At a certain temperature and pressure, 0.20 mol of carbon dioxide has a volume of 3.1 L. A 3.1-L sample of hydrogen at the same temperature and pressure

Question

BlackTom AI · Accepted Answer

Question recap: At a certain temperature and pressure, 0.20 mol of carbon dioxide occupies 3.1 L. A 3.1-L sample of hydrogen at the same temperature and pressure... (the sentence is cut in the prompt, but we can work with the idea that we are comparing volumes at the same T and P).

Option 1: 'has the same mass.' This would require the two gases to have identical mass in the same volume at the same T and P. However, mass depends on molar mass. CO2 has a molar mass of 44 g/mol, so 0.20 mol CO2 has a mass of 8.8 g in 3.1 L. Hydrogen (H2) has a molar mass of 2 g/mol, so 0.20 mol H2 would have a mass of 0.40 g if it contained 0.20 mol. Even if the gases occupy the same volume at the same conditions, the masses are not the same because their molar masses differ. Thus this statement is incorrect.

Option 2: 'contains the same number of atoms.' To compare atom counts, multiply the number of moles by Avogadro's number and by the number of atoms per molecule. CO2 has 3 atoms per molecule, while H2 has 2 atoms per molecule. For the same number of moles, CO2 samples contain more atoms overall than H2 samples. Therefore, this statement is false.

Option 3: 'has a higher density.' Density of a gas at fixed T and P is proportional to its molar mass (density ∝ M in these conditions). CO2 has a molar mass much larger than H2, so a 3.1-L sample at the same T and P would be denser if it is CO2 rather than H2. Since the question compares a 3.1-L H2 sample with a 0.20 mol CO2 sample occupying 3.1 L, the hydrogen sample does not have a higher density than a CO2 sample occupying the same volume; in fact, CO2 would be denser. This statement is incorrect as written if the comparison is within the same conditions.

Option 4: 'contains the same number of molecules.' Under the same temperature and pressure, equal volumes contain equal numbers of moles (Avogadro's law), and equal moles contain equal numbers of molecules. Since the CO2 sample is 0.20 mol, a 3.1-L sample of hydrogen at the same T and P would also contain 0.20 mol, hence the same number of molecules as the CO2 sample. This aligns with the gas-law relationship and the given volumes and moles. Therefore this statement is consistent with the underlying principle and is correct.

At a certain temperature and pressure, 0.20 mol of carbon dioxide has a volume of 3.1 L. A 3.1-L sample of hydrogen at the same temperature and pressureSingle choice

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