why do you think the experimenter conducted this experiment in a lab rather than in the natural world, where this phenomenon was first observed?

The experimenter observed this experiment in a lab rather than natural world because it might be dangerous to the atmosphere if he does the experiment in the natural world and it was still an hypothesis so that's why he did it in the lab.

2h2o2--> 2h2o + o2

this reaction is of the spontaneous decomposition of hydrogen peroxide down into water and oxygen.

add 2 molecules of hydrogen peroxide and 2 molecules of water. since oxygen is naturally diatomic, the total number of atoms of each element is now the same on both sides of the equation so it is balanced.

this may not be entirely correct but let me know.