Determine the density of oxygen at a temperature of 320 K and a pressure of 400 kPa.

Ideal gas equation of state (Mendeleev – Clapeyron equation):

P * V = (m / M) * R * T, where P is the pressure (P = 400 kPa = 400000 Pa), V is the volume of oxygen (V = m / ρ, where m is the mass, ρ is the density), M – molar mass (M = 0.032 kg / mol, diatomic gas), R – universal gas constant (R = 8.31 J / (mol * K)), T – absolute temperature (T = 320 K).

P * m / ρ = (m / M) * R * T.

R / ρ = R * T / M.

ρ = P * M / (R * T) = 400000 * 0.032 / (8.31 * 320) = 4.81 kg / m3.