For a gas, which pair of variables is inversely proportional to each other (provided other conditions are…

1. Analyze the question We need the pair of gas variables that are inversely proportional, with all other conditions held constant.

2. The concept The ideal gas equation is:

PV = nRT

Holding the other variables constant, we get these gas laws:

• Boyle's Law: P ∝ 1/V (constant T, n)
• Charles's Law: V ∝ T (constant P, n)
• Gay-Lussac's (Pressure) Law: P ∝ T (constant V, n)
• Avogadro's Law: V ∝ n, and also P ∝ n at constant V and T

3. Check each option

• A. P, T: P = nRT/V, so P ∝ T. This is directly proportional. ✗
• B. P, V: P = nRT/V, so P ∝ 1/V. This is inversely proportional (Boyle's Law). ✓
• C. n, P: At constant V and T, P ∝ n. This is directly proportional. ✗
• D. V, T: V = nRT/P, so V ∝ T. This is directly proportional (Charles's Law). ✗

4. Answer Only pressure and volume are inversely proportional: when the volume of a gas is reduced, its pressure rises, and vice versa.

5. Exam tip Remember that Boyle's Law is the only classic gas law with an inverse relationship: P × V = constant. Think of squeezing a bicycle pump: reduce the volume and the pressure goes up. The other pairs (P-T, V-T, n-P) all go up together.