One of the main reactions involved in the production of iron from iron(III) oxide as found in iron ore, proceeds according to the following balanced chemical equation:Fe2O3 (s) + 3 C(s) → 2 Fe(s) + 3 CO(g)We will consider the reaction of iron(III) oxide and carbon on a gram scale, although the same stoichiometry applies on the tonne scale.If 15.1 g of carbon is available, what is the maximum mass of iron which can be produced when the iron(III) oxide is present in excess?Enter your answer to three significant figures. Do not include units.
Question
One of the main reactions involved in the production of iron from iron(III) oxide as found in iron ore, proceeds according to the following balanced chemical equation:Fe2O3 (s) + 3 C(s) → 2 Fe(s) + 3 CO(g)We will consider the reaction of iron(III) oxide and carbon on a gram scale, although the same stoichiometry applies on the tonne scale.If 15.1 g of carbon is available, what is the maximum mass of iron which can be produced when the iron(III) oxide is present in excess?Enter your answer to three significant figures. Do not include units.
Solution
To solve this problem, we need to use stoichiometry, which is a method in chemistry that uses balanced chemical equations to predict the product amounts in a chemical reaction.
Step 1: Identify the balanced chemical equation Fe2O3 (s) + 3 C(s) → 2 Fe(s) + 3 CO(g)
Step 2: Calculate the molar mass of carbon (C) and iron (Fe) The molar mass of carbon is approximately 12.01 g/mol and the molar mass of iron is approximately 55.85 g/mol.
Step 3: Convert the mass of carbon to moles 15.1 g C * (1 mol C / 12.01 g C) = 1.26 mol C
Step 4: Use the stoichiometry of the reaction to find the moles of iron From the balanced chemical equation, we can see that 3 moles of carbon will produce 2 moles of iron. So, 1.26 mol C * (2 mol Fe / 3 mol C) = 0.84 mol Fe
Step 5: Convert the moles of iron to grams 0.84 mol Fe * (55.85 g Fe / 1 mol Fe) = 46.9 g Fe
So, the maximum mass of iron that can be produced when the iron(III) oxide is present in excess is 46.9 g.
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