I am currently studying stoichiometry (high school level) and we came across the following equation in school:

$$ 2\ H_2 + 1\ O_2 = 2\ H_2O $$

which is clear to me. We learned in school that reactions in chemistry only happen if there are enough atoms/molecules to react (so every molecule/atom can react), therefore the following reaction won't do anything:

$$ 2 H_2 + 1 O_2 = nothing\ happens $$

So now my first question: Why does the following not happen:

$$ 1\ H_2 + 1\ O_2 = 1\ H_2O + 1\ O $$

And, as a follow up question, why does the following not work?

1 mole of H2 and 1 mole of O2 won't make 1 mole of H2O and 1/2 mole O2.

What do I do wrong? (maybe I simply misunderstood our teacher)

Are there any explanations for this? I'm especially interested in the answer of my example with 1 mole of H2 and 1 mole of O2. According to our teacher nothing will happen at all. I would assume that at least all H2 molecules react with half of the oxygen molecules to H2O - leaving half a mole of O2 left over. (otherwise this would mean that all molecules "know" each other so they are "aware" that not all molecules/atoms can react)

Can somebody help me? Or point out what I do wrong?

Many thanks

stupidSheep