Page 87 - Physical chemistry understanding our chemical world

54 INTRODUCING INTERACTIONS AND BONDS

somewhat, writing it as
pV = Z × (nRT ) (2.1)

where Z is the compressibility or compressibility factor. The value
We sometimes call the
of Z will always be one for an ideal gas, but Z rarely has a value
function ‘pV ÷ nRT’ of one for a real gas, except at very low pressures. As soon as p
the ‘compressibility’
increases, the gas molecules approach close enough to interact and
or ‘compressibility fac-
tor’ Z. pV = nRT . The value of Z tells us a lot about the interactions
between gas particles.

Aside

−1
−1
The gas constant R is generally given the value 8.314 J K mol , but in fact this
numerical value only holds if each unit is the SI standard, i.e. pressure expressed in
pascals, temperature in kelvin and volume in cubic metres.
The value of R changes if we express the ideal-gas equation (Equation (1.13)) with
different units. Table 2.3 gives values of R in various other units. We must note an
important philosophical truth here: the value of the gas constant is truly constant, but
the actual numerical value we cite will depend on the units with which we express it.
We met a similar argument before on p. 19, when we saw how a standard prefix (such as
3
3
3
deca, milli or mega) will change the appearance of a number, so V = 1dm = 10 cm .
In reality, the number remains unaltered.
We extend this concept here by showing how the units themselves alter the numerical
value of a constant.
Table 2.3 Values of the gas constant R
expressed with various units a
8.3145 J K −1 mol −1
2 cal K −1 mol −1
3
0.083 145 dm bar mol −1 K −1
3
83.145 cm bar mol −1 K −1
3
0.082 058 dm atm mol −1 K −1
3
82.058 cm atm mol −1 K −1
5
a 1bar = p O = 10 Pa. 1 atm = 1.013 25 × 10 5
Pa. The ‘calorie’ is a wholly non-SI unit of energy;
1 cal = 4.157 J.

Why is the molar volume of a gas not zero at 0 K?

The van der Waals equation

In Chapter 1 we recalled how Lord Kelvin devised his temperature scale after cooling
gases and observing their volumes. If the simplistic graph in Figure 1.5 was obeyed,