# Reduction of Iron (III) to elemental Iron - How do I calculate the mass of carbon needed?

The equation for reducing iron (iii) oxide with heated carbon is: $\ce{Fe2O3 (s) + 3C (s) + 3CO (g)}$ The mass of carbon needed to produce $100~\mathrm{g}$ iron is?

I honestly do not understand how to do this. Please give me a detailed solution and dumb it down as much as possible.

• Welcome to Chemistry.SE. Please show us what you have tried to accomplish and have a look at our homework policy. You can also improve formatting by following the guidelines in the help center. For a first start you might want to look at this wikipedia article about blast furnace – Martin - マーチン May 22 '14 at 11:53
• @Martin thanks I actually managed to work it out – user5583 May 22 '14 at 13:29
• Would you be kind enough to share your knowledge and post an answer to your question? It might help some other people later on. Thank you very much. – Martin - マーチン May 23 '14 at 1:46

It's easy to calculate the mass of carbon. At first you have to write down the chemical equation:

$2~Fe_2O_3 + 3~C \rightarrow 4~Fe + 3 CO_2$

Now you can solve the following equation:

$\frac{m_{C}}{m_{Fe}}=\frac{n_{C} \cdot M_{C}}{n_{Fe} \cdot M_{Fe}}$

$m_{C}=\frac{n_{C} \cdot M_{C} \cdot m_{Fe}}{n_{Fe} \cdot M_{Fe}}$

$m_{C}=\frac{3~mol \cdot 12~\frac{g}{mol} \cdot 100~g}{4~mol \cdot 56~\frac{g}{mol}}$

$m_{C} = 16~g$

You need 16g Carbon to produce 100g Iron.