Concept:Using a balanced stoichiometric equation, we can determine the mass of reactant required to yield a specific mass of product.
Formula:$$ \text{Fe}_2\text{O}_3 \rightarrow 2\text{Fe} $$
Solution:- From the given balanced equation: 1 mole of Hematite (\( \text{Fe}_2\text{O}_3 \)) produces 2 moles of Iron (Fe).
- Molar mass of \( \text{Fe}_2\text{O}_3 = (56 \times 2) + (16 \times 3) = 112 + 48 = 160 \text{ g/mol} \).
- Molar mass of \( 2\text{Fe} = 2 \times 56 = 112 \text{ g} \).
- Therefore, 160g of ore produces 112g of iron.
- The question asks for the ore required to make 56g of iron (which is exactly half of 112g).
- Since the required iron is cut in half, the required ore is also cut in half: \( 160 / 2 = 80 \text{ g} \).
Why other options are incorrect:- 160g: This is the amount needed to produce 112g of iron, not 56g.
- 112g: This is merely the mass of 2 moles of iron.
- 280g: A random number generated from incorrect molar ratios.
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