The ideal-gas equation

Gases are the easiest state to understand, because their molecules are far apart and interact only during collisions.

At low pressure, and at temperatures well above the point where they liquefy or solidify, gases nearly obey PV = KT for a given sample, with T in kelvin.

K grows with the amount of gas: K = Nk, where N is the number of molecules. Experiment shows k is the same for every gas; it is the Boltzmann constant, k_B = 1.38 × 10⁻²³ J K⁻¹.

So P₁V₁/(N₁T₁) = P₂V₂/(N₂T₂) = k_B. If two gases share P, V and T, they have the same N: this is Avogadro's hypothesis, and kinetic theory backs it up.

At STP (273 K and 1 atm), 22.4 L of any gas holds 6.02 × 10²³ molecules (Avogadro's number N_A) and has a mass equal to the molecular weight in grams. This amount is one mole.

Perfect-gas equation: PV = μRT, where μ is the number of moles and R = N_A k_B is universal. With T in kelvin, R = 8.314 J mol⁻¹ K⁻¹.

μ = M/M₀ = N/N_A, where M is the sample's mass, M₀ the molar mass and N the number of molecules.

Other forms: PV = k_B N T; P = k_B n T, where n = N/V is the number density; and P = ρRT/M₀, where ρ is the mass density.

An ideal gas is one that obeys PV = μRT exactly at every pressure and temperature. It is a model; no real gas is truly ideal.