Compressibility factor Z for an ideal gas:\nSelect the correct statement about Z for an ideal gas over all temperatures and pressures.

Introduction / Context:
The compressibility factor Z = PV/(nRT) measures deviation from ideal-gas behavior. For real gases, Z departs from unity, especially near condensation conditions or at high pressures/low temperatures. Understanding the exact behavior for an ideal gas avoids confusion in state estimation and property calculations.

Given Data / Assumptions:

• Ideal-gas equation of state, PV = nRT.
• No interactions or excluded volume.
• All temperatures and pressures are mathematically admissible under the model.

Concept / Approach:
By definition, an ideal gas is one whose P–V–T relationship follows PV = nRT. Substituting into Z = PV/(nRT) yields Z = 1 identically. Boyle’s temperature is a real-gas concept where first-order deviations vanish (B2 ≈ 0), making Z ≈ 1 over a range, but that pertains to real gases only—not the ideal-gas postulate.

Step-by-Step Solution:

Verification / Alternative check:
Virial EOS for real gases: Z = 1 + B2P/RT + …; setting all virial coefficients to zero recovers the ideal gas where Z = 1 identically.

Why Other Options Are Wrong:

• (a), (d), (e) contradict the identity Z ≡ 1.
• (c) confuses real-gas Boyle’s temperature with the ideal-gas definition.

Common Pitfalls:
Applying real-gas intuition (e.g., Z trends) to the ideal gas; misusing Boyle’s temperature as a universal condition.

Final Answer:
Z equals exactly 1 at all temperatures and pressures.