Gas Laws

The Ideal Gas Law relates pressure, volume, molecular quantity, and temperature of an ideal gas together in one neat mathematical expression:

P V = nRT

Where,

P = Absolute pressure (atmospheres)

V = Volume (liters)

n = Gas quantity (moles)

R = Universal gas constant (0.0821 L · atm / mol · K)

T = Absolute temperature (K)

An alternative form of the Ideal Gas Law uses the number of actual gas molecules (N) instead of the number of moles of molecules (n):

P V = NkT

Where,

P = Absolute pressure (atmospheres)

V = Volume (liters)

N = Gas quantity (moles)

k = Boltzmann’s constant (1.38 × 10−23 J / K)

T = Absolute temperature (K)

Although no gas in real life is ideal, the Ideal Gas Law is a close approximation for conditions of modest gas density, and no phase changes (gas turning into liquid or visa-versa).

Since the molecular quantity of an enclosed gas is constant, and the universal gas constant must be constant, the Ideal Gas Law may be written as a proportionality instead of an equation:

P V ∝ T

Several “gas laws” are derived from this Ideal Gas Law. They are as follows:

P V = Constant Boyle’s Law (assuming constant temperature T)

V ∝ T Charles’s Law (assuming constant pressure P)

P ∝ T Gay-Lussac’s Law (assuming constant volume V )

You will see these laws referenced in explanations where the specified quantity is constant (or very nearly constant).

For non-ideal conditions, the “Real” Gas Law formula incorporates a corrected term for the

compressibility of the gas:

P V = ZnRT

Where,

P = Absolute pressure (atmospheres)

V = Volume (liters)

Z = Gas compressibility factor (unitless)

n = Gas quantity (moles)

R = Universal gas constant (0.0821 L · atm / mol · K)

T = Absolute temperature (K)

The compressibility factor for an ideal gas is unity (Z = 1), making the Ideal Gas Law a limiting case of the Real Gas Law. Real gases have compressibility factors less than unity (< 1). What this means is real gases tend to compress more than the Ideal Gas Law would predict (i.e. occupies less volume for a given amount of pressure than predicted, and/or exerts less pressure for a given volume than predicted).