Which pair of gas samples at standard temperature and pressure (STP) contains the same total number of molecules?

• A. 2.0 L of CO2 and 1.0 L of He
• B. 1.0 L of O2 and 1.0 L of N2
• C. 5.0 L of CH4 and 10.0 L of N2
• D. 22.4 L of H2 and 11.2 L of O2

Answer: (B)

Verified step by step guidance

1. Recall that at standard temperature and pressure (STP), one mole of any ideal gas occupies 22.4 liters. This means the volume of a gas sample at STP is directly proportional to the number of moles, and thus to the number of molecules.
2. Use the relationship: \(\text{Number of moles} = \frac{\text{Volume of gas at STP}}{22.4\, \text{L}}\) to find the moles of each gas sample in the pairs given.
3. Calculate the moles for each gas in the pairs and then sum the moles for each pair to find the total number of moles (and thus molecules) in each pair.
4. Compare the total moles of gas in each pair. The pair with equal total moles will have the same total number of molecules because the number of molecules is proportional to the number of moles.
5. Identify the pair where the volumes add up to the same total number of moles, confirming that this pair contains the same total number of molecules.