Determine the density of nitrogen at a temperature of 300 K and a pressure of 2 atm.

Determine the density of nitrogen at a temperature of 300 K and a pressure of 2 atm. The molar mass of nitrogen is M = 0.028 kg / mol.

T = 300 K.

P = 2 atm = 202650 Pa.

M = 0.028 kg / mol.

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

ρ -?

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

The density of a substance ρ is the ratio of the mass of a substance m to its volume V: ρ = m / V.

From the Mendeleev-Cliperon equation, we express: m / V = P * M / R * T.

ρ = P * M / R * T.

ρ = 202650 Pa * 0.028 kg / mol / 8.31 kg * m ^ 2 / s ^ 2 * K * mol * 300 K = 2.27 kg / m ^ 3.

Answer: the density of the gas is ρ = 2.27 kg / m ^ 3.