Law of corresponding states: At equal reduced pressure and equal reduced temperature (corresponding states), which property of different gases is nearly the same?

Introduction / Context:The corresponding states principle normalizes fluid behavior using critical properties. When two gases have the same reduced temperature Tr = T/Tc and reduced pressure Pr = P/Pc, many of their dimensionless properties align. Most notably, their compressibility factors become similar, enabling generalized correlations valid across substances.

Given Data / Assumptions:

• Equal reduced temperature and pressure for different gases.
• We seek the property that is nearly the same under these corresponding conditions.

Concept / Approach:Empirical evidence and theory show that compressibility factor Z collapses across gases at equal Tr and Pr. This is the basis of generalized compressibility charts and PVT correlations. Molecular weight or humidity are not state functions tied to corresponding states in this way; viscosity can be partially correlated but is not 'nearly the same' in the strict sense like Z.

Step-by-Step Solution:

Verification / Alternative check:Generalized compressibility charts (Standing–Katz style) demonstrate the collapse of Z vs. Pr at given Tr for a wide class of gases.

Why Other Options Are Wrong:

• Molecular weight: intrinsic to species, does not equalize at corresponding states.
• Humidity: pertains to mixtures like moist air, not a pure-gas corresponding property.
• Viscosity: only loosely correlates; not 'nearly the same' across all gases at equal Tr, Pr.
• Molar refractivity: not governed by corresponding-states equality in this context.

Common Pitfalls:Overgeneralizing corresponding states to transport properties; confusing mixture properties with pure-fluid corresponding states.

Final Answer:Compressibility (Z)