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

Monday, 10 August 2015

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, $\displaystyle{F}{e}_{{2}}{O}_{{3}}$ . Carbon monoxide is identified as $\displaystyle{C}{O}$ , and carbon dioxide is identified as $\displaystyle{C}{O}_{{2}}$ .

The unbalanced reaction is $\displaystyle{F}{e}_{{2}}{O}_{{3}}+{C}{O}\to{F}{e}+{C}{O}_{{2}}$ . To balance it, place undetermined coefficients before each molecule and find them:

$\displaystyle{a}_{{1}}\cdot{F}{e}_{{2}}{O}_{{3}}+{a}_{{2}}\cdot{C}{O}={a}_{{3}}\cdot{F}{e}+{a}_{{4}}\cdot{C}{O}_{{2}}$ .

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

The unbalanced reaction is $\displaystyle{F}{e}_{{2}}{O}_{{3}}+{C}{O}\to{F}{e}+{C}{O}_{{2}}$ . To balance it, place undetermined coefficients before each molecule and find them:

$\displaystyle{a}_{{1}}\cdot{F}{e}_{{2}}{O}_{{3}}+{a}_{{2}}\cdot{C}{O}={a}_{{3}}\cdot{F}{e}+{a}_{{4}}\cdot{C}{O}_{{2}}$ .

The quantities of each atom on both sides must be the same. There are three types of atoms in this reaction: $\displaystyle{F}{e}$ , $\displaystyle{C}$ , and $\displaystyle{O}.$ For $\displaystyle{F}{e}$ atoms, we have $\displaystyle{2}{a}_{{1}}={a}_{{3}}$ , for $\displaystyle{C}$ atoms, we have $\displaystyle{a}_{{2}}={a}_{{4}}$ , and for $\displaystyle{O}$ atoms we have $\displaystyle{3}{a}_{{1}}+{a}_{{2}}={2}{a}_{{4}}$ .

Substitute $\displaystyle{a}_{{4}}={a}_{{2}}$ from the second equation to the third and obtain $\displaystyle{3}{a}_{{1}}+{a}_{{2}}={2}{a}_{{2}}$ or $\displaystyle{a}_{{1}}=\frac{{1}}{{3}}{a}_{{2}}$ . Substitute this into the first equation and obtain $\displaystyle\frac{{2}}{{3}}{a}_{{2}}={a}_{{3}}$ .

All coefficients must be natural numbers, so the smallest value for $\displaystyle{a}_{{2}}$ is $\displaystyle{3}$ . Then, we get $\displaystyle{a}_{{3}}=\frac{{2}}{{3}}{a}_{{2}}={2}$ , $\displaystyle{a}_{{1}}=\frac{{1}}{{3}}{a}_{{2}}={1}$ , and $\displaystyle{a}_{{4}}={a}_{{2}}={3}.$