1. Write the balanced chemical equation:

The reaction between carbon (C) and hematite (Fe₂O₃) produces iron (Fe) and carbon dioxide (CO₂):

2 Fe₂O₃ + 3 C → 4 Fe + 3 CO₂

2. Calculate the moles of hematite:

* Find the molar mass of hematite (Fe₂O₃): (2 * 55.845 g/mol Fe) + (3 * 16.00 g/mol O) = 159.69 g/mol

* Divide the mass of hematite by its molar mass: 580 g / 159.69 g/mol = 3.63 mol Fe₂O₃

3. Determine the mole ratio from the balanced equation:

* The balanced equation shows that 3 moles of carbon react with 2 moles of hematite.

4. Calculate the moles of carbon needed:

* Set up a proportion: (3 mol C / 2 mol Fe₂O₃) = (x mol C / 3.63 mol Fe₂O₃)

* Solve for x: x = (3 mol C * 3.63 mol Fe₂O₃) / 2 mol Fe₂O₃ = 5.45 mol C

Therefore, you would need 5.45 moles of carbon to react with 580 g of hematite.