Page 88 - Physical chemistry understanding our chemical world

QUANTIFYING THE INTERACTIONS AND THEIR INFLUENCE 55

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then a gas would have a zero volume at −273.15 C. In fact, the molar volume of
a gas is always significant, even at temperatures close to absolute zero. Why the
deviation from Kelvin’s concept?
Every gas consists of particles, whether as atoms (such as neon) or as molecules
(such as methane). To a relatively good first approximation, any atom can be regarded
as a small, incompressible sphere. The reason why we can compress a gas relates to
the large separation between the gas particles. The first effect of compressing a gas
is to decrease these interparticle distances.
Particles attract whenever they approach to within a minimum distance. Whatever
the magnitude of the interparticle attraction, energetic molecules will separate and
continue moving after their encounter; but, conversely, molecules of lower energy do
not separate after the collision because the attraction force is enough to overwhelm the
momentum that would cause the particles to bounce apart. The process of coalescence
has begun.
Compressing a gas brings the particles into close proximity, thereby increasing the
probability of interparticle collisions, and magnifying the number of interactions. At
this point, we need to consider two physicochemical effects that operate in opposing
directions. Firstly, interparticle interactions are usually attractive, encouraging the
particles to get closer, with the result that the gas has a smaller molar volume than
expected. Secondly, since the particles have their own intrinsic volume, the molar
volume of a gas is described not only by the separations between particles but also
by the particles themselves. We need to account for these two factors when we
describe the physical properties of a real gas.
The Dutch scientist van der Waals was well aware that the ideal-
gas equation was simplistic, and suggested an adaptation, which The a term reflects
we now call the van der Waals equation of state: the strength of the
interaction between
gas particles, and the
2
n a b term reflects the
p + (V − nb) = nRT (2.2)
V 2 particle’s size.

where the constants a and b are called the ‘van der Waals constants’, the values
of which depend on the gas and which are best obtained experimentally. Table 2.4
contains a few sample values. The constant a reflects the strength of the interaction
between gas molecules; so, a value of 18.9 for benzene suggests a strong interaction
whereas 0.03 for helium represents a negligible interaction. Incidentally, this latter
value reinforces the idea that inert gases are truly inert. The magnitude of the constant
b reflects the physical size of the gas particles, and are again seen
to follow a predictable trend. The magnitudes of a and b dictate
Equation (2.2) simpli-
the extent to which the gases deviate from ideality.
fies to become the
Note how Equation (2.2) simplifies to become the ideal-gas equa-
ideal-gas equation
tion (Equation (1.13)) if the volume V is large. We expect this
(Equation (1.13))
result, because a large volume not only implies a low pressure, whenever the volume
but also yields the best conditions for minimizing all instances of V is large.
interparticle collisions.