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18 November, 08:42

An unknown gas effuses 2.3 times faster than N2O4 at the same temperature. What is the identity of the unknown gas?

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  1. 18 November, 12:28
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    The molar mass of the unknown gas is 17.3 g/mol. The molar mass matches that of ammonia (NH₃) the most (17 g/mol)

    Explanation:

    Let the unknown gas be gas 1

    Let N₂O₄ gas be gas 2

    Rate of effusion ∝ [1/√ (Molar Mass) ]

    R ∝ [1/√ (M) ]

    R = k/√ (M) (where k is the constant of proportionality) ₁₂

    R₁ = k/√ (M₁)

    k = R₁√ (M₁)

    R₂ = k/√ (M₂)

    k = R₂√ (M₂)

    k = k

    R₁√ (M₁) = R₂√ (M₂)

    (R₁/R₂) = [√ (M₂) / √ (M₁) ]

    (R₁/R₂) = √ (M₂/M₁)

    R₁ = 2.3 R₂

    M₁ = Molar Mass of unknown gas

    M₂ = Molar Mass of N₂O₄ = 92.01 g/mol

    (2.3R₂/R₂) = √ (92.01/M₁)

    2.3 = √ (92.01/M₁)

    92.01/M₁ = 2.3²

    M₁ = 92.01/5.29

    M₁ = 17.3 g/mol

    The molar mass matches that of ammonia the most (17 g/mol)
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