Question

What is the density of Kripton gas at standard temperature and pressure? The atomic mass of Kripton is 83.80 atomic mass unit.

What is the density of Methane gas under the same conditions?

Answer 1

PV = NRT Ideal Gas Equation

V = n∙R∙T/P..........(1)

density ρ = m/V .......(2)

Substitutin 1, we get

ρ = m∙P/(n∙R∙T)............(3)

and molar mass M = m/n..........(4)

Substitutin 4 in 3, we get

ρ = M∙p / (R∙T).............(5)

For Krypton,

M = 83.80 g∙mol⁻¹ = 8.38×10⁻² kg∙mol⁻¹
Standard conditions :
P = 101,325 Pa & T = 273.15 K
Hence, ρ = 8.38×10⁻² kg∙mol⁻¹ ∙ 101325 Pa / (8.314472 Pa∙m³∙K⁻¹∙mol⁻¹ ∙ 273.15 K) = 3.74 kg∙mol⁻³ (Ans)

The density of an ideal gas at same conditions is proportional to its molar mass. *as can be seen from eqn 5
ρ ~ M

ρ(CH₄) / ρ(Kr) = M(CH₄)/M(Kr)............(6)

Rearranging the above eqn 6, we get

ρ(CH₄) = ρ(Kr) ∙ (M(CH₄)/M(Kr))

The molar mass of methane is: M(CH₄) = 16.04 g∙mol⁻¹

Therefore, ρ(CH₄) = 3.74 kg∙mol⁻³ ∙ (16.04 g∙mol⁻¹ / 83.8 g∙mol⁻¹) = 0.716 kg∙mol⁻³(Ans)