In lever rule for a two-phase region, which statement about wα is correct when the overall composition moves toward the end of the two-phase region?

• A. wα increases toward 1.
• B. wα decreases toward 0.
• C. wα remains constant.
• D. wα becomes negative.

Answer: (B)

When you use the lever rule in a two-phase region, you connect the phase fractions to how far the overall composition lies from the phase boundaries. The weight fraction of the α phase is wα = (Cβ − C0) / (Cβ − Cα), where Cα and Cβ are the compositions of the α and β phases at equilibrium with each other, and C0 is the overall composition.

As the overall composition moves toward the end near the β-rich boundary (toward Cβ), the distance from C0 to Cβ gets smaller, so the numerator (Cβ − C0) decreases. This drives wα down toward zero, meaning the α phase becomes less abundant and can vanish at the β boundary. Conversely, moving toward the α-rich end (toward Cα) would make wα approach one, since the numerator would approach the full separation (Cβ − Cα). The idea that wα would stay constant or become negative doesn’t fit the lever rule, which ties wα to those compositional distances.