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I know that you can not split poly-atomic ions but I am confused on how to balance the following equation:

9PbSO4 -> 10PBSO3 + 3O2

Pb = 9 Pb = 10 S = 9 S = 10 O = 36 O = 36

Obviously the equation is not balanced and there is an oxygen outside of a poly-atomic ion which makes it harder to balance. Do I count the oxygen with the oxygen in SO?

What numbers could I use to get PB and S the same on both sides?

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Start with the original unbalanced equation $\ce{PbSO4 -> PbSO3 + O2}.$

$\ce{PbSO3}$ needs only one more oxygen atom to balance $\ce{PbSO4}$; one atom of oxygen is $\frac{1}{2}\ce{O2}$.

This balances, then, as $\ce{PbSO4 -> PbSO3 + 1/2 O2}$.

Since half molecules are not permitted, double everything to:

$\ce{2 PbSO4 -> 2 PbSO3 + O2}$

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