Which statement can best be concluded from the ideal gas law?

• A. At constant volume and temperature, the pressure of a gas is inversely proportional to the number of moles.
• B. At constant pressure and number of moles, the volume of a gas is inversely proportional to temperature.
• C. At constant temperature and number of moles, the pressure of a gas is directly proportional to volume.
• D. At constant temperature and pressure, the volume of a gas is directly proportional to the number of moles.

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 number of moles, \(R\) is the ideal gas constant, and \(T\) is temperature.
2. Analyze each statement by considering which variables are held constant and how the remaining variables relate to each other according to the ideal gas law.
3. For the first statement: At constant volume (\(V\)) and temperature (\(T\)), rearrange the ideal gas law to \(P = \frac{nRT}{V}\). Since \(R\), \(T\), and \(V\) are constant, pressure \(P\) is directly proportional to \(n\), not inversely proportional.
4. For the second statement: At constant pressure (\(P\)) and number of moles (\(n\)), rearrange to \(V = \frac{nRT}{P}\). With \(n\) and \(P\) constant, volume \(V\) is directly proportional to temperature \(T\), not inversely proportional.
5. For the third statement: At constant temperature (\(T\)) and number of moles (\(n\)), rearrange to \(P = \frac{nRT}{V}\). Here, pressure \(P\) is inversely proportional to volume \(V\), not directly proportional.