PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 323

Example

Every hour, two trucks loaded with clay bricks enter a brick kiln and two trucks loaded with burnt

bricks leave it. The kiln can hold a total of 100 trucks. What is the truck’s residence time in the

kiln?

Solution

The process can be modelled using a plug flow reactor. The “feed” isF = 2 trucks/hour, and

the “volume” is V = 100 trucks. We apply relation (9.167) to obtain

τr=

100

2

= 50hours.

From the definition of the reaction rate (9.4), from the general reaction (9.1), and from the
relation (9.166) it follows that
1
νi

dci

dV

=

r

F

. (9.168)

From this we obtain a relation for the reactor volume

Vr=

1

νi

F

∫ci

ci 0

dci

r

, (9.169)

whereciin the upper limit of the integral is the concentration of the chosen componentiat
the exit from the reactor.

Example

Derive the relation for the volume of a reactor in which a first-order reactionA

k

→ P.proceeds.

Solution

The rate of a first-order reaction isr=kcA. We substitute it into (9.169) and integrate

Vr=

1

− 1

F

∫cA

cA0

dcA

kcA

=

F

k

ln

cA0

cA

.