Page 221 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 191

Determine the order of the reaction and the rate constant.

Solution
(
Paraldehyde decomposition is represented by CH CHO) →
k 1
3
3
3CH CHO . The stoichiometry of the reaction is of the form
3

A → 3 B. Assuming that the reaction is first order, then the
k 1
rate equation for a constant volume batch system is:
− ( r A ) =− dC A = kC A (3-278)
1
dt
If the reactant and product obey the ideal gas law, the concentration is

C = n A = p A (3-279)
A
V RT
In terms of the partial pressure p ,
A

− dp A = kp A (3-280)
1
dt

Rearranging Equation 3-280 and integrating between the boundary
conditions (at t = 0, p = p and at t = t, p = p ) gives:
A AO A A

p A dp t
∫ − k 1 ∫ dt
p (3-281)
p AO A 0

Equation 3-281 gives

p
ln A =− kt (3-282)
1
p
AO
If n is the number of moles of paraldehyde at time t and n AO , the
A
moles of paraldehyde at t = 0, then at time t, moles of acetaldehyde
from stoichiometry are: