Question

For a first order reaction, where k is the first order rate constant, the conversion for N tanks in series is obtained as ____

(a) XA = 1-\(\frac{1}{(1+\frac{τk}{N})^N} \)

(b) XA = 1+\(\frac{1}{(1+\frac{τk}{N})^N} \)

(c) XA = \(\frac{1}{(1+\frac{τk}{N})^N} \)

(d) XA = \(\frac{1}{(1+\frac{τk}{N})^N} \)– 1

The question was posed to me by my school principal while I was bunking the class.

I'm obligated to ask this question of Tanks in Series Model in chapter Compartment Models, Models for Non Ideal Reactors of Chemical Reaction Engineering

Answer 1

Correct choice is (a) XA = 1-\(\frac{1}{(1+\frac{τk}{N})^N} \)

The best explanation: For N tanks in series, the combination approaches non – ideal PFR behaviour. The concentration in the N^th CSTR is given as CN = \(\frac{C_0}{(1+ τk)^N}.\frac{C_N}{C_0} = \frac{1}{(1+ τk)^N}.\) XA = 1 – \(\frac{C_N}{C_0}.\) For N – tanks, XA = 1-\(\frac{1}{(1+\frac{τk}{N})^N}. \)