How many cubic feet of air at a pressure of 760 torr and 0 °C is required per ton of Fe_{2}O_{3} to convert that Fe_{2}O_{3} into iron in a blast furnace? For this exercise, assume air is 19% oxygen by volume.

**My answer**:

In a blast furnace, iron(III) oxide (Fe_{2}O_{3}) 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 Fe_{2}O_{3} converted to iron, 3 moles of CO are required.

The molar mass of Fe_{2}O_{3} is 159.69 g/mol. One ton of Fe_{2}O_{3} is equivalent to 907185 g, so the number of moles of Fe_{2}O_{3} in one ton is 907185 g / 159.69 g/mol = 5680.9 mol.

Since 3 moles of CO are required for every mole of Fe_{2}O_{3}, the number of moles of CO required to convert one ton of Fe_{2}O_{3} 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?