Page 64 - Physical chemistry understanding our chemical world

PROPERTIES OF GASES AND THE GAS LAWS 31

Table 1.4 The average speeds of gas
molecules at 273.15 K, given in order of
increasing molecular mass. The speeds
c are in fact root-mean-square speeds,
obtained by squaring each velocity, tak-
ing their mean and then taking the square
root of the sum
Gas Speed c/ms −1
Monatomic gases
Helium 1204.0
Argon 380.8
Mercury 170.0
Diatomic gases
Hydrogen 1692.0
Deuterium 1196.0
Nitrogen 454.2
Oxygen 425.1
Carbon monoxide 454.5
Chlorine 285.6
Polyatomic gases
Methane 600.6
Ammonia 582.7
Water 566.5
Carbon dioxide 362.5
Benzene 272.8

Worked Example 1.5 What is the molar volume of neon, assuming it to be a straight-
forward solid?
We must first note how the neon must be extremely cold if it is to be
The ‘molar volume’ is
a solid – probably no colder than about 20 K.
We know that the radius of a neon atom from tables of X-ray crystal- thenamewegiveto
lographic data is about 10 −10 m, so the volume of one atom (from the the volume ‘per mole’.
4
3
3
equation of a sphere, V = πr )is 4.2 × 10 −30 m . If we assume the
3
neon to be a simple solid, then 1 mol of neon would occupy a volume of 4.2 × 10 −30 m 3
23
3
−1
per atom × 6.022 × 10 atoms per mole = 2.5 × 10 −6 m mol . This volume represents
−1
3
2.5cm mol .
3
A volume of 2.5cm mol −1 is clearly much smaller than the value we calculated
earlier in Worked Example 1.3 with the ideal-gas equation, Equation (1.13). It is
also smaller than the volume of solid neon made in a cryostat,
suggesting the atoms in a solid are also separated by much empty By corollary, if the gas
space, albeit not so widely separated as in a gas. particles move fast and
the gas is ideal, the gas
In summary, we realize how each particle of gas has enor-
particles must travel in
mous kinetic energy and are separated widely. Yet, like popcorn
straight lines between
in a popcorn maker, these particles cannot be classed as wholly
collisions.
independent, one from another, because they collide. They collide