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?

Verified step by step guidance

1. 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.
2. 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.
3. 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.
4. 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: \( \frac{\text{Rate of effusion of gas 1}}{\text{Rate of effusion of gas 2}} = \sqrt{\frac{M_2}{M_1}} \).
5. 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.