Question

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)+3Cl2(g)+3C(s)→3CO(g)+FeCl2(s)+TiCl4(g)TiCl4(g)+2Mg(s)→2MgCl2(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?

Answer 1

Mass of ilmenite in the ilmenite - sand mixture = 1.30 kg x (22.6 / 100) = 0.2938 Kg = 293.8 g

molecular mass of ilmenite, FeTiO3(s) = 151.71 g/mol

Hence moles fo ilmenite in ilmenite - sand mixture = mass/molar mass = 293.8 g / 151.71 g/mol = 1.9366 mol

For the first reaction, the percentage yiels = 91.1 %

FeTiO3(s)+3Cl2(g)+3C(s) -------- > 3CO(g)+FeCl2(s)+TiCl4(g)

1 mol, ----- 3 mol, -- 3 mol, ---------- 3 mol, 1 mol, ---- 1 mol

1 mol of ilmenite FeTiO3(s) forms1 mol TiCl4

Hence 1.9366 mol ilmenite that will form the moles of TiCl4 with 91.1 % yield

= 1.9366 mol ilmenite x (1 mol TiCl4 / 1 mol ilmenite) x (91.1 / 100)

= 1.764 mol TiCl4

For the first reaction, the percentage yiels = 86.1 %

TiCl4(g)+2Mg(s) --------- > 2MgCl2(l)+Ti(s)

1 mol, -- 2 mol--------------- 2 mol, ------ 1mol

1 mol of TiCl4 forms1 mol Ti(s)

Hence 1.764 mol TiCl4 that will form the moles of Ti(s) with 86.1 % yield

= 1.764 mol ilmenite x (1 mol TiCl4 / 1 mol ilmenite) x (86.1 / 100)

= 1.519 mol Ti(s)

Atomic mass of Ti(s) = 47.867 g/mol

Hence mass of Ti(s) formed = 1.519 mol x 47.867 g/mol = 72.7 g (answer)