PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 322

Example

A first-order reaction A

k

→ P, wherek = 0.1 hour−^1 , proceeds in a batch reactor. The

initial concentration of the reactant iscA0= 2.6 mol dm−^3. The reaction terminates when the

concentration of the substanceAfalls tocA= 0. 1 mol dm−^3. A total ofnP= 250 moles of the

product is to be produced. What must be the reactor volume and how long will the reaction

proceed?

Solution

cP=cA0−cA= 2. 5 mol dm−^3 =⇒ V =nP/cP= 250/ 2 .5 = 100dm^3.

The reaction time will be calculated from equation (9.24)

τ=

1

k

ln

cA0

cA

=

1

0. 1

ln

2. 6

0. 1

= 32. 58 hours.

9.7.3 Flow reactor.

If the reacting mixture flows through the reactor at a constant flow (volume rate), we have

dV

dτ

=F , (9.166)

whereF is the feed, i.e. the volume of reactants entering the reactor per unit time. By
integrating this relation we obtain

τr=

Vr

F

, (9.167)

whereτris theresidence time, i.e. the time in which the reacting mixture passes through the
reactor, andVris the reactor volume.

Note:Relation (9.167) and the relations ensuing from it do not apply if the total amount

of substance changes in the course of the reaction.