PHYSICAL CHEMISTRY IN BRIEF

CHAP. 8: CHEMICAL EQUILIBRIUM [CONTENTS] 230

Note:The degree of conversion is an intensive quantity.

U Main unit:dimensionless quantity.

Example

The following reaction proceeds in a closed system

0 =SO 3 (g)−SO 2 (g)−

1

2

O 2 (g).

What is the extent of reaction of a system at equilibrium if there is initially

a) 1 mol SO 2 and 1 mol O 2 ,

b) 2 mol SO 2 and 3 mol O 2 , 4 mol SO 3 and 20 mol N 2 in the system?

Solution

If we useξto denote the extent of reaction andni,eqto denote the amount of thei-th component

at equilibrium, then

Substance ni, 0 ni,eq ni, 0 ni,eq

a) b)

SO 2 1 1−ξ 2 2 −ξ

O 2 1 1−^12 ξ 3 3−^12 ξ

SO 3 0 ξ 4 4 +ξ

N 2 0 0 20 20

∑k

i=1ni 2 2−

1

2 ξ 29 29−

1

2 ξ

In the case a)ξis a number between 0 and 1. In the case b), when the products are also present

in the initial mixture, the reaction may also proceed in the opposite direction andξ∈(− 4 ,2).

• Material balance at constant volume
  When a reaction proceeds in the gas phase in a closed system at constant temperature and
  volume with a change in the total amount of substance (and thus also pressure), and if ideal
  behaviour may be assumed, pressure is often balanced instead.