Step-by-step explanation:
Iron (III) oxide will react with hydrogen gas to produce iron and water. They will react according to the following equation.
Fe₂O₃ + 3 H₂ -----> 2 Fe + 3 H₂O
We have to find the grams of Fe that can be made from 24.5 g of Fe₂O₃. So, first we have to convert those grams into moles using the molar mass of iron (III) oxide.
molar mass of Fe₂O₃ = 159.69 g/mol
mass of Fe₂O₃ = 24.5 g
moles of Fe₂O₃ = 24.5 g * 1 mol/(159.69 g)
moles of Fe₂O₃ = 0.153 mol
Fe₂O₃ + 3 H₂ -----> 2 Fe + 3 H₂O
According to the coefficients of the equation, we know that 1 mol of Fe₂O₃ will react with 3 moles of H₂ to give 2 moles of Fe and 3 moles of H₂O. So the molar ratio between Fe₂O₃ and Fe is 1 to 2. We can use that relationship to find the number of moles of Fe that can be made from 0.153 moles of Fe₂O₃.
1 mol of Fe₂O₃ : 2 moles of Fe molar ratio
moles of Fe = 0.153 moles of Fe₂O₃ * 2 moles of Fe/(1 mol of Fe₂O₃)
moles of Fe = 0.306 moles
So we found that we can produce 0.306 moles of Fe from 0.153 moles of Fe₂O₃ or 24.5 g of it. Finally we can convert the 0.306 moles of Fe into grams using the molar mass of Fe.
molar mass of Fe = 55.85 g/mol
mass of Fe = 0.306 moles * 55.85 g/mol
mass of Fe = 17.1 g
Answer: 17.1 g of iron can be made from 24.5 g of iron (III) oxide.