Which of the following relationships is described by the ideal gas law?

• A. The volume of a gas is directly proportional to its pressure at constant temperature and amount.
• B. The volume of a gas is inversely proportional to its temperature at constant pressure and amount.
• C. The pressure of a gas is directly proportional to its temperature at constant volume and amount.
• D. The pressure of a gas is inversely proportional to its amount at constant volume and temperature.

Answer: (C)

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 in Kelvin.
2. Understand that the ideal gas law relates pressure, volume, temperature, and amount of gas simultaneously, so changes in one variable affect the others according to this equation.
3. Analyze each statement by considering which variables are held constant and how the remaining variables relate according to the ideal gas law.
4. For example, if volume \(V\) and amount \(n\) are constant, then pressure \(P\) is directly proportional to temperature \(T\), because \(P = \frac{nRT}{V}\), showing a direct proportionality between \(P\) and \(T\).
5. Use similar reasoning to check the other statements, noting that the ideal gas law does not support volume being directly proportional to pressure at constant temperature and amount, nor volume being inversely proportional to temperature at constant pressure and amount.