The Ideal Gas Law
The pressure of a gas varies in direct proportion
to the concentration of gas molecules and to the
temperature of the gas. The proportionality
constant is Boltzmann's constant. p = ρRT
...where ρ is density (kg/m³), p is pressure in N/m²,
T is temperature, and k_B is Boltzmann's Constant.

Boltzmann's Constant
k_B = 1.38 * 10^-23 J/K
This constant relates temperature to the thermal
energy of motion of single molecules. This constant
is probably one of the most frequently used
constants in descriptions of gases and their mechanical
and thermodynamic behavior.

The Universal Gas Constant is related to
Boltzmann's Constant in that it also relates temperature
with energy. The difference being that the Universal
Gas Constant expresses energy in per mole of gas,
rather than energy per molecule. Therefore, it can
be defined in terms of Boltzmann's Constant and
Avogadro's Number.

Avogadro's Number (6.0225 * 10²³ molecules/mole)
defines a mole of a substance. A mole is the amount of a
substance that contains as many atoms, molecules, ions,
or other elementary units as the number of atoms in
0.012 kilogram of carbon 12. The number is 6.0225 × 10²³,
or Avogadro's number. Also called gram molecule.

The Maxwell-Boltzmann Velocity Distribution Function
implies that the average, or most probable (for you quantum physicists),
velocity of a molecule in a gas is directly proportional
to the square root of the temperature of the gas and inversely
proportional to the square root of the mass of the molecule.