Gases

Gas Laws
Boyle's Law
At a constant temperature and pressure, the volume occupied by a fixed amount of gas is inversely proportional to the applied (external) pressure.

V = (1/P) * constant

Charles's Law
At a constant pressure the volume occupied by a fixed amount of gas is directly proportional to its absolute temperature.

V = constant * T

Combined Gas Law
Combining the relationships in Charles's and Boyle's gives the combined gas law which is:
V = constant * (T/P)

The relationship between pressure and temperature for a gas is:

P = T * constant

(At constant volume, the pressure exerted by a fixed amount of gas is directly proportional to the absolute temperature.)

Avogadro's Law
At fixed temperature and pressure, equal volumes of any ideal gas contain equal numbers of particles (or moles).
Thus we can see that:
At a fixed temperature and pressure, the volume occupied by a gas is directly proportional to the amount (mol) of a gas. So

V = constant * n
(n=number of moles)

The Ideal Gas Law
Combining all these relationships together we get:

PV = nRT

Where R is the universal gas constant and = 0.0821, in units of (atm*L)/(mol*K).


Extensions of the Ideal Gas Law
Finding the Density of a Gas
Because number of moles = (mass/molar mass)

n=m/M

we can rearrange the ideal gas law from

PV = nRT

to

PV = (m/M)RT

and because density(d) = m/V we can rearrange the formula to see that:

m/V = d = MP/RT

Finding Molar Mass of a Gas
Rearranging the ideal gas law again:

n = PV/RT

As n = m/M,

M= mRT/PV

or (as m/V = d)

Deviations from ideal behavior
These relationships ignore the intermolecular attractions between molecules of a gas because under normal conditions they are so small as to be insignificant. However, under very high pressures the molecules of a gas are forced closer together, so the attractions between them are much stronger and the gas' behavior is affected. The same applies at very low temperatures, where the kinetic energy of the molecules is much lower and no longer enough to overcome intermolecular attractions.