Chapter 17, Problem 17.5P

A step tracer input was used on a real reactor with the following results:

For t ≤ 10 min, then C_T = 0.

For 10 ≤ t ≤ 30 min, then C_T = 10 g/dm³.

For t ≥ 30 min, then C_T = 40 g/dm³.

The second-order reaction A → B with k = 0.1 dm³/mol • min is to be carried out in the real reactor with an entering concentration of A of 1.25 mol/dm³ at a volumetric flow rate of 10 dm³/min. Here, k is given at 325 K.

1. (a) What is the mean residence time t_m?
2. (b) What is the variance σ²?
3. (c) What conversions do you expect from an ideal PFR and an ideal CSTR in a real reactor with t_m?
4. (d) What is the conversion predicted by
   1. (1) the segregation model?
   2. (2) the maximum mixedness model?
5. (e) What conversion is predicted by an ideal laminar flow reactor?