How many moles of Fe2O3 are required to produce 38.4 moles of Fe?
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To determine the number of moles of Fe2O3 required to produce 38.4 moles of Fe, we need to use the balanced chemical equation for the reaction. The balanced equation for the reaction of Fe2O3 producing Fe is:
2 Fe2O3 + 3 C → 4 Fe + 3 CO2
From the equation, we can see that 2 moles of Fe2O3 produce 4 moles of Fe. This means that the mole ratio of Fe2O3 to Fe is 2:4, or 1:2.
Using this mole ratio, we can set up a proportion to find the number of moles of Fe2O3 needed:
1 mole of Fe2O3 / 2 moles of Fe = x moles of Fe2O3 / 38.4 moles of Fe
Cross-multiplying the proportion, we get:
1 * 38.4 = 2 * x
38.4 = 2x
Dividing both sides by 2:
x = 19.2
Therefore, 19.2 moles of Fe2O3 are required to produce 38.4 moles of Fe.