Kinetic-Molecular Theory
The ideal gas equation
pV = nRT
Has been presented as a compliation of empirical observation, i.e. the historically
significant Gas Laws, but does The Ideal Gas equation have some deeper, more
fundamental meaning?
The Kinetic-Molecular Theory ("the theory of moving molecules"; Rudolf Clausius,
1857)
1. Gases consist of large numbers of molecules (or atoms, in the case of the noble
gases) that are in continuous, random motion. Usually there is a great distance
between each other, so the molecules travel in straight lines between abrupt
collisions at the walls and between each other. These collisions randomize the
motion of the molecules. Most of the collisions between molecules are binary,
in that only two molecules are involved.
2. The volume of the molecules of the gas is negligible compared to the total
volume in which the gas is contained. A common bond length between atoms is
about 10-10 m or 1 Angstrom. Small molecules are therefore on the order of 10
Angstroms in diameter, or less than 10-24 Liters in Molecular Volume, quite tiny
indeed! Remember, however that there can be a great many molecules in the
sample of gas, perhaps on the order of a mole, or 6 x 1023. So that when
concentrations of molecules exceed about 1 mol/liter, then the approximation
that the volume of ALL the molecules in the container is much less than the
volume of the container itself, fails. In the case of an ideal gas, we will assume
that molecules are point masses, i.e., the volume of a mole of gas molecules (as
if they were at rest) is zero, so molecular and container volumes never become
comparable.
3. Attractive forces between gas molecules are negligible. We know that if these
forces were significant, the molecules would stick together. This happens when
it rains and gaseous water molecules stick together to form a liquid. Water
vapor is a condensible gas, and this shows us that gas molecules are sticky, but
at a high enough temperature they form only a permanent gas, because their
stickiness can be considered negligible. We will assume that in an ideal gas,
molecular attractive forces are not just small, but identically zero.
Consequences:
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The average kinetic energy of the molecules does not change with time. The
molecules bounce and bounce but, on average, do not slow down as long as the
temperature of the gas remains constant. Energy can be transferred between
molecules during collisions but not lost because the collisions are perfectly
elastic (not sticky)
The average kinetic energy of the molecules is proportional to absolute
temperature (A result of Thermodynamics). At a given temperature the
molecules of all species of gas, no matter what size shape or weight, have the
same average kinetic energy.