Question

A reaction 2A --> B takes place in solution and is second order (d[A]/dt = -k[A]2 ). The required degree of conversion is 99%, and this takes place in 10 minutes batch wise. Determine: (a) What would be the necessary detention time in a PFR? (b) What would be the necessary detention time in a CSTR?

Answer 1

given that,

rate = k (A)²

For batch or PFR , the retention time will be the same.

Given that t= 10 min

Here k is unknown.

Batch reactor:

Let Initial conc = 100 M

Final concentration = 1 M

For second order rate law in PFR

( 1/ C_final - 1/C_initial ) = k xt

1- 0.01 = k x 10

k = 0.99/10 == 0.099 M^-1s^-1

Now, as detention time for PFR and BATCH reactor are same.

Detention time for PFR = 10 min

(2) CSTR:

Governing equation:

kt = ( C_initial - C_final ) / (C_final )²

0.099 x t = (100 -1 )/ ( 1)²

t= 99 /0.099

= 1000 min

For CSTR t= 1000 min