in a blast furnace, iron(III) oxide is used to produce iron by the following (unbalanced) reaction:
Fe2O3 + CO = Fe + CO2
a. if 4 kg Fe2O3 are available to react, how many moles of CO are needed?
Balance the equation.
Convert 4000 g Fe2O3 to mols. mols = grams/molar mass
Use the coefficients in the balanced equation to convert mols Fe2O3 to mols CO.
Well, I'm not 100% sure this is right but I believe it is 2,100 mol. of CO.
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To find out how many moles of CO are needed, we first need to balance the equation:
Fe2O3 + 3CO = 2Fe + 3CO2
Now we can use the balanced equation to determine the stoichiometry between Fe2O3 and CO. The stoichiometry can be interpreted as the ratio of the coefficients from the balanced equation.
To do this, we compare the coefficient of Fe2O3 to the coefficient of CO. From the balanced equation, we see that the coefficient of Fe2O3 is 1, and the coefficient of CO is 3.
So, the stoichiometry between Fe2O3 and CO is 1:3, meaning for every 1 mole of Fe2O3, we need 3 moles of CO.
Now, let's calculate the moles of CO needed when we have 4 kg of Fe2O3.
First, we need to calculate the molar mass of Fe2O3:
Molar mass of Fe2O3 = (2 x Atomic mass of Fe) + (3 x Atomic mass of O)
Atomic mass of Fe = 55.845 grams/mol
Atomic mass of O = 16.00 grams/mol
Molar mass of Fe2O3 = (2 x 55.845) + (3 x 16.00) = 159.69 grams/mol
Now, we can use the molar mass and the given mass of Fe2O3 to calculate the moles of Fe2O3:
Moles of Fe2O3 = Mass of Fe2O3 / Molar mass of Fe2O3
Given: Mass of Fe2O3 = 4 kg = 4000 grams
Moles of Fe2O3 = 4000 grams / 159.69 grams/mol ≈ 25.04 moles
Since the stoichiometry between Fe2O3 and CO is 1:3, we know that we need 3 moles of CO for every 1 mole of Fe2O3.
Therefore, to calculate the moles of CO needed when we have 25.04 moles of Fe2O3, we multiply the moles of Fe2O3 by the stoichiometric ratio:
Moles of CO = 25.04 moles of Fe2O3 × (3 moles of CO / 1 mole of Fe2O3) = 75.12 moles of CO
So, when 4 kg of Fe2O3 are available to react, we need approximately 75.12 moles of CO.