::The former chemistry teacher enters the room::
Gosh. Where to begin. The toughest part here is to explain with out pictures.
K.
Lets go over some basic points.
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Coefficients give the number of molecules (“groups” if you will).
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Subscripts give the number of the specific type of atom chemically bonded to form the moleucle.
I assume by this that “to not using them” means “to use subscripts instead”.
You can’t do that. to change the subscript changes the compound. Example. CO[sub]2[/sub] is a molecule that has 2 Oxygen atoms chemically bonded to 1 Carbon atom. To change the subscript “creates” a completely different compound. Again, example. CO is a molecule that has 1 Oxygen atom chemically bonded to 1 Carbon atom. Though both molecules have the same components (carbon and oxygen) they are very different compounds because of the number of each type of atom. As you well know, CO[sub]2[/sub] is Carbon dioxide while CO is Carbon monoxide. This is why one can not change subscripts when balancing equations.
Ok, on to the next part. The coefficient gives the number of molecules of the stuff that is “used” in the chemical reaction. In your first example
Fe + O[sub]2[/sub] --> FeO
You have an equation that, when written out in words, says:
Iron reacts with Oxygen to form Iron Oxide (more correctly, it forms Iron II oxide, recall that Iron can have a +2 or +3 charge).
If you consider the number of atoms in the equation, you are currently showing that if you start with 1 atom of Iron and 2 atoms of Oxygen (bonded together in the diatomic molecule) you somehow end up with 1 atom of Iron and 1 atom of Oxygen. This can’t be correct, unless you’ve discovered some way to delete matter from existence. Where did the other atom of oxygen go?
Like the other dollar in the hotel puzzle, it didn’t “go” anywhere. The equation as written is quite qualitative; it lists formulas for the compounds/elements, but that’s it.
Since you start with 2 atoms of oxygen, you must finish with 2 atoms of oxygen. The only way this is possible, without changing subscripts (and therefore compounds) is if you actually end up with 2 molecules of FeO, as such:
Fe + O[sub]2[/sub] --> 2FeO
This shows that by having two molecules of Iron II oxide produced, all oxygen is accounted for. However, now it seems as if an atom of Iron was generated.
Recall that the the coefficient is distributed when calculating the number of atoms present. It stands to reason that if you have 2 molecules of FeO and each molecule has 1 Fe and 1 O you have a total of 2 Fe and 2 O.
The only way to end up with 2 Fe atoms is to start with 2 Fe atoms. Again, since you can’t change subscripts, you must change the coefficient on the reactant side to show 2 iron atoms.
2Fe + O[sub]2[/sub] --> 2FeO
now this shows that:
2 atoms of Iron combine with 1 molecule of Oxygen to form 2 molecules of Iron II oxide. All numbers of starting materials are accounted for after the reaction.
Things to watch out for:
Diatomic molecules (I[sub]2[/sub], Br[sub]2[/sub], Cl[sub]2[/sub], F[sub]2[/sub], O[sub]2[/sub], N[sub]2[/sub], and H[sub]2[/sub]
I’ve gone on far too long. (gosh and I didn’t even get to talk about Red-Ox reactions!!)
Feel free to print this out and show it to your Chem teacher for further explanation.
Also, feel free to e-mail me if you need more.