A continuously stirred tank reactor is designed to remove the hazardous waste compound trichloroethylene (TCE) from industrial wastewater. The tank is 3250 liters. The wastewater flows into the tank at 200 L/min with a TCE concentration of 25 mg/L. The reactor decays TCE at a reaction rate of 0.20 min-1 . What is the steady-state concentration of TCE in the treated water leaving the reactor

the steady-state concentration of TCE in the treated water leaving the reactor is 5.88 mg/L  

Explanation:

Given that;

Tank volume v = 3250 liters

wastewater flows into the tank Q = 200 L/min

TCE concentration Co= 25 mg/L

reactor decays TCE at a reaction rate K = 0.20 min-1

mass balance

we know that;

Accumulation = inflow - outflow ± generation

⇒dc/dt = QCo - Qc ± rc.V

now at a steady state; dc/dt = 0

so

0 = QCo - Qc + rcV

where rc = -kc

0 = QCo - Qc - kcV

Qc + kcV = QCo

c(Q + kV) = QCo  

c = QCo / (Q + kV)

so we substitute

c = (200 × 25) / (200 + (0.2×3250))

c = 5000 / 850

c = 5.88 mg/L      

Therefore,  the steady-state concentration of TCE in the treated water leaving the reactor is 5.88 mg/L