Fugacity in mixtures: For a stable binary mixture at constant temperature and pressure, how does the fugacity of a component change as its mole fraction increases?

Introduction / Context:
Fugacity generalizes the idea of an effective pressure for real fluids and appears in equilibrium criteria. In mixtures at fixed temperature and pressure, component fugacity is closely tied to composition through activity (liquids) or partial pressure (gases). This question probes the qualitative trend with composition.

Given Data / Assumptions:

• Binary mixture at fixed T and P.
• No chemical reaction; single phase stable region.
• Regular behavior without azeotropic anomalies for the qualitative trend.

Concept / Approach:

For gases, f_i ≈ y_i * φ_i * P; as y_i (the mole fraction in the gas phase) increases at fixed P and T, f_i typically increases. For liquids, f_i ≈ x_i * γ_i * f_i^sat(T); while γ_i can vary with composition, the basic trend for small to moderate nonideality is that increasing x_i raises the product x_i * γ_i, and hence fugacity, unless extreme nonideal effects intervene. Therefore, under ordinary stable conditions, fugacity of a component increases with its mole fraction.

Step-by-Step Solution:

Verification / Alternative check:

Modified Raoult’s law and equations of state lead to monotonic increases of f_i with x_i or y_i in stable single-phase regions away from critical anomalies.

Why Other Options Are Wrong:

Decrease or constancy contradicts standard thermodynamic relations; oscillation lacks physical basis in stable mixtures.

Common Pitfalls:

Confusing fugacity with activity coefficient alone; overlooking that fugacity depends on the product with composition (x_i or y_i).

Final Answer:

increases