At standard temperature and pressure (STP), which gas sample contains the same number of molecules as 2.0 liters of CH_4(g) at STP?

• A. 4.0 liters of CO_2(g) at STP
• B. 1.0 liter of N_2(g) at STP
• C. 22.4 liters of He(g) at STP
• D. 2.0 liters of O_2(g) at STP

Answer: (D)

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 that the number of molecules in a gas sample is directly proportional to its volume at STP.
2. Calculate the number of moles of CH_4 in 2.0 liters at STP using the formula: \(\text{moles} = \frac{\text{volume}}{22.4\,\text{L/mol}}\). So, \(n_{CH_4} = \frac{2.0}{22.4}\) moles.
3. Since the number of molecules is proportional to the number of moles, find the volume of another gas that contains the same number of moles (and thus molecules) by setting its volume equal to 2.0 liters, because the mole ratio depends only on volume at STP.
4. Compare the given volumes of other gases to 2.0 liters. The gas sample with a volume of 2.0 liters at STP will have the same number of molecules as 2.0 liters of CH_4 at STP, regardless of the gas identity.
5. Conclude that the gas sample with 2.0 liters at STP (in this case, O_2) contains the same number of molecules as 2.0 liters of CH_4 at STP.