Identify the relation that is not an equation of state for real gases:

Introduction / Context:
Equations of state (EoS) relate P, V, and T of a fluid, enabling prediction of densities, fugacities, and phase behavior. Distinguishing EoS from empirical vapor-pressure correlations is critical when choosing models for design and simulation.

Given Data / Assumptions:

• Real-gas behavior; need P–V–T relations for the bulk phase.
• Well-known EoS include virial, van der Waals, Redlich–Kwong, Peng–Robinson, etc.
• Antoine correlation gives p^sat(T) for a pure component; it is not a P–V–T relation.

Concept / Approach:
An equation of state must connect pressure, temperature, and molar (or specific) volume. The virial equation expands compressibility in powers of 1/V (or in Z). Van der Waals and Redlich–Kwong are cubic EoS directly providing P as a function of T and V. The Antoine equation, however, correlates saturation pressure with temperature only for a pure component and does not provide V; it is a property correlation, not an EoS.

Step-by-Step Solution:
List options: (a) virial → EoS; (b) van der Waals → EoS; (d) Redlich–Kwong → EoS; (c) Antoine → vapor-pressure correlation.Identify the odd one out: Antoine equation is not an equation of state.

Verification / Alternative check:
Software workflows use Antoine for bubble/dew calculations together with an EoS or activity model; this division of roles underscores that Antoine is not an EoS.

Why Other Options Are Wrong:
They are true equations of state connecting P–V–T for gases/fluids.

Common Pitfalls:
Confusing property correlations (Antoine) with EoS; assuming any pressure–temperature formula is an EoS.

Final Answer:
Antoine equation for vapor pressure: log10 p^sat = A − B/(C + T)