According to the kinetic molecular theory, which of the following gases has molecules with the greatest average molecular speed at 25°C?

• A. He
• B. O2
• C. CO2
• D. N2

Answer: (A)

Verified step by step guidance

1. Recall that according to the kinetic molecular theory, the average molecular speed of a gas is related to its temperature and molar mass. Specifically, the average speed increases with temperature and decreases with increasing molar mass.
2. Use the formula for the root-mean-square (rms) speed of gas molecules: \[ v_{rms} = \sqrt{\frac{3RT}{M}} \] where \(R\) is the gas constant, \(T\) is the absolute temperature in Kelvin, and \(M\) is the molar mass of the gas in kilograms per mole.
3. Since the temperature is the same for all gases (25°C, which is 298 K), the variable that affects the average molecular speed is the molar mass \(M\). Gases with smaller molar masses will have higher average molecular speeds.
4. Identify the molar masses of the gases: - Helium (He): approximately 4 g/mol - Oxygen (O\(_2\)): approximately 32 g/mol - Carbon dioxide (CO\(_2\)): approximately 44 g/mol - Nitrogen (N\(_2\)): approximately 28 g/mol
5. Compare the molar masses and conclude that helium, having the smallest molar mass, will have the greatest average molecular speed at 25°C.