Question

How many cubic feet of air at a pressure of 760 torr and 0 °C is required per ton of Fe₂O₃ to convert that Fe₂O₃ into iron in a blast furnace? For this exercise, assume air is 19% oxygen by volume.

a. 7,888 cubic feet
b. 11,422 cubic feet
c. 14,956 cubic feet
d. 18,490 cubic feet

Answer 1

To convert Fe2O3 into iron in a blast furnace, approximately 381,947 cubic feet of air at a pressure of 760 torr and 0 °C is required per ton of Fe2O3.

Step-by-step explanation:

In order to answer the question, we need to know the molar masses of Fe2O3 and Fe. The molar mass of Fe2O3 is 159.69 g/mol and the molar mass of Fe is 55.85 g/mol. From the balanced equation: 4H2O(g) + 3Fe (s) → Fe3O4 (s) + 4H2(g), we can see that 3 moles of Fe are needed to produce 1 mole of Fe2O3.

1. Calculate the molar mass of Fe2O3: 1 ton of Fe2O3 is 907,185 grams (1 ton = 2000 pounds, 1 pound = 454 grams).
2. Convert the mass of Fe2O3 to moles using the molar mass: 907,185 g / 159.69 g/mol = 5,682.73 mol.
3. Using the stoichiometry from the balanced equation, determine the moles of Fe: 5,682.73 mol Fe2O3 x (3 mol Fe / 1 mol Fe2O3) = 17,048.19 mol Fe.
4. Calculate the volume of air needed by multiplying the moles of Fe by the moles of air needed per mole of Fe: 17,048.19 mol Fe x (22.4 L/mol) = 381,947.23 L.

Therefore, the answer is approximately 381,947 cubic feet of air (since 1 L = 0.0353 cubic feet).