Titanium dioxide (TIO2) is a white molecule that is used as a pigment for white paint.

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Titanium dioxide (TIO2) is a white molecule that is used as a pigment for white paint. It is produced industrially by treating a mineral called ilmenite (FeTiO3) with sulfuric acid according the molecular equation below. In one particular reaction, 8,000 Kg of FeTiO3was used as a starting material for the reaction. What is the theoretical yield of TiO2? MW FeTiO3= 151.72 g/mol, MW TiO2= 79.88 g/mol. FeTiO3+ H2SO4→ TiO2+ FeSO4+ H2O
Titanium dioxide (TIO2) is a white molecule that is used as a pigment for white paint. It is produced industrially by treating a mineral called ilmenite (FeTiO3) with sulfuric acid according the molecular equation below. In one particular reaction, 8,000 Kg of FeTiO3was used as a starting material for the reaction. What is the theoretical yield of TiO2? MW FeTiO3= 151.72 g/mol, MW TiO2= 79.88 g/mol.

FeTiO3+ H2SO4→ TiO2+ FeSO4+ H2O

The Correct Answer and Explanation is:

Theoretical Yield of TiO₂ from FeTiO₃ Reaction

Given:

  • Reaction:
    FeTiO₃ + H₂SO₄ → TiO₂ + FeSO₄ + H₂O
  • Starting amount of FeTiO₃: 8000 kg = 8,000,000 g
  • Molar mass (MW) of FeTiO₃: 151.72 g/mol
  • Molar mass (MW) of TiO₂: 79.88 g/mol

Step-by-Step Calculation:

  1. Convert mass of FeTiO₃ to moles:

Moles of FeTiO₃=8,000,000 g151.72 g/mol≈52,712.68 mol\text{Moles of FeTiO₃} = \frac{8,000,000\ \text{g}}{151.72\ \text{g/mol}} \approx 52,712.68\ \text{mol}

  1. Use the mole ratio from the balanced equation:

From the reaction:
1 mol FeTiO₃ → 1 mol TiO₂
So, moles of TiO₂ produced = moles of FeTiO₃ = 52,712.68 mol

  1. Convert moles of TiO₂ to grams:

Mass of TiO₂=52,712.68 mol×79.88 g/mol≈4,211,751.78 g\text{Mass of TiO₂} = 52,712.68\ \text{mol} \times 79.88\ \text{g/mol} \approx 4,211,751.78\ \text{g}

  1. Convert grams to kilograms:

4,211,751.78 g1000=4211.75 kg\frac{4,211,751.78\ \text{g}}{1000} = \boxed{4211.75\ \text{kg}}

✅ Theoretical Yield of TiO₂: 4211.75 kg

Explanation

Titanium dioxide (TiO₂) is a crucial white pigment widely used in paint, sunscreen, and food products due to its brightness and opacity. Industrially, TiO₂ is produced from ilmenite (FeTiO₃), a naturally occurring ore, by reacting it with sulfuric acid (H₂SO₄). The balanced chemical equation is: FeTiO₃+H₂SO₄→TiO₂+FeSO₄+H₂O\text{FeTiO₃} + \text{H₂SO₄} \rightarrow \text{TiO₂} + \text{FeSO₄} + \text{H₂O}

This indicates a 1:1 molar ratio between FeTiO₃ and TiO₂—each mole of FeTiO₃ yields one mole of TiO₂.

In this problem, the goal is to find the theoretical yield of TiO₂ when 8000 kg (8,000,000 g) of FeTiO₃ is used. First, we determine how many moles of FeTiO₃ are present by dividing its mass by its molar mass (151.72 g/mol). This gives approximately 52,712.68 moles. Since the reaction produces TiO₂ in a 1:1 molar ratio, the same number of moles of TiO₂ is produced.

Next, to find the mass of TiO₂ produced, we multiply the moles by the molar mass of TiO₂ (79.88 g/mol), which results in approximately 4,211,751.78 grams, or 4211.75 kilograms.

This value represents the theoretical yield—the maximum possible mass of TiO₂ that can be produced under ideal conditions, assuming the reaction goes to completion and there are no losses. In practice, actual yield may be less due to incomplete reactions or process inefficiencies.

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