Question

Four MFR’s are operated in series the total space time is 5 minutes. If it is replaced by a single PFR, What will be the space time? First order reaction with rate constant 2 min^-1, concentration reduces from 50 to 10 mol/m^3.

(a) 0.805

(b) 0.123

(c) 0562

(d) 0.439

I have been asked this question in my homework.

This interesting question is from Choosing of Right Reactor Series or Connections (Maximum Profitability) in division Ideal Reactors for a Single Reaction, Conversion and Reactor Sizing of Chemical Reaction Engineering

Answer 1

Correct option is (a) 0.805

Easy explanation: The design equation of PFR is τ = \(\int_{CA0}^{CAf}\frac{-dCA}{-rA} \)

For the 1^st order reaction the equation is simplified as kτ = -ln⁡(\(\frac{CA}{CA0}\))

τ = -0.5ln⁡(\(\frac{10}{50}\)) = 0.805 minutes.