Fugacity and Activity

This topic makes the equilibrium criterion quantitative for non-ideal systems. You compute vapour fugacity from an equation of state through φ, and liquid fugacity from an activity-coefficient model (Wilson, NRTL, UNIQUAC or the group-contribution UNIFAC). The purpose is to feed accurate γ and φ values into the phase-equilibria and distillation calculations that follow.

(fugacity definition at constant T)

(vapour phase fugacity)

(liquid phase, standard state f_i^0)

Relation 1 —

(fugacity definition at constant T)

Write this relation with symbols exactly as in Introduction to Chemical Engineering Thermodynamics — Smith, Van Ness & Abbott before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 2 —

(vapour phase fugacity)

Write this relation with symbols exactly as in Introduction to Chemical Engineering Thermodynamics — Smith, Van Ness & Abbott before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Relation 3 —

(liquid phase, standard state f_i^0)

Write this relation with symbols exactly as in Introduction to Chemical Engineering Thermodynamics — Smith, Van Ness & Abbott before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Because chemical potential is awkward to use directly, Lewis introduced fugacity so that μ − μ° = RT ln(f/f°). For an ideal gas f equals the partial pressure, so the fugacity coefficient φ = f/(yP) measures vapour non-ideality. In the liquid, activity a = γx measures departure from an ideal solution: γ > 1 signals positive deviation (like-molecules prefer their own kind, promoting azeotropes), γ < 1 signals negative deviation. Setting liquid and vapour fugacities equal is the rigorous, model-independent statement of equilibrium.

State assumptions explicitly before using any relation for fugacity and activity — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.

Wrong assumptions invalidate the entire solution even when the formula is correct. In Chemical Engineering Thermodynamics viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

1. Read the question and list given data with SI units (common in Chemical Engineering Thermodynamics papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to fugacity and activity.
4. Use equation 1: .
5. Use equation 2: .
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Fugacity and Activity appears in separation and reaction design. In Indian chemical curricula this topic is tested because it connects theory to phase equilibria and property models.

GATE and semester exams often combine fugacity and activity with earlier units — revise prerequisites before attempting mixed problems.

Industry interview panels sometimes ask: "Where did you use fugacity and activity?" — answer with a lab, mini-project, or plant visit example if possible.

Students confuse fugacity coefficient φ (vapour non-ideality) with activity coefficient γ (liquid non-ideality), and forget to reference activity to a defined standard state. Applying an activity model outside its fitted composition range also produces large errors.

Before attempting fugacity and activity problems, confirm you can:

1.
2.
3. Activity coefficients from UNIFAC, NRTL, or Wilson models

Revise the solved examples in Introduction to Chemical Engineering Thermodynamics — Smith, Van Ness & Abbott and one previous-year GATE or university paper for this unit.