Page 229 - Modeling of Chemical Kinetics and Reactor Design

Reaction Rate Expression 199

Example 3-8
The hydrolysis of methyl acetate is an autocatalytic reaction and is
first order with respect to both methyl acetate and acetic acid. The
reaction is elementary, bimolecular and can be considered irreversible
at constant volume for design purposes. The following data are given:

• Initial concentration of methyl acetate = 0.45 gmol/l
• Initial concentration of acetic acid = 0.045 gmol/l

The conversion in 1 hr is 65% in a batch reactor. Calculate (1) the
rate constant and specify the rate equation, (2) the time at which the
rate passes through the maximum, and (3) the type of optimum reactor
3
system needed for the plant to process 200 m /hr. What would be the
reactor volume in this system?

Solution

The hydrolysis of methly acetate can be represented by

CH COOCH + H O  → CH COOH + CH OH

k 1
3
3
3
2
3
( A) ( B)
That is, A → B. For an autocatalytic reaction A + B → B + B and
the rate of disappearance of species A is

− ( r ) =− dC A = kC C (3-295)
A 1 A B
dt
The solution for an autocatalytic reaction is

θ + X
k t
ln B A = C ( AO + C BO) 1 (3-296)
θ (1 − X A )
B
where

.
θ = C BO = 0 045 =01 . at t = 1 hr, X = 0.65
B
C AO 045 A
.