Q:

Why is the energy needed to transform PbO+CO into Pb+O2+C equal to the sum of breaking down PbO and CO?

Since PbO to Pb+(1/2)O2 releases 217.3kJ and CO to C+(1/2)O2 releases 110.5kJ, what I think is that PbO+CO to Pb+(1/2)O2+C+(1/2)O2 releases 327.8kJ. Now, the book says PbO+CO to Pb+C+O2 releases 327.8kJ.
My question is, why does is there no energy involved making Pb+(1/2)O2+C+(1/2)O2 into Pb+C+O2? Wouldn't there be some energy released joining the two halfs of oxygen?

A:

There are no two halfs of oxygen. The half denotes that there is $\frac{1}{2}$ a mole of oxygen produced for every mole of $\ce{PbO}$ (or $\ce{CO}$) reacting. So there is no such "joining of oxygen halves" going on.

