Solution: Titanium occurs in the magnetic mineral ilmenite (FeTiO3), which is often found mixed up with sand. The ilmenite can be separated from the sand with magnets. The titanium can then be extracted from th

Titanium occurs in the magnetic mineral ilmenite (FeTiO₃), which is often found mixed up with sand. The ilmenite can be separated from the sand with magnets. The titanium can then be extracted from the ilmenite by the following set of reactions:
FeTiO₃(s) + 3 Cl₂ (g) + 3 C(s) → 3 CO(g) + FeCl₂(s) + TiCl₄(g)
TiCl₄(g) + 2 Mg(s) → MgCl₂(l) + Ti(s)

Suppose that an ilmenite-sand mixture contains 22.6 % ilmenite by mass and that the first reaction is carried out with a 91.1 % yield. If the second reaction is carried out with an 86.1 % yield, what mass of titanium can be obtained from 1.30 kg of the ilmenite-sand mixture?