At 25 °C, which of the following correctly arranges the gases He, O2, CO2, and N2 in order of increasing average molecular speed?

• A. O2 < CO2 < N2 < He
• B. N2 < CO2 < O2 < He
• C. He < N2 < O2 < CO2
• D. CO2 < O2 < N2 < He

Answer: (D)

Verified step by step guidance

1. Recall that the average molecular speed of a gas is related to its molar mass and temperature by the equation for root-mean-square speed: \(v_{rms} = \sqrt{\frac{3RT}{M}}\), where \(R\) is the gas constant, \(T\) is the temperature in Kelvin, and \(M\) is the molar mass in kilograms per mole.
2. Since the temperature is constant (25 °C), the average molecular speed depends inversely on the square root of the molar mass: gases with lower molar mass move faster on average.
3. Determine the molar masses of the gases: He (about 4 g/mol), O\(_2\) (about 32 g/mol), CO\(_2\) (about 44 g/mol), and N\(_2\) (about 28 g/mol).
4. Arrange the gases in order of increasing molar mass: He < N\(_2\) < O\(_2\) < CO\(_2\).
5. Therefore, the order of increasing average molecular speed is the reverse of the molar mass order: CO\(_2\) < O\(_2\) < N\(_2\) < He.