Question

Pure iron, Fe , can be produced from an ore called hematite, Fe2O3 , by reaction with carbon at high temperatures. 2Fe2O3+3C⟶4Fe+3CO2 How many tons of hematite must react with carbon if an iron company needs to make 49 tons of iron?

Answer 1

70 tons of hematite (Fe₂O₃) is needed to produce 49 tons of iron (Fe).

We'll begin by calculating the tons of hematite (Fe₂O₃) that reacted and the tons of Fe produced from the balanced equation. This is illustrated below:

2Fe₂O₃ + 3C —> 4Fe + 3CO₂

Molar mass of Fe₂O₃ = (56×2) + (16×3) = 160 g/mol

Mass of Fe₂O₃ from the balanced equation = 2 × 160 = 320 g

Divide by 907185 to express in ton

320 / 907185 = 0.000353 ton

Molar mass of Fe = 56 g/mol

Mass of Fe from the balanced equation = 56 × 4 = 224 g

Divide by 907185 to express in ton

224 / 907185 = 0.000247 ton

SUMMARY

From the balanced equation above,

0.000353 ton of Fe₂O₃ reacted to produce 0.000247 ton of Fe.

Finally, we shall determine the tons of hematite (Fe₂O₃) needed to produce 49 tons of Fe. This can be obtained as follow:

From the balanced equation above,

0.000353 ton of Fe₂O₃ reacted to produce 0.000247 ton of Fe.

Therefore,

X ton of Fe₂O₃ will react to produce 49 tons of Fe i.e

X ton of Fe₂O₃ = $\frac{0.000353 * 49}{0.000247}$

X ton of Fe₂O₃ = 70 tons

Thus, 70 tons of hematite (Fe₂O₃) is needed to produce 49 tons of Fe.

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