There is a concept called Activation Energy, which is the energy you need to put in to a system in order for a reaction to start. Think of this like the amount of energy you need to push on a domino in order for it to tip over, or the heat that the friction of striking a match generates.
There’s another concept called a Maxwell-Boltzmann distribution, which basically says that the molecules in a substance is not all the same temperature. Some of them are hotter than the average, some of them colder. This means that even if the solution of Hydrogen Peroxide isn’t hot enough for it all to decompose, a couple of molecules will be above the Activation Energy, a couple of them will be. So at room temperature, Hydrogen Peroxide will slowly decompose on it’s own.
What catalysts do is they lower the Activation Energy so that more of the molecules in a substance have enough energy. It’s thought that the shape of the active site on catalase is structured in such a way that when Hydrogen Peroxide attaches to it, it can decompose through an alternate route made up of two reactions which take less energy to start (lower Activation Energy). At the end, the water and O2 are released and the catalase is free to act upon the next H2O2 it encounters.
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