Answer :
The new actual yield of potassium chromate would be 263.80 kg when the percentage yield is 89.9%.
Given the balanced chemical reaction: 4FeCr₂O₄ + 8K₂CO₃ + 7O₂ → 8CO₂ + 2Fe₂O₃ + 8K₂CrO₄, the reagents initially used were 169 kg of chromite (FeCr₂O₄), 298 kg of potassium carbonate (K₂CO₃), and 75.0 kg of oxygen (O₂).
- Calculate the moles of each reactant to find the limiting reagent.
- Calculate the theoretical yield of K₂CrO₄ based on the moles of the limiting reagent.
- Apply the percentage yield to find the actual yield.
1. Molecular weights: (FeCr₂O₄),= 223.84 g/mol, K₂CO₃ = 138.205 g/mol, O2 = 32 g/mol
- Moles of (FeCr₂O₄),: 169 kg × (1000 g/kg) / 223.84 g/mol ≈ 755.1 mol
- Moles of K₂CO₃ : 298 kg × (1000 g/kg) / 138.205 g/mol ≈ 2156 mol
- Moles of O₂: 75 kg × (1000 g/kg) / 32 g/mol ≈ 2344 mol
2. Based on the stoichiometry, (FeCr₂O₄),is the limiting reagent:
- Theoretical yield of K₂CrO₄: 755.1 mol FeCr₂O₄ × (8 mol K₂CrO₄/ 4 mol FeCr₂O) ≈ 1510.2 mol
- Theoretical mass of K₂CrO₄: 1510.2 mol × 194.19 g/mol ≈ 293,222.4 g or 293.22 kg
3. Actual yield with 89.9% efficiency:
New actual yield = 293.22 kg × 0.899
= 263.80 kg