You follow a systematic procedure to balance the equation.
Start with the unbalanced equation:
"CH"_4"O" + "O"_2 → "CO"_2 + "H"_2"O"
A method that often works is to balance everything other than "O" and "H" first, then balance "O", and finally balance "H".
Another useful procedure is to start with what looks like the most complicated formula.
The most complicated formula looks like "CH"_4"O". We put a 1 in front of it to remind ourselves that the coefficient is now fixed.
We start with
color(red)(1)"CH"_4"O" + "O"_2 → "CO"_2 + "H"_2"O"
Balance "C":
We have fixed 1 "C" atom on the left-hand side, so we need 1 "C" atom on the right-hand side. We put a 1 in front of the "CO"_2.
color(red)(1)"CH"_4"O" + "O"_2 → color(blue)(1)"CO"_2 + "H"_2"O"
Balance "O":
We can't balance "O" yet, because we have two formulas that contain "O" and lack coefficients. So we balance "H" instead.
Balance "H":
We have fixed 4 "H" atoms on the left-hand side, so we need 4 "H" atoms on the right-hand side. We put an 2 in front of the "H"_2"O".
color(red)(1)"CH"_4"O" + "O"_2 → color(blue)(1)"CO"_2 + color(green)(2)"H"_2"O"
Now we balance "O":
We have fixed 4 "O" atoms on the right-hand side: 2 from the "CO"_2 and 2 from the "H"_2"O".
We have fixed 1 "O" atom on the left-hand side, so we need 3 more from the "O"_2.
Oops. We would need a fraction of an "O"_2 molecule.
We start over, multiplying every coefficient by 2.
color(red)(2)"CH"_4"O" + "O"_2 → color(blue)(2)"CO"_2 + color(green)(4)"H"_2"O"
Now we have fixed 8 "O" atoms on the right and 2 on the left. We need 6 more "O" atoms on the left. We put a 3 in front of the "O"_2.
color(red)(2)"CH"_4"O" + color(brown)(3)"O"_2 → color(blue)(2)"CO"_2 + color(green)(4)"H"_2"O"
Every formula now has a fixed coefficient. We should have a balanced equation.
Let’s check:
mathbf(color(white)(m)"Element"color(white)(m)"Left-hand side"color(white)(m)"Right-hand side")
color(white)(mmll)"C"color(white)(mmmmmml)2color(white)(mmmmmmmmll)2
color(white)(mmll)"H"color(white)(mmmmmml)8color(white)(mmmmmmmmll)8
color(white)(mmll)"O"color(white)(mmmmmml)8color(white)(mmmmmmmmll)8
All atoms balance. The balanced equation is
"2CH"_4"O" + "3O"_2 → "2CO"_2 + "4H"_2"O"
