In lever rule, what does wβ do as the overall composition C0 moves toward Cβ?

• A. wβ decreases toward 0.
• B. wβ increases toward 0.5.
• C. wβ increases toward 1.
• D. wβ remains constant.

Answer: (C)

In the lever rule for a two-phase region, the weight fraction of phase β is wβ = (C0 − Cα) / (Cβ − Cα). This tells us how far the overall composition sits between the two phase compositions.

As the overall composition C0 moves toward the β end, C0 gets closer to Cβ, so the numerator (C0 − Cα) grows toward the full gap (Cβ − Cα) while the denominator stays the same. That makes wβ approach 1, meaning the mixture becomes almost entirely β phase. At the limit where C0 equals Cβ, wβ is 1 (and the α fraction goes to zero).