At standard temperature and pressure (STP), which of the following cylinders will contain the greatest number of gas particles?

• A. A 5.0 L cylinder filled with CO2 gas
• B. A 15.0 L cylinder filled with He gas
• C. A 10.0 L cylinder filled with O2 gas
• D. A 20.0 L cylinder filled with N2 gas

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 is a key concept from the ideal gas law and allows us to relate volume directly to the number of moles (and thus particles) of gas.
2. Use the relationship between volume and moles at STP: \(n = \frac{V}{22.4\, \text{L/mol}}\), where \(n\) is the number of moles and \(V\) is the volume of the gas in liters.
3. Calculate the number of moles for each cylinder by dividing its volume by 22.4 L/mol. For example, for the 5.0 L CO\(_2\) cylinder, \(n = \frac{5.0}{22.4}\) moles.
4. Compare the number of moles (and therefore the number of particles, since 1 mole contains Avogadro's number of particles) for each cylinder. The cylinder with the largest volume will have the greatest number of moles and thus the greatest number of gas particles at STP.
5. Conclude that the 20.0 L cylinder filled with N\(_2\) gas contains the greatest number of gas particles because it has the largest volume, and at STP, volume is directly proportional to the number of gas particles regardless of the gas identity.