Page 261 - Physical chemistry understanding our chemical world

228 PHASE EQUILIBRIA

Because these two liquids, when mixed, obey Raoult’s law, we
An ideal mixture com- say they form an ideal mixture. In fact, relatively few pairs of
prises a pair (or more) liquids form ideal mixtures: a few examples include benzene and
of liquids that obey
Raoult’s law. bromobenzene, benzene and toluene, bromobenzene and chloroben-
zene, n-pentane and i-pentane. Note how each set represents a pair
of liquids showing a significant extent of similarity.

SAQ 5.8 Benzene and toluene form an ideal mixture, i.e. they obey
◦ O
Raoult’s law. At 20 C, the pressure p of benzene and toluene are 0.747 ×
p O and 0.223 × p O respectively. What is the pressure above a mixture of
these two liquids that contains 12 mol% of benzene?

Worked Example 5.9 (Continuing from Worked Example 5.8.) What are the mole frac-
tions of benzene and bromobenzene in the vapour?

From the definition of mole fraction x in Equation (5.11) above, we say

moles of benzene in the vapour
x (benzene, vapour) =
total number of moles in the vapour phase
The numbers of moles n i are directly proportional to the partial pressures p i if we assume
that each vapour behaves as an ideal gas (we assume here that T , R and V are constant).
Accordingly, we can say

pressure of benzene
x (benzene) =
total pressure

Substituting numbers from Worked Example 5.8:
Note how the units
cancel to yield a dimen- 42.9kPa
x (benzene) =
sionless mole fraction. 77.4kPa
x (benzene) = 0.554

The mole fraction of benzene in the vapour is 0.554, so it contains 55.4
per cent benzene. The remainder of the vapour comprises the second
We need four mole
fractions to define this component bromobenzene, so the vapour contains (100 − 55.4)% =
two-component sys- 44.6% of bromobenzene.
tem – two for the liquid Note how the liquid comprises 43 per cent benzene and 57 per
phases and two for the cent bromobenzene, but the vapour contains proportionately more of
vapour phases. the volatile benzene. We should expect the vapour to be richer in the
more volatile component.

SAQ 5.9 Continuing with the system in SAQ 5.8, what is the mole fraction
of toluene in the vapour above the mixture?

In fact, most liquid mixtures do not obey Raoult’s law particularly well, owing to
molecular interactions.