Answer:
There is 100.4652 kg of iron produced from 390 kg of Fe2O3
Explanation:
<u>Step 1</u>: Given data
3Fe2O3 + CO → 2Fe3O4 + CO2
Fe3O4 + CO → 3FeO + CO2
FeO + CO → Fe + CO2
Mass of Fe2O3 = 390 kg = 390000 grams
Molar mass of Fe2O3 = 159.69 g/moles
<u>Step 2: </u>Calculate moles of Fe2O3
Moles of Fe2O3 = mass of Fe2O3 / Molar mass of Fe2O3
Moles of Fe2O3 = 390000 grams / 159.69 g/moles = 2442.2 moles
<u>Step 3</u>: Calculate expected moles of Fe3O4
In the first equation, for 3 moles of Fe2O3 consumed ,we get 2 moles of Fe3O4. The mole ratio is 3:2
This means if we consume 2442.2 moles of Fe2O3, there will be produced 2/3 * 2442.2 = 1628.2 moles of Fe3O4
Since the yield for the step is only 84.6 %
This will be 0.846 * 1628.2 = 1377.4 moles of Fe3O4
<u>Step 4:</u> Calculate expected moles of FeO
In the second equation, for 1 mole of Fe3O4 consumed, there is produced 3 moles of FeO
This means for 1377.4 moles of Fe3O4 consumed, there is 3*1377.4 = 4132.2 moles of FeO produced
Since the yield for the step is only 50.8%
This will be 0.508 * 4132.2 = 2099.2 moles of FeO
<u>Step 5:</u> Calculate expected moles of Fe
In the third equation, for 1 mole of FeO consumed, there is produced 1 mole of Fe.
This means for 2099.2 moles of FeO consumed, there is also 2099.2 moles of Fe produced
Since the yield is only 85.7%
This will be 0.857 * 2099.2 = 1799 moles of Fe
<u>Step 6:</u> Calculate mass of Fe
Mass of Fe = moles of Fe * Molar mass of Fe
Mass of Fe = 1799 moles of Fe * 55.845 g/moles = 100465.2 grams = 100.4652 kg of Fe
There is 100.4652 kg of iron produced from 390 kg of Fe2O3
