In the ideal gas law, if n and temperature T are held constant, what is the relation between pressure P and volume V?

• A. P is proportional to 1/V
• B. P is proportional to V^2
• C. P is independent of V
• D. P is proportional to V

Answer: (A)

When you hold the number of moles and the temperature fixed in the ideal gas law, the pressure falls out as P = nRT / V. Since n and T are constants, nRT is a constant, so pressure is inversely proportional to volume: P ∝ 1/V. That means doubling the volume halves the pressure, and halving the volume doubles the pressure.

This is why the correct relationship is an inverse one. The other possibilities would require pressure to rise with volume, to rise even faster with volume squared, or to stay the same regardless of volume, which contradicts P = nRT / V.