The vessel is evacuated to a pressure of p = 1.33 * 10 ^ -9 Pa. Air temperature t = 15’C find the density of the air in the vessel.

P = 1.33 * 10 ^ -9 Pa.

R = 8.31 m ^ 2 * kg / s ^ 2 * K * mol.

T = 288 ° K.

M = 0.029 kg / mol.

ρ -?

Let us write down the Mendeleev-Cliperon law for air: P * V = m * R * T / M, where P is the air pressure, V is the air volume, m is the air mass, R is the universal gas constant, T is the absolute temperature, M is the molar air mass.

m / V = P * M / R * T.

Air density ρ is determined by the formula: ρ = m / V.

ρ = P * M / R * T.

ρ = 1.33 * 10 ^ -9 Pa * 0.029 kg / mol / 8.31 m ^ 2 * kg / s ^ 2 * K * mol * 288 ° K = 16 * -15 kg / m ^ 3.

Answer: the air density is ρ = 16 * -15 kg / m ^ 3.