Gas-phase nonideality in VLE modeling: In vapor–liquid equilibrium calculations, which of the following does <em>not</em> represent gas-phase deviation from ideal-gas behavior?

Introduction / Context:Accurate VLE modeling requires accounting for nonideal behavior in both phases. Gas-phase deviations are often treated via equations of state or fugacity coefficients, while liquid-phase deviations are captured by activity coefficients. Knowing which tool belongs to which phase avoids modeling errors.

Given Data / Assumptions:

• Nonreacting vapor–liquid equilibrium.
• Potential nonideality in either phase.
• Standard thermodynamic framework using fugacity to express chemical potential.

Concept / Approach:The vapor-phase fugacity of component i is f_i^v = φ_i y_i P, where φ_i is the fugacity coefficient computed from an equation of state or virial method. The liquid-phase fugacity is f_i^l = γ_i x_i f_i^0 (or γ_i x_i p_i^sat for simple models), where γ_i is the activity coefficient from a liquid nonideality model (e.g., Wilson, NRTL, UNIQUAC). Thus, equations of state and φ are vapor-phase nonideality tools; γ belongs to the liquid phase.

Step-by-Step Solution:Identify phase: (a) and (b) are vapor-phase corrections.Recognize that γ belongs to liquid-phase modeling.Therefore, the item that does not address gas-phase nonideality is the activity coefficient.

Verification / Alternative check:Common practice: φ–φ methods (EoS for both phases) or γ–φ methods (activity model for liquid, EoS for vapor) illustrate the separation of roles.

Why Other Options Are Wrong:Equation of state and fugacity coefficient specifically target vapor-phase nonideality; they are not incorrect.

Common Pitfalls:Using γ for the gas phase; forgetting that γ approaches 1 for ideal liquids, while φ approaches 1 for ideal gases under low P and high T.

Final Answer:Activity coefficient (γ) for the liquid phase