Question

A hypothetical A-B alloy of composition 57 wt% B-43 wt% A at some temperature is found to consist of mass fractions of 0.5 for both and phases. If the composition of the phase is 87 wt% B-13 wt% A, what is the composition of the phase

Answer 1

Answer:

composition of alpha phase is 27% B

Explanation:

given data

mass fractions  = 0.5 for both

composition = 57 wt% B-43 wt% A

composition = 87 wt% B-13 wt% A

solution

as by total composition Co = 57 and by beta phase composition  Cβ = 87  

we use here lever rule that is

Wα = Wβ   ...............1

Wα = Wβ = 0.5

now we take here left side of equation

we will get

$\frac{C_\beta - Co}{C_\beta - Ca}$   = 0.5

$\frac{87 - 57}{87 - Ca}$ = 0.5  

solve it we get

Ca = 27

so composition of alpha phase is 27% B

Answer 2

The composition of the phase is; 27

What is the composition of the alloy?

Mass fractions for both; w_a = w_b = 0.5 for both

Composition of A-B alloy; C_o = 57 wt% B - 43 wt% A

New composition of the phase; C_b = 87 wt% B - 13 wt% A

Using the Lever rule that is used to determine the mole fraction (x_i) or the mass fraction (w_i) of each phase of a binary equilibrium phase, we have;

W_a = W_b = 0.5

This gives us;

(C_b - C_o)/(C_b - C_a) = 0.5

(87 - 57)/(87 - C_a) = 0.5

30/0.5 = 87 - C_a

60 = 87 - C_a

C_a = 87 - 60

C_a = 27

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