For a fixed amount of gas at a fixed temperature, which of the following statements about the relationship between pressure and volume is correct according to the ideal gas law?

• A. Pressure and volume are independent of each other.
• B. Pressure and volume are directly proportional.
• C. Pressure and volume both remain constant.
• D. Pressure and volume are inversely proportional.

Answer: (D)

Verified step by step guidance

1. Recall the ideal gas law: \(P \times V = n \times R \times T\), where \(P\) is pressure, \(V\) is volume, \(n\) is the amount of gas (in moles), \(R\) is the ideal gas constant, and \(T\) is temperature.
2. Since the problem states that the amount of gas (\(n\)) and temperature (\(T\)) are fixed, the product \(n \times R \times T\) is a constant.
3. Rearranging the ideal gas law for fixed \(n\) and \(T\), we get \(P \times V = \text{constant}\), which means pressure multiplied by volume is constant.
4. From this relationship, if volume increases, pressure must decrease to keep the product constant, and vice versa, indicating an inverse proportionality.
5. Therefore, pressure and volume are inversely proportional for a fixed amount of gas at a fixed temperature, consistent with Boyle's Law.