A magnesium-lead alloy of mass 5.5 kg consists of a solid α phase that has a composition that is just slightly below the solubility limit at 200 C (390 F). (a) What mass of lead is in the alloy? (b) If the alloy is heated to 350 C (660 F), how much more lead may be dissolved in the α phase without exceeding the solubility limit of this phase?

a) The mass of lead in the alloy = 0.28 kg

b) There can be dissolved 1.46 kg more of lead.

Explanation:

Step 1: Data given

mass of the magnesium-lead alloy = 5.5 kg

200 °C → 5 wt% Pb

350 °C → 25 wt% Pb

a) What mass of lead is in the alloy?

We have to calculate (for the magnesium-lead alloy) the mass of lead in 5.5 kg of the solid α phase at 200°C just below the solubility limit. The solubility limit for the α phase at 200°C is about 5 wt% Pb.

The mass of lead in the alloy = (0.05) * (5.5 kg) = 0.28 kg

b) If the alloy is heated to 350°C, how much more lead may be dissolved in the α phase without exceeding the solubility limit of this phase?

At 350°C, the solubility limit of the a phase increases to approximately 25 wt% Pb.

C (lead) = ((mass fo lead in alloy) + (mass lead)) / ((magnesium-lead alloy mass) + (mass lead))

0.25 = (0.28 + m (Pb)) / (5.5 + m (Pb))

0.25 * (5.5 + m (Pb)) = (0.28 + m (Pb))

1.375 + 0.25 m (Pb) = 0.28 + m (Pb)

1.095 = 0.75 m (Pb)

m (Pb) = 1.095 / 0.75

m (Pb) = 1.46

There can be dissolved 1.46 kg more of lead.