Answer: 10.51 kg of iron is produced in the reaction.
Explanation: The balanced equation for the reaction between iron III oxide and iron is:
2Fe2O3 + 3C → 4Fe + 3CO2
From the equation, we can see that 2 moles of Fe2O3 react to produce 4 moles of Fe. We can use the molar mass of Fe2O3 to convert the given mass to moles, and then use the mole ratio to calculate the moles of Fe produced. Finally, we can convert the moles of Fe to mass using the molar mass of Fe.
The molar mass of Fe2O3 is:
2(55.85 g/mol Fe) + 3(16.00 g/mol O) = 159.69 g/mol Fe2O3
So, 15 kg (or 15000 g) of Fe2O3 is equal to:
15000 g / 159.69 g/mol = 94.03 mol Fe2O3
According to the balanced equation, 2 moles of Fe2O3 produce 4 moles of Fe. So, 94.03 moles of Fe2O3 will produce:
4/2 x 94.03 = 188.06 moles of Fe
The molar mass of Fe is 55.85 g/mol, so the mass of Fe produced is:
188.06 mol x 55.85 g/mol = 10507.8 g or 10.51 kg