What volume of PFR (report in m3) is required for steady state removal of 95% of a substance that decays according to first order kinetics with a rate constant of 0.07 d-1

The volume of the PFR is 4.28m3

Explanation: A Plug Flow Reactor (PFR) is a type of reactor that has a steady state flow. Therefore the flow rate is a constant, which is always measured in liters.

In a PFR, the rate of conversion is always dependent on the rate of flow.

For any PFR to have a conversion rate of 90% and above, that means the flow rate should be 100l/min or 100l/day depending on the rate constant.

Therefore since our conversation is 95% and our rate constant is 0.07per day, that means our flow rate is 100liters/day

The equation for a first order PFR is

dFa/dV = Ra(1)

To calculate volume, the equation becomes

(R/K) ln(Cao/Ca) = V(2)

R = flow rate = 100l/day = 0.1m3/day

K= rate constant = 0.07/day

Cao= initial conversion rate

Ca = conversion rate = 95%

V= volume

STEP 1: FIND Cao,

Cao + Ca = 100%

Cao = 100% - 95%= 5% = 0.05

Therefore

0.05 = Ca/ Cao

Ca = 0.05Cao(3)

STEP3 : Find the volume.

Using equation 2 and substituting equation 3 in equation 2.

(0.1m3/day ÷ 0.07/day)ln(Cao/0.05Cao) =

1.43m3 × ln20 = 4.98m3

Therefore the volume of the PFR is

4.98m3