Real-gas compressibility factor Z (defined as actual volume / ideal-gas-predicted volume):\nAs the pressure of the gas approaches 0 (very low-pressure limit), to what value does Z tend?

Introduction / Context:
The compressibility factor Z is a convenient, dimensionless measure of non-ideality for real gases. It is defined as Z = (actual molar volume) / (ideal-gas molar volume at the same T and P). Equivalently, Z = P * V / (n * R * T). This question examines the limiting behavior of Z as the pressure becomes very small, which is fundamental to chemical engineering thermodynamics and real-gas equations of state.

Given Data / Assumptions:

• Z is defined as the ratio of actual volume to ideal-gas-predicted volume at the same T and P.
• We consider the limit as P → 0 at fixed temperature (the low-density limit).
• No specific gas is singled out; we are concerned with general limiting behavior.

Concept / Approach:
At very low pressures (and hence low densities), all real gases approach ideal-gas behavior because the molecules are far apart and intermolecular forces become negligible. In the virial formulation, Z = 1 + B(T) * P / (R * T) + higher-order terms. As P → 0, the correction terms vanish and Z → 1. This limiting behavior is independent of gas identity, provided we are sufficiently close to zero pressure.

Step-by-Step Solution:

Verification / Alternative check:
Any cubic equation of state (e.g., van der Waals, Redlich–Kwong, Peng–Robinson) reduces to the ideal-gas form as density → 0, delivering Z = 1 in the low-pressure limit.

Why Other Options Are Wrong:

• 0 or 0.24: imply vanishing or fixed non-ideal behavior at low P, which contradicts theory.
• Infinity: impossible as P → 0; gases do not become infinitely non-ideal at vanishing pressure.
• 'Depends strongly on gas species': species differences vanish in the limit P → 0.

Common Pitfalls:
Confusing high-pressure deviations (Z ≠ 1) with low-pressure behavior; forgetting that all equations of state recover ideal-gas behavior at sufficiently low density.

Final Answer:
1