Which of the following gases has the lowest root mean square speed at 25°C?

• A. He
• B. O2
• C. N2
• D. CO2

Answer: (D)

Verified step by step guidance

1. Recall that the root mean square (rms) speed of a gas molecule is given by the formula: \(v_{rms} = \sqrt{\frac{3RT}{M}}\), where \(R\) is the gas constant, \(T\) is the temperature in Kelvin, and \(M\) is the molar mass of the gas in kilograms per mole.
2. Note that the temperature \(T\) is the same for all gases since the problem specifies 25°C, which is 298 K (convert Celsius to Kelvin by adding 273).
3. Since \(R\) and \(T\) are constants for all gases at the same temperature, the rms speed depends inversely on the square root of the molar mass \(M\). This means gases with higher molar mass have lower rms speeds.
4. Determine the molar masses of the gases: He (about 4 g/mol), O2 (about 32 g/mol), N2 (about 28 g/mol), and CO2 (about 44 g/mol).
5. Compare the molar masses to identify which gas has the highest molar mass, as that gas will have the lowest rms speed. The gas with the highest molar mass among the options is CO2, so it has the lowest root mean square speed at 25°C.