Pure elements A and B are mixed in some proportion to form a solid solution with overall composition x0 (which stands for the mole fraction of B). Determine the fractions of the pure phases, fA and fB, that are needed to form this solution. Use conservation of atoms to form the basic equation, and use
the sum of fractions constraint to eliminate one of the variables.
Fraction of pure phase A = fA
Fraction of pure phase B = fB
Since the sum of fractions is always equal to unity (or 1) [sum of fractions constraint], we get:
fA + fB = 1
Mole fraction of a species is the ratio of its molar content to the total amount of moles of all the species in that solution.
Mole fraction of B: fB/(fA + fB) = X0
or, fB = X0 (since the denominator is equal to 1)
This substituting this value of fB in previous equation, we get,
fA = 1-fB = 1-X0.
Thus the final fractions fA and fB are equal to (1-X0) and X0, respectively.
Hope this helps.