Which of the following gases has the greatest density at a given temperature and pressure?

• A. N\(_2\)
• B. O\(_2\)
• C. CO\(_2\)
• D. He

Answer: (C)

Verified step by step guidance

1. Recall that the density (\(\rho\)) of a gas at a given temperature and pressure can be related to its molar mass (\(M\)) using the ideal gas law. The formula for density is \(\rho = \frac{PM}{RT}\), where \(P\) is pressure, \(T\) is temperature, \(R\) is the gas constant, and \(M\) is the molar mass of the gas.
2. Since the problem states the gases are at the same temperature and pressure, and \(R\) is a constant, the density is directly proportional to the molar mass: \(\rho \propto M\).
3. Determine the molar masses of the gases: \(N_2\) (approximately 28 g/mol), \(O_2\) (approximately 32 g/mol), \(CO_2\) (approximately 44 g/mol), and \(He\) (approximately 4 g/mol).
4. Compare the molar masses to find which gas has the greatest molar mass, and therefore the greatest density under the same conditions.
5. Conclude that the gas with the greatest molar mass will have the greatest density at the given temperature and pressure.