Page 17 - Instant notes

Perfect gases 3

The four parameters are not independent, and the relations between them are expressed in
the gas laws. The gas laws are unified into a single equation of state for a gas which
fully expresses the relationships between all four properties. These relationships,
however, are based on approximations to experimental observations, and only apply to a
perfect gas. In what might be deemed a circular argument, a perfect gas is defined as one
which obeys the perfect gas equation of state. In practical terms, however, adherence to
the perfect gas equation of state requires that the particles which make up the gas are
infinitesimally small, and that they interact only as if they were hard spheres, and so
perfect gases do not exist. Fortunately, it is found that the behavior of most gases
approximates to that of a perfect gas at sufficiently low pressure, with the lighter noble
gases (He, Ne) showing the most ideal behavior. The greatest deviations are observed
where strong intermolecular interactions exist, such as water and ammonia. The behavior
of non-ideal gases is explored in topic A3.

The perfect gas equations

Historically, several separate gas laws were independently developed:
Boyle’s law; p.V=constant at constant temperature;

Charles’ law; at constant pressure;
Avogadro’s principle; at constant pressure and temperature.

These three laws are combined in the perfect gas equation of state (also known as the
ideal gas law or the perfect gas equation) which is usually quoted in the form
pV=nRT

As written, both sides of the ideal gas equation have the dimensions of energy where R is
−1
−1
the gas constant, with a value of 8.3145J K mol . The perfect gas equation may also
be expressed in the form pV m=RT, where V m is the molar gas volume, that is, the volume
occupied by one mole of gas at the temperature and pressure of interest. The gas laws are
illustrated graphically in Fig. 1, with lines representing Boyle’s and Charles’ laws
indicated on the perfect gas equation surface.
The gas constant appears frequently in chemistry, as it is often possible to substitute f
or temperature, pressure or volume in an expression using the perfect gas equation—and
hence the gas constant—when developing mathematical expressions.

Partial pressure

When two or more gases are mixed, it is often important to know the relationship
between the quantity of each gas, the pressure of each gas, and the overall pressure of the
mixture. If the ideal gas mixture occupies a volume, V, then the pressure exerted by each
component equals the pressure which that component would exert if it were alone in that
volume. This pressure is called the partial pressure, and is denoted as p A for component