What is a balanced chemical equation for iron oxide reacting with carbon monoxide that produces atomic iron and carbon dioxide?

Hello! Most likely, it is iron (III) oxide, `Fe_2 O_3`. Carbon monoxide is identified as `CO`, and carbon dioxide is identified as`CO_2`.

The unbalanced reaction is `Fe_2 O_3 + CO -> Fe + CO_2`. To balance it, place undetermined coefficients before each molecule and find them:

`a_1 * Fe_2 O_3 + a_2 * CO = a_3 * Fe + a_4 * CO_2`.

The quantities of each atom on both sides must be the same. There...

Hello! Most likely, it is iron (III) oxide, `Fe_2 O_3`. Carbon monoxide is identified as `CO`, and carbon dioxide is identified as`CO_2`.

The unbalanced reaction is `Fe_2 O_3 + CO -> Fe + CO_2`. To balance it, place undetermined coefficients before each molecule and find them:

`a_1 * Fe_2 O_3 + a_2 * CO = a_3 * Fe + a_4 * CO_2`.

The quantities of each atom on both sides must be the same. There are three types of atoms in this reaction: `Fe`, `C`, and `O.` For `Fe` atoms, we have `2a_1 = a_3`, for `C` atoms, we have `a_2 = a_4`, and for `O` atoms we have `3a_1 + a_2 = 2a_4`.

Substitute `a_4 = a_2` from the second equation to the third and obtain `3a_1 + a_2 = 2a_2` or `a_1 = 1/3 a_2`. Substitute this into the first equation and obtain `2/3 a_2 = a_3`.

All coefficients must be natural numbers, so the smallest value for `a_2` is `3`. Then, we get `a_3 = 2/3 a_2 = 2`, `a_1 = 1/3 a_2 = 1`, and `a_4 = a_2 = 3.`

The balanced reaction is as follows:

`Fe_2 O_3 + 3 CO -> 2 Fe + 3 CO_2`.