Corresponding states — Gases at the same reduced temperature (Tr) and reduced pressure (Pr) will exhibit which common behavior?

Introduction / Context:
The principle of corresponding states underpins generalized compressibility charts and equations of state. By normalizing temperature and pressure with respect to critical properties, many gases exhibit similar non-ideal behavior at the same reduced conditions. This allows engineers to estimate deviations from ideality without species-specific data for every case.

Given Data / Assumptions:

• Reduced temperature Tr = T/Tc and reduced pressure Pr = P/Pc.
• Gases are not in reactive mixtures; behavior is compared at identical Tr and Pr.
• Acentric factor effects are modest (first-order corresponding states).

Concept / Approach:

At the same Tr and Pr, many gases show nearly the same compressibility factor Z. Similar Z implies a similar degree of deviation from ideal-gas behavior because Z quantifies PV/(nR*T). While exact equality is not guaranteed (acentric factor ω refines predictions), the “nearly same” behavior forms the basis of generalized charts and correlations.

Step-by-Step Solution:

Verification / Alternative check:

Comparisons across nitrogen, methane, and argon at identical Tr and Pr show comparable Z values, validating the principle, with small adjustments captured by ω in the Lee–Kesler method.

Why Other Options Are Wrong:

D rejects a well-founded principle. E concerns critical constants themselves, not reduced-condition behavior.

Common Pitfalls:

Using corresponding states near phase boundaries without caution; neglecting acentric factor corrections for polar or associating molecules.

Final Answer:

both (a) and (b)