to be the ideal gas equation except that the volume Vis reduced by the
quantity nb. The inclusion of a term that reduces the volume reflects the
fact that real gases occupy a certain volume, and so the volume of space
they have to occupy is less that the total volume. The reduction of volume
depends both on how many molecules are present (n) and the volume of
each gas molecule (b). The second term of eqn 1.20 incorporates the inter-
actions between molecules. The fraction n/Vis essentially the concentration
of the gas. The effect of the interaction between gases is approximately
dependent upon the product of the interaction strength, a, and the con-
centration of the gas molecules, n/V, squared. This dependence upon the
concentration arises from the argument that the probability of two mole-
cules being close enough together to interact depends on the probabil-
ity of molecule A and molecule B both being in a small volume element.
Each of these probabilities depends on the concentration, so the probability
of both molecules being in the small volume element is proportional to
the concentration squared. The parameter is a measure of the ion. These
modifications of the ideal gas equation are not perfect but they provide a
useful means of considering the effects that size and interactions should
have on ideal gas behavior. Each of these parameters, aand b, has been
determined for each type of gas molecule; for example, oxygen has values
of 1.36 L^2 atm mol−^1 and 0.032 L mol−^1 for aand brespectively whereas
helium, which is smaller and interacts much more weakly, has values of
0.034 L^2 atm mol−^1 and 0.024 L mol−^1 (Table 1.3).
Liquifying gases for low-temperature spectroscopy
The existence of interactions between gases is most evident by the fact
that gases can be condensed into liquids by reducing the temperature to
below a certain critical temperature. For example, we know that water boils
when it is brought to a temperature of 100°C at atmospheric pressures.
Gases can be liquefied by suddenly changing the pressure (Figure 1.4).
12 CHAPTER 1 BASIC THERMODYNAMIC AND BIOCHEMICAL CONCEPTS
Table 1.3
van der Waals parameters for gases.
Gas a(L^2 atm mol−−^1 ) b(L mol−−^1 )
Argon 1.35 0.032
Carbon dioxide 3.60 0.043
Ethane 5.49 0.064
Helium 0.034 0.024
Hydrogen 0.244 0.027
Nitrogen 1.39 0.039
Oxygen 1.36 0.032
