**Explanation:**

To determine the number of moles of O3 (ozone) molecules that will contain 1 mole of oxygen atoms, we need to understand the molar ratios between O3 molecules and oxygen atoms.

**1. Balanced Chemical Equation:**
The balanced chemical equation for the formation of ozone is:

2 O2(g) ⟶ 2 O3(g)

This equation tells us that for every 2 moles of O2 gas, we can produce 2 moles of O3 gas.

**2. Molar Ratio:**
From the balanced equation, we can determine the molar ratio between O2 and O3. This ratio is 1:1, meaning that for every 1 mole of O2, we produce 1 mole of O3.

**3. Avogadro's Number:**
Avogadro's number (6.022 x 10^23) represents the number of particles (atoms, molecules, ions) in one mole of a substance.

**4. Moles to Moles Conversion:**
Using the molar ratio of 1:1, we can calculate the number of moles of O3 that will contain 1 mole of oxygen atoms.

Since 1 mole of O2 produces 1 mole of O3, and 1 mole of O3 contains 3 moles of oxygen atoms, we can say that 2 moles of O2 produce 3 moles of oxygen atoms.

Therefore, for every 3 moles of oxygen atoms, we will have 2 moles of O2.

**5. Calculation:**
To determine how many moles of O3 will contain 1 mole of oxygen atoms, we can set up a proportion using the molar ratio:

(2 moles of O2) / (3 moles of oxygen atoms) = (1 mole of O2) / (x moles of oxygen atoms)

Cross-multiplying and solving for x, we find:

x = (1 mole of O2) * (3 moles of oxygen atoms) / (2 moles of O2) = 1.5 moles of oxygen atoms

Therefore, 1 mole of oxygen atoms will contain 1.5 moles of O3 molecules.

**Conclusion:**
In conclusion, 1 mole of oxygen atoms will contain 1.5 moles of O3 molecules according to the balanced chemical equation and the molar ratio between O2 and O3. This calculation is based on Avogadro's number and the stoichiometry of the chemical reaction.