PHYSICAL CHEMISTRY IN BRIEF

CHAP. 9: CHEMICAL KINETICS [CONTENTS] 295

Example

Two simultaneous reactions proceed in a system:

A

k 1

→ R + 2S + B, (1)

A + B

k 2

→ M + S. (2)

The reaction (1) is first order. The reaction (2) is second order, i.e. first order with respect to

bothAandB. Write the relations for the rate of formation of substancesA,BandS.

Solution

The rate of the first reaction isr 1 =k 1 cA, and the rate of the second reaction isr 2 =k 2 cAcB.

From relation (9.94) we obtain

dcA

dτ

= −r 1 −r 2 =−k 1 cA−k 2 cAcB,

dcB

dτ

= r 1 −r 2 =k 1 cA−k 2 cAcB,

dcS

dτ

= 2r 1 +r 2 = 2k 1 cA+k 2 cAcB.

9.4.3 Material balance in simultaneous reactions

For simultaneous reactions, the material balance equations (9.10) generalize to

cA=cA0+

∑n

i=1

νAixi, (9.95)

whereνAihas the same meaning as in equation (9.94), andxiis an analogy to the quantityx
in equation (9.10) for thei-th reaction.