I had a friend who had trouble with that. As stupid as it may be, consider the molecules to be sthing you like.
You want to do 2 bowls of fruit salad. You know that to do two bowls, you need 1 orange for every 2 apples (so if you have 1 apple, you put in 0.5 oranges and do one bowl).
It's the same case in the SO2 + 1/2 O2 --> SO3 reaction. To do one SO3 molecule (fruit salad), you need 1 S02 molecule and half of a 02 molecule.
They tell ya in the problem, that 25g of O2 is useable. When you see grams, you just always make it into moles, because 1 mole of 02 has the same number of molecules than any other grouping. I'm sure you saw how to find the number of moles already (mass/formula weight).
The number you find is the available amount of *oranges* to do your salad. So imagine you have like 10 oranges, and you know that there is 0.5 oranges per bowl. You can conclude that you can do 20 bowls of fruit salad. And to do so, you'll need 20 apples because there is one apple per bowl.
It works the same way in chemistry. If you have, let's say 10 moles of 02, you'll be able to do 20 moles of S03 if you have enough SO2 (20 moles too). The easiest way for me is to find the proportion. Let n = number of moles. so nO2 = number of moles of 02 and nSO3 = number of moles of S03.
First step, you balance your equation. Then just put nO2 = 1/2 (the stoechiometric coefficient) and nSO3 = 1. Now just divide nSO3/n02 = 1/(1/2) = 2. By rearranging the equation, you get: 2nO2 = nS03. When you have that, the moment you find either n02 or nSO3 with the data you have stated in the problem, you are set
Hopefully that wasn't too long and clear enough