Page 307 - Modeling of Chemical Kinetics and Reactor Design

Introduction to Reactor Design Fundamentals for Ideal Systems 277

N =2 N X (5-49)
B AO A
ε is the fractional change in volume of the system between no
A
conversion and complete conversion of reactant A given by

V X A =1 − V X A =0
ε = (5-20)
A
V X A =0
For the gas phase reaction A → 2B, ε = (2 – 1)/1 =1 or
A

V= V (1 + ε X ) (5-18)
O A A
Since two moles of B are formed for every mole of A that dis-
appears, then the mole balance table becomes

Mole initially
Component at time t = 0 Moles at t = t
A N N = N (1 –X )
AO A AO A
B 0 2N X
AO A
Total moles N N (1 + X )
AO AO A
Volume V V (1 + X )
O O A
The batch reactor design equation for component A is

− ( r A )=− 1 dN A = kC 2 A (5-50)
V dt

Substituting Equations 5-9, 5-10, and 5-18 into Equation 5-50 yields

N

− ( r )= N AO dX A =  AO − (1 X A )  2
k
A (5-51)
V O (1 + X A ) dt  V O (1 + X A ) 


Rearranging Equation 5-51 gives
1+ ( X A )dX A N AO

1− ( X A ) 2 = k V O dt (5-52)