A single gram of hydrogen peroxide contains 17690000000000000000000 molecules.
So even if you dissolve that in 32 grams of water to get a 3% solution, you still have a staggering number of reactions that can occur.
In this case the low concentration is necessary to render the solution safe for use. Hydrogen peroxide is an incredibly reactive chemical that is dangerously corrosive and explosive in high concentrations.
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