How many grams of C are required to react with 64.6 g of Fe2O3 ?

14.6 g

Explanation:

Fe₂O₃  +  3 C  →  2 Fe  +  3 CO₃

First, convert grams of Fe₂O₃ to moles.  The molar mass is 159.69 g/mol.

(64.6 g)/(159.69 g/mol) = 0.4045 mol

Now, use stoichiometry to convert moles of Fe₂O₃ to moles of C.  By looking at the chemical equation, you can see that for every 1 mole of Fe₂O₃, you need 3 moles of C.  Use this relationship.

(0.4045 mol Fe₂O₃) × (3 mol C/1 mol Fe₂O₃) = 1.214 mol C

Now, convert moles of C to grams.  The molar mass is 12.01 g/mol.

(1.214 mol C) × (12.01 g/mol) = 14.58 g

You need to use significant figures.

14.58 g ≈ 14.6 g