At a constant temperature and amount of gas, which of the following relationships between pressure and volume is described by the ideal gas law?

• A. Pressure and volume are independent of each other.
• B. Pressure is proportional to the square of the volume.
• C. Pressure is directly proportional to volume.
• D. Pressure is inversely proportional to volume.

Answer: (D)

Verified step by step guidance

1. Recall the ideal gas law equation: \(P \times V = n \times R \times T\), 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 temperature (\(T\)) and amount of gas (\(n\)) are constant, the product \(n \times R \times T\) is a constant value.
3. Rearrange the ideal gas law to express pressure in terms of volume: \(P = \frac{n \times R \times T}{V}\). This shows that pressure is inversely proportional to volume.
4. Understand that 'inversely proportional' means that if volume increases, pressure decreases, and vice versa, such that their product remains constant.
5. Therefore, among the given options, the relationship described by the ideal gas law is that pressure is inversely proportional to volume.