Given the three-step "blast furnace" process that converts iron ore,Fe₂O₃,into molten "pig iron": 3 Fe₂O₃(l)+ CO(g)→ 2 Fe₃O₄(l)+ CO₂(g)
Fe₃O₄(l)+ CO(g)→ 3 FeO(l)+ CO₂(g)
FeO(l)+ CO(g)→ Fe(l)+ CO₂(g)
What mass of Fe₂O₃ is required to produce 1.00 metric ton (1000 kg)of iron?

Question

Quizplus · Accepted Answer

To find the mass of $Fe_2O_3$ required to produce 1.00 metric ton (1000 kg) of iron, we need to use stoichiometry based on the balanced chemical equations provided. The overall reaction, combining the three steps, is:$$Fe_2O_3 + 3CO \rightarrow 2Fe + 3CO_2$$From the balanced equation, 1 mole of $Fe_2O_3$ produces 2 moles of $Fe$. The molar mass of $Fe_2O_3$ is approximately 159.7 g/mol, and the molar mass of $Fe$ is approximately 55.85 g/mol.To produce 1000 kg (or 1,000,000 g) of $Fe$, we calculate the moles of $Fe$ produced:$$1000\,kg \times \frac{1000\,g}{1\,kg} \times \frac{1\,mol\,Fe}{55.85\,g} \approx 17907\,mol\,Fe$$Since 1 mole of $Fe_2O_3$ produces 2 moles of $Fe$, the moles of $Fe_2O_3$ required are half of the moles of $Fe$ produced:$$17907\,mol\,Fe \times \frac{1\,mol\,Fe_2O_3}{2\,mol\,Fe} \approx 8953.5\,mol\,Fe_2O_3$$The mass of $Fe_2O_3$ required is then:$$8953.5\,mol \times 159.7\,g/mol \approx 1430000\,g$$Converting to kilograms:$$1430000\,g \times \frac{1\,kg}{1000\,g} = 1430\,kg$$Therefore, 1430 kg of $Fe_2O_3$ is required to produce 1.00 metric ton (1000 kg) of iron.

Given the Three-Step "Blast Furnace" Process That Converts Iron Ore,Fe₂O₃,into