c02 JWBS043-Rogers September 13, 2010 11:23 Printer Name: Yet to Come

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REAL GASES:

EMPIRICAL EQUATIONS

The ideal gas laws are based on two assumptions, neither of which is true. First,

atoms or molecules comprising the ideal gas are assumed to have no volume. They

are treated as mathematical point masses for convenience. Second, they are assumed

to have no interactions with each other. Attractive and repulsive forces are ignored

by setting them to zero.

2.1 THE VAN DER WAALS EQUATION

The Dutch physicist van der Waals remedied both of these failures. He treated the first

of them by simply subtracting an empirical parameter taken to represent the volume

of the particles, called theexcluded volume b, from the total volumeVof the gas to

leave aneffective volumeof (V–b). There is less space for each molecule to move in

because of the space taken up by its neighbors.

Attractive and repulsive forces often operate through an inverse square law. For

example, gravitational force on massesm 1 andm 2 at a separation ofris

F=G

m 1 m 2

r^2

whereGis the gravitational constant. The constantsG,m 1 , andm 2 can be grouped

as a single constantkin the numerator to give an attractive or repulsive forceFthat

varies asF=k/r^2. Van der Waals reasoned that thedistancebetween gas particles

Concise Physical Chemistry,by Donald W. Rogers

Copyright©C2011 John Wiley & Sons, Inc.

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