Iron is extracted from the mineral magnetite, Fe3O4:
Fe3O4 (s) + 2 C (s) 3 Fe (s) + 2 CO2 (s)
A 35.0 g sample of magnetite is reacted with 4.0 g of carbon, and 15.0 g of iron is produced.
Determine the percentage yield of this reaction. (6)
molar mass of Fe3O4 ... 232 g
molar mass of C ... 12.0 g
molar mass of Fe ... 55.8 g
find the moles reacted , and the moles produced
... divide by the appropriate molar mass
carbon is the limiting reactant
theoretical yield (from the reaction equation) is 3 moles of Fe for every 2 moles of C
what % of the theoretical occurred?
To calculate the percentage yield of a reaction, you need to compare the actual yield of the desired product to the theoretical yield. The actual yield is the amount of product that is obtained experimentally, while the theoretical yield is the maximum amount of product that could be obtained based on the stoichiometry of the reaction.
In this case, the balanced chemical equation tells us that 1 mole of magnetite (Fe3O4) reacts with 2 moles of carbon (C) to produce 3 moles of iron (Fe) and 2 moles of carbon dioxide (CO2). So, we need to determine the moles of magnetite, carbon, and iron in the reaction.
1. Calculate the moles of magnetite:
molar mass of magnetite (Fe3O4) = (3 x atomic mass of Fe) + (4 x atomic mass of O)
= (3 x 55.85 g/mol) + (4 x 16.00 g/mol)
= 231.55 g/mol
moles of magnetite = mass of magnetite / molar mass
= 35.0 g / 231.55 g/mol
2. Calculate the moles of carbon:
molar mass of carbon (C) = 12.01 g/mol
moles of carbon = mass of carbon / molar mass
= 4.0 g / 12.01 g/mol
3. Calculate the moles of iron:
molar mass of iron (Fe) = 55.85 g/mol
moles of iron = mass of iron / molar mass
= 15.0 g / 55.85 g/mol
Now, we can determine the theoretical yield of iron based on the stoichiometry of the reaction. According to the balanced chemical equation, the mole ratio of iron to magnetite is 3:1. Therefore, the theoretical yield of iron is:
moles of iron x (3 moles of iron / 1 mole of magnetite) x molar mass of iron
(actual yield of iron is given as 15.0 g)
Finally, we can calculate the percentage yield using the formula:
percentage yield = (actual yield / theoretical yield) x 100
I hope this explanation helps you understand how to calculate the percentage yield in this reaction!