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

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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