Fugacity and activity: identifying the incorrect real-gas statement: Choose the WRONG statement regarding activity coefficients, fugacity, and the fugacity coefficient for ideal gases and mixtures.

Introduction:
Fugacity and activity are corrected pressures and concentrations that account for nonideal behavior in gases and solutions. They appear in equilibrium expressions and chemical potential formulations. Distinguishing correct from incorrect statements avoids mistakes in reaction and phase-equilibrium calculations.

Given Data / Assumptions:

• Ideal-gas limit is approached as pressure → 0 or via idealized models.
• Definitions: fugacity f, fugacity coefficient φ = f / P.
• Activity coefficients γ apply to solutions and are dimensionless.

Concept / Approach:
For an ideal gas, fugacity equals pressure (f = P), hence the fugacity coefficient φ = f / P = 1, not zero. In ideal-gas mixtures, each component’s fugacity equals its partial pressure yi P. Activity coefficients are dimensionless measures of deviation from ideal-solution behavior. Therefore, any statement claiming φ = 0 for an ideal gas is incorrect.

Step-by-Step Solution:
Recall: ideal gas → f = P, φ = 1.Mixtures: fi = yi P for ideal-gas mixture.Activities in solutions use γ and dimensionless conventions.Conclude that the incorrect statement is “fugacity coefficient is zero for an ideal gas.”

Verification / Alternative check:
Taking the limit as P → 0 for any real gas, φ → 1, confirming the ideal-gas reference state.

Why Other Options Are Wrong:

• Options (a), (b), (c), (e) are correct statements consistent with standard thermodynamics.

Common Pitfalls:
Confusing φ (dimensionless) with compressibility factor Z; both → 1 in the ideal limit but represent different corrections.

Final Answer:
The fugacity co-efficient is zero for an ideal gas.