Which of the following best describes the relationship between the volume of a gas and the number of moles at constant temperature and pressure?

• A. The volume of a gas is inversely proportional to the number of moles.
• B. The volume of a gas is independent of the number of moles.
• C. The volume of a gas is directly proportional to the number of moles.
• D. The volume of a gas decreases as the number of moles increases.

Answer: (C)

Verified step by step guidance

1. Recall the Ideal Gas Law, which relates pressure (P), volume (V), number of moles (n), gas constant (R), and temperature (T): \(P \times V = n \times R \times T\).
2. Since the problem states that temperature (T) and pressure (P) are constant, and R is always constant, we can rearrange the equation to express volume (V) in terms of number of moles (n): \(V = \frac{n \times R \times T}{P}\).
3. With P, R, and T constant, the equation simplifies to show that volume (V) is directly proportional to the number of moles (n): \(V \propto n\).
4. This means that if the number of moles increases, the volume increases proportionally, and if the number of moles decreases, the volume decreases proportionally.
5. Therefore, the correct description is that the volume of a gas is directly proportional to the number of moles at constant temperature and pressure.