Real gases approximate ideal behavior best under which conditions of pressure and temperature?

Introduction / Context:
Ideal-gas behavior is a useful approximation when intermolecular forces and molecular sizes are negligible compared with the average spacing of molecules. Recognizing when this holds is crucial for deciding whether PV = nRT is acceptable or whether real-gas equations of state (e.g., van der Waals, Peng–Robinson) are required for accuracy.

Given Data / Assumptions:

• Real gases deviate due to finite molecular volume and attractive/repulsive forces.
• Deviation decreases when the molecules are far apart and kinetic energy dominates.
• Critical region and saturation conditions promote nonideality.

Concept / Approach:
At low pressure, the average distance between molecules is large, so excluded volume and pairwise attractions contribute less to the equation of state. At high temperature, molecules have higher kinetic energy, which reduces the relative importance of attractive interactions. The combination of low P and high T therefore minimizes nonideality and makes the ideal gas law most reliable.

Step-by-Step Solution:
Relate nonideality to intermolecular forces and finite size.Identify conditions that minimize these effects: low P (reduces density) and high T (increases kinetic energy).Conclude that low pressure and high temperature approach ideal behavior.Select the corresponding option.

Verification / Alternative check:
Compressibility factor Z approaches 1 for many gases as P → 0 and T » Tc; generalized charts show Z ≈ 1 under these conditions.

Why Other Options Are Wrong:
High P and/or low T push gases toward condensation and large deviations from ideality.

Common Pitfalls:
Using the ideal gas law near saturation lines or the critical point; ignoring strong polarity or association that causes deviations even at moderate conditions.

Final Answer:
Low pressure and high temperature