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Anonymous asked in Science & MathematicsPhysics · 9 years ago

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

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?

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  • 9 years ago
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    Assuming ideal gas behavior:

    p∙V = n∙R∙T

    <=>

    V = n∙R∙T/p

    So the density is

    ρ = m/V = m∙p/(n∙R∙T)

    with molar mass

    M = m/n

    follows

    ρ = M∙p / (R∙T)

    For Krypton

    M = 83.80 g∙mol⁻¹ = 8.38×10⁻² kg∙mol⁻¹

    Standard conditions

    P = 101325 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

    As shown above the density of an ideal gas at same conditions is proportional to its molar mass.

    ρ ~ M

    =>

    ρ(CH₄) / ρ(Kr) = M(CH₄)/M(Kr)

    =>

    ρ(CH₄) = ρ(Kr) ∙ (M(CH₄)/M(Kr))

    The molar mass of methane is:

    M(CH₄) = 16.04 g∙mol⁻¹

    =>

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

    = 0.716 kg∙mol⁻³

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