Questions: Which of the following gas samples would have the largest volume, if all samples are at the same temperature and pressure? 65.7 grams of Xe 9 × 10^23 molecules of H2 5.00 moles CO2 they would all have the same volume

Solution Steps

To compare the volumes of the gas samples, we need to determine the number of moles for each sample, as volume is directly proportional to the number of moles at constant temperature and pressure (according to Avogadro's Law).

1. Xenon (Xe):
   The molar mass of Xe is approximately 131.29 g/mol.
   \[ \text{Moles of Xe} = \frac{65.7 \, \text{g}}{131.29 \, \text{g/mol}} \approx 0.5003 \, \text{mol} \]

2. Hydrogen (\(\mathrm{H}_2\)):
   Avogadro's number is \(6.022 \times 10^{23}\) molecules/mol.
   \[ \text{Moles of } \mathrm{H}_2 = \frac{9 \times 10^{23} \, \text{molecules}}{6.022 \times 10^{23} \, \text{molecules/mol}} \approx 1.494 \, \text{mol} \]

3. Carbon Dioxide (\(\mathrm{CO}_2\)):
   The number of moles is given directly as 5.00 moles.

Since the volume of a gas is directly proportional to the number of moles at constant temperature and pressure, we compare the moles calculated:

• Moles of Xe: \(0.5003\)
• Moles of \(\mathrm{H}_2\): \(1.494\)
• Moles of \(\mathrm{CO}_2\): \(5.00\)

The gas with the largest number of moles will have the largest volume.

Final Answer