Page 151 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 121

Equation 3-39 shows that in the first order reactions, the half-life
is independent of the concentration of the reactant. This basis can be
used to test whether a reaction obeys first order kinetics by measur-
ing half-lives of the reaction at various initial concentrations of
the reactant.

SECOND ORDER REACTIONS

A second order reaction occurs when two reactants A and B interact
in such a way that the rate of reaction is proportional to the first power
of the product of their concentrations. Another type of a second order
reaction includes systems involving a single reactant. The rate at any
instant is proportional to the square of the concentration of a single
reacting species.

Case 1

k
Consider the reaction A B+ → products. The rate equation for a
constant volume batch system (i.e., constant density) is:

− ( r A ) = −dC A = −dC B = kC C B (3-40)
A
dt dt
The amount of A and B that have reacted at any time t can be
described by the following mechanism and set of equations.
From stoichiometry:
A B

Amount at time t = 0 C AO C BO
Amount at time t = t C A C B
Amounts that have reacted C – C C – C
AO A BO B

C = C – (C – C ) (3-41)
B BO AO A
Substituting Equation 3-41 into Equation 3-40, rearranging and
integrating between the limits gives

C A −dC t
∫
∫ A )] = kdt (3-42)
[
CC BO − (C AO − C A
A
C AO 0