1. Avogadro's Number:

* Avogadro's number tells us that there are 6.022 x 10²³ particles (atoms, molecules, etc.) in one mole of a substance.

2. Calculation:

* Divide the number of molecules by Avogadro's number:

(1,000,000,000 molecules) / (6.022 x 10²³ molecules/mole) = 1.66 x 10⁻¹⁵ moles

Therefore, there are approximately 1.66 x 10⁻¹⁵ moles in 1,000,000,000 molecules of H₂O₂.