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PHASE EQUILIBRIA INVOLVING VAPOUR PRESSURE 221

5.6 Phase equilibria involving
vapour pressure

Why does petrol sometimes have a strong smell
and sometimes not?

Dalton’s law

The acrid smell of petrol on a station forecourt is sometimes overpoweringly strong,
yet at other times it is so weak as to be almost absent. The smell is usually stronger
on a still day with no wind, and inspection shows that someone has spilled some
petrol on the ground nearby. At the other extreme, the smell is weaker when there
is a breeze, which either blows away the spilt liquid or merely dilutes the petrol in
the air.
The subjective experience of how strong a smell is relates to the amount of petrol
in the air; and the amount is directly proportional to the pressure of gaseous petrol.
We call this pressure of petrol the ‘partial pressure’ p (petrol) .
And if several gases exist together, which is the case for petrol in air, then the total
pressure equals the sum of the partial pressures according to Dalton’s law:

p (total) = p i (5.19)
In the case of a petrol smell near a station forecourt, the smell is strong when the
partial pressure of the petrol vapour is large, and it is slight when p (petrol) is small.
These differences in p (petrol) need not mean any difference in the overall pressure
p (total) , merely that the composition of the gaseous mixture we breathe is variable.

SAQ 5.7 What is the total pressure of 10 g of nitrogen gas and 15 g
of methane at 298 K, and what is the partial pressure of nitrogen in the
mixture? [Hint: you must first calculate the number of moles involved.]

Justification Box 5.4

The total number of moles equals the sum of its constituents, so

n (total) = n A + n B + ...

The ideal-gas equation (Equation (1.13)) says pV = nRT; thus p (petrol) V = n (petrol) RT,
so n (petrol) = p (petrol) V ÷ RT.
Accordingly, in a mixture of gases such as petrol, oxygen and nitrogen:

p (total) V p (petrol) V p (oxygen) V p (nitrogen) V
= + +
RT RT RT RT