Which of the following relationships is consistent with the ideal gas law?

• A. At constant pressure and amount of gas, temperature is inversely proportional to volume (T ∝ 1/V).
• B. At constant temperature and amount of gas, pressure is inversely proportional to volume (P ∝ 1/V).
• C. At constant volume and amount of gas, pressure is inversely proportional to temperature (P ∝ 1/T).
• D. At constant volume and temperature, pressure is inversely proportional to the amount of gas (P ∝ 1/n).

Answer: (B)

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. To analyze each relationship, consider which variables are held constant and how the remaining variables relate to each other according to the ideal gas law.
3. For the first option (constant \(P\) and \(n\)), rearrange the ideal gas law to express \(T\) in terms of \(V\): \(T = \frac{P \times V}{n \times R}\). This shows \(T\) is directly proportional to \(V\), not inversely proportional.
4. For the second option (constant \(T\) and \(n\)), rearrange to express \(P\) in terms of \(V\): \(P = \frac{n \times R \times T}{V}\). This shows \(P\) is inversely proportional to \(V\), consistent with the ideal gas law.
5. For the third and fourth options, similarly rearrange the ideal gas law holding the specified variables constant to check if the proposed proportionalities match the equation.