Law of corresponding states — Select the statement that most directly expresses this law for gases and liquids.

Introduction:
The law of corresponding states provides a powerful similarity principle for fluids. It rationalizes how diverse gases and liquids can be represented on the same generalized compressibility or equation-of-state charts when expressed in reduced variables.

Given Data / Assumptions:

• Reduced variables: P_r = P/P_c, T_r = T/T_c, and V_r or Z are defined with respect to critical properties.
• Focus is on qualitative statement of the law.

Concept / Approach:
The law asserts that many gases and liquids have approximately the same compressibility factor Z and related behavior at equal values of reduced temperature and reduced pressure. This underlies generalized charts for Z, enthalpy departure, fugacity coefficients, etc. Options (b) and (c) are true statements about the critical point and liquefaction, but they are not the statement of the law.

Step-by-Step Solution:
Identify the definition-based option: similarity at equal reduced properties.Recognize critical-point facts (b), (c) as corollaries but not the law itself.Select option (a) as the direct expression of the law.

Verification / Alternative check:
Generalized compressibility charts collapse data for many substances when plotted vs. P_r and T_r, validating the law’s practical utility.

Why Other Options Are Wrong:

• (b) and (c) are correct but are narrow facts about critical phenomena.
• (d) is not universally correct; heat capacities vary and are temperature-dependent.
• (e) is false; real gases deviate from ideal behavior near critical conditions.

Common Pitfalls:
Confusing the law’s statement with separate critical-point properties; assuming universal constancy of heat capacities.

Final Answer:
Two different gases behave similarly if their reduced properties (reduced P, V, and T) are the same