A 1.2 m ^ 3 tank contains a mixture of 10 kg of nitrogen and 4 kg of hydrogen

A 1.2 m ^ 3 tank contains a mixture of 10 kg of nitrogen and 4 kg of hydrogen at a temperature of 27 C. Determine the molar mass of the gas mixture.

In a tank with a volume of V = 1.2 m ^ 3 there is a mixture of gases consisting of nitrogen with a mass of m₁ = 10 kg and hydrogen with a mass of m₂ = 4 kg at a temperature of T = 27 C = (27 + 273) K = 300 K. According to the periodic table we determine the molar masses of nitrogen M₁ = 0.028 kg / mol and hydrogen M₂ = 0.002 kg / mol. The average molar mass of a gas mixture is determined by the formula:

M = m / ν, where m = m₁ + m₂; ν = ν₁ + ν₂; ν₁ = m₁ / M₁; ν₂ = m₂ / М₂, then:

M = (m₁ + m₂): (m₁ / M₁ + m₂ / M₂).

Substitute the values ​​of physical quantities in the calculation formula:

M = (10 kg + 4 kg): (10 kg / 0.028 kg / mol + 4 kg / 0.002 kg / mol);

M ≈ 0.025 kg / mol.

Answer: molar mass of a mixture of gases ≈ 0.025 kg / mol