Which of the following best explains why the pressure of a fixed amount of gas decreases as altitude increases in Earth's atmosphere, assuming temperature remains constant?

• A. The molar mass of air increases with altitude.
• B. The number of gas molecules per unit volume decreases with altitude.
• C. The gas constant R decreases with altitude.
• D. The temperature of the gas increases with altitude.

Answer: (B)

Verified step by step guidance

1. Recall that the pressure of a gas is related to the number of gas molecules colliding with the walls of a container or a given volume. More molecules per unit volume mean higher pressure.
2. Understand that as altitude increases, the density of the air (number of molecules per unit volume) decreases because the atmosphere becomes less dense farther from Earth's surface.
3. Recognize that the ideal gas law, \(P = \frac{nRT}{V}\), relates pressure \(P\) to the number of moles \(n\) (which corresponds to the number of molecules), temperature \(T\), volume \(V\), and the gas constant \(R\). If temperature and volume are constant, pressure depends directly on the number of molecules per volume.
4. Note that the molar mass of air and the gas constant \(R\) do not change significantly with altitude, and the problem states temperature remains constant, so these factors do not explain the pressure decrease.
5. Conclude that the best explanation is that the number of gas molecules per unit volume decreases with altitude, leading to a decrease in pressure.