Question

Iron is produced by heating iron(III) oxide with carbon (in form of coke) to give iron and carbon dioxide. Calculate the mass of coke needed to react completely with 1kg iron(III) oxide?

Answer 1

Answer on Question #42645 - Chemistry - Other

Question:

Iron is produced by heating iron(III) oxide with carbon (in form of coke) to give iron and carbon dioxide. Calculate the mass of coke needed to react completely with 1kg iron(III) oxide?

Answer:

The reaction is:

$$2 \mathrm{Fe_2O_3} + 3 \mathrm{C} = 4 \mathrm{Fe} + 3 \mathrm{CO_2}$$

Molar mass of $\mathrm{Fe_2O_3}$ equals:

$$M(\mathrm{Fe_2O_3}) = 2M(\mathrm{Fe}) + 3M(\mathrm{O}) = 2 \cdot 56 + 3 \cdot 16 = 160 \ \frac{\mathrm{g}}{\mathrm{mole}}$$

Therefore, mass of 2 moles of $\mathrm{Fe_2O_3}$ equals $320\ \mathrm{g}$.

Molar mass of coke (C) equals $12\ \mathrm{g/mole}$. Therefore, mass of 3 moles of C equals $36\ \mathrm{g}$.

Then we make a proportion:

$$320\ \mathrm{g} \text{ of } \mathrm{Fe_2O_3} \text{ reacts with } 36\ \mathrm{g} \text{ of C}$$ $$1000\ \mathrm{g} \text{ of } \mathrm{Fe_2O_3} - x\ \mathrm{g} \text{ of C}$$ $$x = \frac{1000 \cdot 36}{320} = 112.5\ \mathrm{g}$$

So, the mass of coke needed to react completely with 1kg iron(III) oxide equals $112.5\ \mathrm{g}$.

Answer: $m(C) = 112.5\ \mathrm{g}$

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