A Cu-35 wt% Ni alloy is held at a temperature where two phases coexist: liquid (31.5 wt% Ni) and solid α (42.5 wt% Ni). Which value is closest to the mass fraction of liquid?

Answer: B. About 0.68

With the lever rule, the fraction of a phase is the distance from the alloy composition to the composition of the opposite phase, divided by the total length of the tie line. The liquid fraction is W_L = (Cα − C₀)/(Cα − C_L) = (42.5 − 35)/(42.5 − 31.5) = 7.5/11.0 ≈ 0.68. About 0.32 is the mistake of taking the distance on the same side, (35 − 31.5)/11.0, which is the fraction of α. About 0.82 is the ratio of the alloy composition to the solid composition, 35/42.5, which is not the lever rule. The fractions of the two phases always sum to 1, which you can use as a check once you have found one of them.