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Chap 1.5
So far, we have dealt entirely with ideal gases. These gases take up no space and have no
interactions. While many gases behave in a nearly ideal way, none are perfectly ideal
and many others are not ideal at all. In order to deal with this fact, a modified form of the
ideal gas equation was developed that contains some empirical constants that take the
size and interactions into account. This is called the Van Der Waals equation:
nRT
n
P
 a 
V  nb
V 
2
Ok, what is going on here? The first term of the equation is simple. It looks just like the
ideal gas equation except that V is reduced by nb. Why? Because real gases take up
volume and so the real volume of space they have to occupy is less that the total volume.
How much less depends on how many molecules there are (n) and the volume of each
molecule (b). You can look up b in a table like Table 1.6 in your book. How about the
other term? This takes into account interactions. As we will discuss later when we look
at reaction kinetics, interactions between molecules tend to depend on the square of the
concentration of the molecules. (This is because the probability of two molecules being
close enough together to interact depends on the probability 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.) Since n/V (the number of molecules in the
volume) is essentially a concentration, this term just says that the interactions between
molecules should be proportional to the concentration of molecules squared. This
equation is still far from perfect, but it is intellectually important because it allows us to
consider the effects that size and interactions should have on ideal gas behavior.