PHYSICAL CHEMISTRY IN BRIEF

CHAP. 7: PHASE EQUILIBRIA [CONTENTS] 188

7.4.5 Material balance

Let us have a system composed ofkcomponents andfcoexisting phases. Each component of
this system must satisfy the balance equation

ni=

∑f

j=1

x(ij)n(j), i= 1, 2 ,... , k , (7.8)

whereniis the amount of substance of componentiin the system,x(ij)is the molar fraction of
theithcomponent in thejthphase, andn(j)is the total amount of substance in thejthphase,

n(j)=

∑k

i=1

n(ij), j= 1, 2 ,... , k. (7.9)

Heren
(j)
i is the amount of substance of thei
thcomponent in thejthphase.

Example

If we mix 4 moles of methanol (1) and 6 moles of n-hexane (2) at 25◦C and a standard pressure,

two liquid phases will be formed of the compositionx( 1 `^1 )= 0. 10 andx( 1 `^2 )= 0. 86. Calculate the

amount of substance of the resulting phases.

Solution

Substituting into (7.8) gives

4 = 0. 1 n(`^1 )+ 0. 86 n(`^2 ),

6 = 0. 9 n(`^1 )+ 0. 14 n(`^2 ),

From this we calculaten(`^1 )= 6. 05 mol andn(`^2 )= 3. 95 mol.

7.4.5.1 Lever rule.

In a two-phase system, the material balance can be interpreted using the so-called lever rule.
From Figure7.2it is evident that a two-component mixture of global compositionZ 1 at tem-
peratureT 1 splits into two phases of the compositionx( 1 γ)andx( 1 β). The amounts of substance