What sort of set up would I use to solve problems such as the following?

1) determine the mass of the  zinc metal
2) determine the mass of the zinc oxide
3) determine the mass of oxygen reacted by subtracting mass 1) from mass 2)

For this kind of problem, you have to use stoichiometry.

1. Write out the balanced equation. This is very important so you get the ratios correct. In this case, your equation is:

2Zn + O2 ZnO

2. If you notice, the ratio of Zn to O2 is 2:1. So, if you're given the moles of zinc (or mass of zinc; you'd have to convert it to moles) used in the reaction, you can find that the moles of oxygen is half of that in a 2:1 ratio. Then, you multiply the moles by the molar mass of O2 (32) to find the mass of oxygen.

Basically, to find the mass of reacted oxygen without actually measuring it, you need the mass or number of moles of zinc used. It'd be even easier if you had the moles of oxygen, so you could convert straight to grams.