A flask at room temperature contains exactly equal amounts (in moles) of nitrogen and xenon. b. The molecules or atoms of which gas have the greater average velocity? d. If a small hole were opened in the flask, which gas effuses more quickly?

검증된 단계별 안내

insert step 1> Determine the relationship between the average velocity of gas molecules and their molar mass using the equation for root-mean-square speed: \( v_{rms} = \sqrt{\frac{3kT}{m}} \) or \( v_{rms} = \sqrt{\frac{3RT}{M}} \), where \( M \) is the molar mass.

insert step 2> Compare the molar masses of nitrogen (N_2) and xenon (Xe). Nitrogen has a molar mass of approximately 28 g/mol, while xenon has a molar mass of approximately 131 g/mol.

insert step 3> Conclude that the gas with the lower molar mass (nitrogen) will have a greater average velocity, as velocity is inversely proportional to the square root of the molar mass.

insert step 4> Use Graham's law of effusion to determine which gas effuses more quickly. Graham's law states that the rate of effusion is inversely proportional to the square root of the molar mass: \( \frac{\text{Rate of effusion of gas 1}}{\text{Rate of effusion of gas 2}} = \sqrt{\frac{M_2}{M_1}} \).

insert step 5> Apply Graham's law to compare the effusion rates of nitrogen and xenon. Since nitrogen has a lower molar mass, it will effuse more quickly than xenon.

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주요 개념

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Graham's Law of Effusion

Graham's Law states that the rate of effusion of a gas is inversely proportional to the square root of its molar mass. This means that lighter gases will effuse more quickly than heavier gases. In the context of the question, this principle helps determine which gas, nitrogen or xenon, will escape through a small hole faster.

Kinetic Molecular Theory

The Kinetic Molecular Theory explains the behavior of gases in terms of particles in constant motion. According to this theory, the average kinetic energy of gas particles is directly proportional to the temperature of the gas. Since nitrogen (N2) has a lower molar mass than xenon (Xe), it will have a higher average velocity at the same temperature, as lighter particles move faster.

Molar Mass

Molar mass is the mass of one mole of a substance, typically expressed in grams per mole (g/mol). In this question, nitrogen has a molar mass of approximately 28 g/mol, while xenon has a molar mass of about 131 g/mol. Understanding molar mass is crucial for comparing the velocities and effusion rates of the two gases, as it directly influences their behavior according to Graham's Law.