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from a certain apparatus the diffusion rate of hy...

Question:
From a certain apparatus, the diffusion rate of hydrogen has an average value of 28.7 cm³s^-1. The diffusion of another gas under the same conditions is measured to have an average rate of 7.2 cm³s^-1. Identify the gas.

[Hint:Use Graham's law of diffusion: R₁/R₂= (M₂/M₁)^1/2, where R₁, R₂ are diffusion rates of gases 1 and 2, and M₁ and M₂their respective molecular masses. The law is a simple consequence of kinetic theory.]

Answer:

Rate of diffusion of hydrogen, R₁ = 28.7 cm³s^-1

Rate of diffusion of another gas, R₂= 7.2 cm³s^-1

According to Graham's Law of diffusion, we have:

R₁/ R₂ = Underroot M₂/M₁

Where, M₁ is the molecular mass of hydrogen = 2.020 g

M₂ is the molecular mass of the unknown gas

∴ M₂ =M₁(R₁/ R₂)²

=2.02 (28.7 / 7.2)²

= 32.09 g

32 g is the molecular mass of oxygen. Hence, the unknown gas is oxygen.

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