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Difficulty: MediumGraham's Law of Diffusion and Effusion

Equal volumes of nitrogen (N2N_2) and oxygen (O2O_2) are allowed to effuse through a microscopic orifice under identical conditions of temperature and pressure. Which gas will effuse at a faster rate?

Answer: Nitrogen / N2 / nitrogen / N₂ / Nitrogen gas / nitrogen gas

Answer

Nitrogen (N2N_2) will effuse at a faster rate because it has a lower molar mass (28 g/mol28\text{ g/mol}) compared to oxygen (32 g/mol32\text{ g/mol}).
According to Graham's Law, the rate of diffusion or effusion of a gas is inversely proportional to the square root of its molar mass (r∝1Mr \propto \frac{1}{\sqrt{M}}). Since nitrogen (N2N_2) has a molar mass of 28 g/mol28\text{ g/mol} and oxygen (O2O_2) has a molar mass of 32 g/mol32\text{ g/mol}, nitrogen is lighter and therefore effuses faster under identical conditions.

Step-by-Step Solution

1
Calculate the molar masses of both gases.
Molar mass of N2=2×14=28 g/molN_2 = 2 \times 14 = 28\text{ g/mol}. Molar mass of O2=2×16=32 g/molO_2 = 2 \times 16 = 32\text{ g/mol}.
Graham's Law relates the rate of effusion of a gas directly to its molar mass.
2
Apply Graham's Law of Effusion.
Effusion rate is inversely proportional to the square root of molar mass (r∝1Mr \propto \frac{1}{\sqrt{M}}).
Lighter gas molecules move faster at a given temperature, resulting in higher rates of effusion.
3
Compare rates of effusion.
Since 28 g/mol<32 g/mol28\text{ g/mol} < 32\text{ g/mol}, nitrogen (N2N_2) effuses faster than oxygen (O2O_2).
The gas with lower molar mass has the higher effusion rate.

Key Concept

Graham's Law of Diffusion and Effusion
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Graham's Law of Diffusion and Effusion

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