Which of the following best explains why the pressure of a sample of gas at constant volume could decrease by 75 mm Hg?

• A. The amount of gas in the container increased.
• B. The volume of the container increased.
• C. The gas was compressed to a smaller volume.
• D. The temperature of the gas decreased.

Answer: (D)

Verified step by step guidance

1. Recall the ideal gas law: \(P V = n R T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the amount of gas (in moles), \(R\) is the gas constant, and \(T\) is temperature in Kelvin.
2. Since the volume is constant, and the amount of gas does not change, the relationship simplifies to \(P \propto T\), meaning pressure is directly proportional to temperature.
3. If the pressure decreases by 75 mm Hg while volume and amount of gas remain constant, this implies that the temperature must have decreased to cause the pressure drop.
4. The other options (increase in amount of gas, increase in volume, or compression) would either increase pressure or change volume, which contradicts the condition of constant volume and observed pressure decrease.
5. Therefore, the best explanation is that the temperature of the gas decreased, leading to a proportional decrease in pressure at constant volume.