Page 153 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 123

Figure 3-6 shows that a plot of

   C  C (  BO − C ) + C 
A 
AO
ln   AO   


   C BO  C A 
versus time t gives a straight line with the slope k(C BO – C AO ). If
C BO is much larger than C AO , then the concentration of B remains
approximately constant, and Equation 3-49 approaches Equations
3-33 or 3-38 for the first order reaction. Therefore, the second order
reaction becomes a pseudo-first order reaction.

Case 2

Case 2 involves a system with a single reactant. In this case, the
rate at any instant is proportional to the square of the concentration
k
of A. The reaction mechanism is 2A → products. The rate expres-
sion for a constant volume batch system (i.e., constant density) is

− ( r A )= −dC A = kC 2 A = kC 2 AO (1 − X A ) 2 (3-50)
dt

Figure 3-6. Test for the reaction A + B → products.