Question

Titanium dioxide (TiO2) is used extensively as a white pigment. It is produced from an ore that contains ilmenite (FeTiO3) and ferric oxide (Fe2O3). The ore is digested with an aqueous sulfuric acid solution to produce an aqueous solution of titanyl sulfate [(TiO)SO4 ] and ferrous sulfate (FeSO4 ). Water is added to hydrolyze the titanyl sulfate to H2TiO3, which precipitates, and H2SO4. The precipitate is then roasted, driving off water and leaving a residue of pure titanium dioxide. (Several steps to remove iron from the intermediate solutions as iron sulfate have been omitted from this description.) Suppose an ore containing 24.3% Ti by mass is digested with an 80% H2SO4 solution, supplied in 50% excess of the amount needed to convert all the ilmenite to titanyl sulfate and all the ferric oxide to ferric sulfate [Fe2 (SO4 )3 ]. Further suppose that 89% of the ilmenite actually decomposes. Calculate the masses (kg) of ore and 80% sulfuric acid solution that must be fed to produce 1000 kg of pure TiO2.

Answer 1

Answer:

2928kg of ore are required.

2585kg of the 80% H₂SO₄ solution are required.

Explanation:

To solve this question we need first to find the moles of titanium in 1000kg of TiO₂. Keeping in mind the 89% of descomposition we can find the mass of the ore and the mass of the 80% sulfuric acid required:

Moles TiO₂ -Molar mass: 79.866g/mol-:

1x10⁶g * (1mol / 79.866g) = 12521 moles Titanium

In mass -Molar mass Ti: 47.867g/mol-:

12521 moles Titanium * (47.867g / mol) = 599341.4g of Ti.

As the ore contains 24.3% of Ti:

599341.4g of Ti = 599.34kg Ti * (100 / 24.3) = 2606kg ore

As the descomposition is just of 89%:

2606kg ore * (100 / 89) =

2928kg of ore are required

Mass 80% sulfuric acid:

12521 moles Titanium = 12521 moles H₂SO₄ * (100/89) = 14068.5 moles of H₂SO₄ are required.

In an excess of 50% =

14068.5 moles of H₂SO₄ are required * 1.5 = 21102.8 moles of H₂SO₄.

The mass is:

21102.8 moles of H₂SO₄ * (98g / mol) = 2068075g = 2068kg of sulfuric acid

That is in the 80%:

2068kg of sulfuric acid * (100/ 80) =

2585kg of the 80% H₂SO₄ solution are required