Titanium dioxide (TiO₂) is used extensively as a white pigment. It is produced from an ore that contains ilmenite (FeT_iO₃) 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 [Fez(S04)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 T₁O₂.