)

C1= Concentration of reactant at the oultet of the reactor =0.1*3= 0.3 mole/s

Co =3 mol/L

T= V/Vo= 180/Vo

Vo=180/24=7.5m3/min

3/0.3= (1+K*24)

K*24= 29

K= 29/24= 1.21 min-1

for five mixed reactor s in series CN/CO= (1+KT)N

N=number of reactors=6

3/CN= =(1+1.21)6 , CN= Concentration at the outlet of 6th reactor

CN= 3/116.5074=0.025749 moles/L

when CO =6 moles/L ( Concentration is doubled, Rate constant still remains at 1.21 min-1

6/CN= (1+1.21)6

CN= 0.0515

The reduction % = 100*{(0.0515-0.025749)/ 0.0515} =50%

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