Equilibrium in multicomponent, multiphase systems: Which approach cannot be used to calculate equilibrium relations?

Introduction / Context:
Phase and reaction equilibria require relations (e.g., K-values, activity coefficients) to specify how components distribute among phases. Several approaches exist: measurement, empirical correlations, and theoretical models. The phase rule, however, serves a different purpose.

Given Data / Assumptions:

• Gibbs phase rule: F = C − P + 2 (for nonreactive systems).
• Goal: Obtain actual equilibrium relationships (e.g., y vs. x, distribution ratios), not just degrees of freedom.

Concept / Approach:
The phase rule determines the number of independent intensive variables that must be fixed to define the state. It does not give numerical equilibrium relations. Those must come from experiments, empirical correlations (e.g., Antoine, Wilson, NRTL), or theoretical equations (e.g., EOS with mixing rules).

Step-by-Step Solution:

Verification / Alternative check:
In VLE design, phase rule tells you how many variables to set (e.g., T and P), but K-values still require data or models.

Why Other Options Are Wrong:

• Experimental data, empirical equations, theoretical equations all directly yield or fit equilibrium relations.

Common Pitfalls:
Assuming the phase rule can replace property models; it cannot provide numerical partitioning.

Final Answer:
phase rule