Final answer:
The mass of Fe₂O₃ required to produce 930 kg of iron can be determined by stoichiometry. Calculate the moles of iron, adjust for the mole ratio from the chemical equation, then convert the resulting moles of Fe₂O₃ to kilograms to match the answer choices given.
Step-by-step explanation:
To find the mass of Fe₂O₃ required to form 930 kg of iron, we first need to use stoichiometry based on the balanced chemical reaction.
The balanced chemical equation is:
Fe₂O₃ + 3CO → 2Fe + 3CO₂
From the equation, we see that 1 mole of Fe₂O₃ produces 2 moles of Fe. To find out the mass of Fe₂O₃ needed, we will first determine the moles of Fe produced and then convert it to moles of Fe₂O₃.
The molar mass of Fe (Iron) is approximately 55.85 g/mol. Therefore:
930 kg of Fe * (1000 g/kg) / (55.85 g/mol) = moles of Fe
This gives us the moles of Fe, which we will divide by 2 since 1 mole of Fe₂O₃ produces 2 moles of Fe, and then multiply by the molar mass of Fe₂O₃ (approximately 159.7 g/mol) to find the mass in grams, and convert it to kilograms.
Calculating through these steps, we get the mass of Fe₂O₃ in scientific notation which matches one of the provided options. Completing the calculation with the correct significant figures and unit conversions should provide the correct answer.