Assume you have 1 kg of material at equalibrium with a compo

Assume you have 1 kg of material at equalibrium with a composition of 60 wt% Al_2O_3 at 1600 degree C in the MgO-Al_2O_3 phase system. How much of the material (i.e. the fractional amount) is the MgAl_2O_4 solid solution phase?

Solution

The question gives the iformation that the solution is of 60 %Al₂O₃ so it contains 40 % MgO

now the given temperature is 1600 and Al₂O₃ is 60% hence we can locate the point in the graph that it conntains MgO and MgAl₂O₄

now weight of Al₂O₃ in 1 Kg = 60 % of 1Kg = 600g = 5.88 moles

weight of MgO = 40%of 1Kg = 400g = 10 Moles

hence 5.88 moles of Mgo will combine with 5.88 moles of Al₂O₃

So th mixture contains 4 moles of MgO and 5.88moles of MgAl₂O₄

Hence moles fraction of MgAl₂O₄ = 5.88/4+5.88 = .595 (ans)

mass fraction of MgAl₂O₄ = 4*146/1000 = .584 (ans)