Balancing a redox reaction involving only one apparant product

[CarefulAxe]

Homework Statement

Balance the following red-ox reaction that occurs in acidic solution.

Homework Equations

Pb(s) + PbO_{2}(s) + H_{2}SO_{4}(aq) \rightarrow PbSO_{4}(s)

The Attempt at a Solution

I did not see a change of oxo state from the sulfur, oxygen, or hydrogens. The lead is getting oxidized and the lead dioxide is getting reduced. But there is only one product...I tried leaving in the hydrogen sulfate in one of the half reactions, even though its oxo state does not change, and I ended up with an imbalanced equation. Here are the steps that I follow:

1.separate into two half reactions.
2.Balance the atoms that undergo a change in oxidation state.
3.Balance other atoms, except O's or H's
4.Balance oxygens by adding H2O
5.Balance hydrogen by adding H^{+}
6.Balance the charge by adding electrons (e-) to both sides until the charge is the same on both sides, starting with the most positive side.
7.equalize the electrons on both sides
8.add the two half reactions, cancel like terms.


Sorry for the somewhat long post. Oh and I'm a first time poster on PF, so I hope I didn't screw up anything too badly.

 

[epenguin]

You can no doubt think of it various ways. I found yours too complicated to follow!
I just mentally redistributed the oxygen between your elemental lead and dioxide and then it is easier.

Balancing equations which is all you ask is one thing, thinking what could be a reasonable mechanism for the steps that actually happen is another you could start thinking about. (How to distinguish experimentally between different reasonable mechanisms is another again.)

Here you've got the things that are present and reacting in a lead battery.