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.
In a blast furnace, iron(III) oxide (Fe2O3) is reduced to iron by carbon monoxide (CO) according to the following balanced chemical equation:
[tex]Fe_2O_3 + 3CO \to 2Fe + 3CO_2[/tex]
This means that for every mole of Fe2O3 converted to iron, 3 moles of CO are required.
The molar mass of Fe2O3 is 159.69 g/mol. One ton of Fe2O3 is equivalent to 907185 g, so the number of moles of Fe2O3 in one ton is 907185 g / 159.69 g/mol = 5680.9 mol.
Since 3 moles of CO are required for every mole of Fe2O3, the number of moles of CO required to convert one ton of Fe2O3 into iron is 5680.9 mol * 3 = 20000 mol.
At a pressure of 760 torr and a temperature of 0 °C (273.15 K), the volume occupied by one mole of an ideal gas is given by the ideal gas law: V = nRT/P, where n is the number of moles, R is the ideal gas constant (62.3637 L·torr/K·mol), T is the temperature in kelvins, and P is the pressure in torr.
Substituting the values for n, R, T, and P into the ideal gas law gives the volume occupied by 20000 mol of CO at a pressure of 760 torr and a temperature of 0 °C: V = (20000 mol)(62.3637 L·torr/K·mol)(273.15 K) / (760 torr) = 400000 L.
Since air is assumed to be 19% oxygen by volume and oxygen is converted to CO in the blast furnace, the volume of air required to provide this amount of CO is 400000 L / 0.19 = 2000000 L.
There are approximately 28.317 liters in one cubic foot, so this volume in cubic feet is approximately 70000 cubic feet.
In my opinion, this answer seems to look correct. Do you agree with me?