Determine which gas would have a root mean square speed of 515.59 m/s at 405 K.

• A. Cl₂
• B. CO₂
• C. F₂
• D. NH₃
• E. CH₄

Answer: (C)

Verified step by step guidance

1. Understand that the root mean square speed (v_rms) of a gas is given by the formula: $\sqrt{\frac{3RT}{M}}$, where R is the ideal gas constant (8.314 J/mol·K), T is the temperature in Kelvin, and M is the molar mass of the gas in kg/mol.
2. Convert the molar mass of each gas from g/mol to kg/mol. For example, for Cl2, the molar mass is approximately 70.9 g/mol, which is 0.0709 kg/mol.
3. Substitute the given temperature (T = 405 K) and the molar mass of each gas into the v_rms formula to calculate the root mean square speed for each gas.
4. Compare the calculated root mean square speeds to the given speed of 515.59 m/s to determine which gas matches this speed.
5. Identify the gas with the calculated root mean square speed closest to 515.59 m/s as the correct answer.