The state of any amount of substance is something which chemists often
find it necessary to specify clearly. Such a specification for even the simplest
substance must include at least n, the amount of substance present; p, the
pressure, and T, the temperature. In most cases it is found convenient to
specify a standard state of a system as well. As a standard, the choice of
n = 1 is universal; however, the pressure is commonly chosen as either p
= 100 kPa (1 bar) or as p = 101.325 kPa (1 atm). The temperature is commonly
chosen as either T = 298.15 K (25^{o}C) or as T = 273.15 K (0^{o}C).
Throughout this text the values of p = 100 kPa and T = 298.15 K will be used
as standard. For gases, other works may employ STP (standard temperature
and pressure) as p = 101.325 kPa and T = 273.15 K, or SATP (Standard Ambient
Temperature and Pressure) where p =101.325 kPa and T = 293.15 K.

Ideal Gas Law 
The simplest known equation of state, which is an equation linking
at least the three properties of temperature, pressure, and volume of a chemical
system, is the ideal gas law, pV = nRT. This equation accurately describes
an ideal gas, but it describes a real gas such as oxygen or carbon dioxide
accurately only at pressures below atmospheric. As the pressure increases
or the temperature decreases, real gases are found to deviate significantly
from the behavior expected of ideal gases.

Many more complex equations of state have been proposed to describe
the behavior of gases, liquids, and solids but their physical interpretation
is often not obvious. We will consider only one of them, the van der Waals
equation.

van der Waals Equation 
In 1873, Johannes van der Waals, a physics professor at the University
of Amsterdam, developed an equation to account more accurately for the behavior
of real gases. It was considered a sufficiently important development to
justify the award of the Nobel Prize in 1910. The van der Waals equation is
the second most simple equation of state; only the ideal gas law is simpler.
It is used to describe the behavior of gases when pressures are higher, or
temperatures are lower, than those at which the ideal gas law is sufficiently
accurate. The van der Waals equation describes the relationship between the
physical quantities of pressure, temperature, and volume more accurately
than does the ideal gas law. It does so, however, at the cost of a more complex
equation and the use of a unique set of two van der Waals coefficients for
each different gas. The usual form of the van der Waals equation is:

(p + (n2a/V2))(V  nb) = nRT

In the van der Waals equation, the term n2a/V2 reflects the fact that
the attractive forces between molecules are not zero. The measured pressure
is thus less than it should be because the attractive forces act to reduce
it. The term nb reflects the fact that the volume of the molecules of a real
gas is not zero, and so the volume in which the molecules may move is less
than the total measured volume. A table of the van der Waals coefficients
for several common gases is included in this section. 