PHYSICAL CHEMISTRY IN BRIEF

CHAP. 8: CHEMICAL EQUILIBRIUM [CONTENTS] 260

Solution

Let us useξ 1 to denote the equilibrium extent of the first isomerization reaction, which can be

recorded as

0 =A 2 −A 1

andK 1 to denote its equilibrium constant.

Similarly for the second reaction

0 =A 3 −A 1

we useξ 2 to denote the equilibrium extent of reaction andK 2 to denote the equilibrium constant.

The material balance can be carried out in two steps: at first the first reaction proceeds until

equilibrium, and only then the second reaction starts.

Substance ni, 0 amount of substances amount of substances

after 1streaction at equilibrium

A 1 1 1 −ξ 1 1 −ξ 1 −ξ 2

A 2 0 ξ 1 ξ 1

A 3 0 0 ξ 2

For the equilibrium constants we write [see (8.15)]

K 1 =

ξ 1

1 −ξ 1 −ξ 2

(

p

pst

∑k

i=1ni

) 0

=

ξ 1

1 −ξ 1 −ξ 2

and

K 2 =

ξ 2

1 −ξ 1 −ξ 2

(

p

pst

∑k

i=1ni

) 0

=

ξ 2

1 −ξ 1 −ξ 2

8.6.2 Chemical equilibrium of a complex system

When solving the task of finding the equilibrium composition in a system in whichmchemical
reactions may proceed withkchemical substances involved, we search for the minimum Gibbs