Based on the figure below showing an alloy with two soluble components (A & B),

Question

Based on the figure below showing an alloy with two soluble components (A & B), calculate the masses of the alloy that are in the liquid and solid phases at a given temperature if the total alloy mass is 200 g, Component B represents 60% of the total alloy, 25% of the liquid phase is Component B, and 70% of the solid is Component B.

100 Melting temperature of material A Percent weight of material A 50 25 Liquid Liquid and solid Solid 50 Percent weight of material B N Melting temperature of material B 100

Explanation / Answer

Total mass of alloy = 200 g.

Mass of B in total alloy = 200 * 60 / 100 = 120 g.

Then mass of A in total alloy = 200 - 120 = 80 g.

Mass of liquid phase of B + mass of solid phase of B = toal mass of B

L*25/100 + S*70/100 = 120

25 L + 70 S = 12000 ------(1)

similarly, L*75/100 + S*30/100 = 80 for companant 'A'

75 L + 30 S = 8000 ---(2)

(1) *3 - (2)

75 L + 240 S = 36000

75 L + 30 S = 8000

(-)

210 S = 24000

S = 114.28 g.

Therefore total mass of alloy in solid phase = 114.28 g.

and total mass of alloy in liquid phase = 200 - 114.28 = 85.72 g.

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