Iron is obtained commercially by the reaction of hematite #Fe_2O_3# with carbon monoxide. How many grams of iron is produced when 25.0 mol of hematite reacts with 30.0 mol of carbon monoxide?

Question

The reaction is #Fe_2O_3(s) + 3CO(g) -> 2Fe(s) + 3CO_2(g)#.

Mateo Aguilar · Accepted Answer

1117 grams of iron

As can be seen from the chemical equation, each mole of #Fe_2CO_3# needs 3 moles of #CO#. If 30 moles of #CO# are used, only 10 moles of #Fe_2CO_3# can be reduced, generating 20 moles of #Fe#, corresponding to 1117 grams of iron.

Wyatt Atkins · Answer

undefined To find the grams of iron produced, you first need to determine the limiting reactant. Then, use the stoichiometry of the balanced chemical equation to calculate the mass of iron produced.

Given the balanced equation:

Fe₂O₃ + 3CO → 2Fe + 3CO₂

Calculate the moles of iron produced from each reactant:

Moles of Fe₂O₃ = 25.0 mol
Moles of CO = 30.0 mol

From the stoichiometry, for every 1 mole of Fe₂O₃, 2 moles of Fe are produced, and for every 3 moles of CO, 2 moles of Fe are produced.

Compare the moles of iron produced from each reactant:

Moles of Fe from Fe₂O₃ = (25.0 mol Fe₂O₃) × (2 mol Fe / 1 mol Fe₂O₃) = 50.0 mol Fe
Moles of Fe from CO = (30.0 mol CO) × (2 mol Fe / 3 mol CO) = 20.0 mol Fe

Since CO produces fewer moles of Fe, it is the limiting reactant.

Calculate the mass of iron produced using the molar mass of Fe:

Mass of Fe = (20.0 mol Fe) × (55.845 g/mol Fe) = 1116.9 g Fe