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The problem states:

- We have a 12.2 L sample containing 0.50 mol of \( O_2 \) gas.
- Conditions: 1.0 atm pressure and 25°C.
- All \( O_2 \) is converted into \( O_3 \) (ozone) at the same temperature and pressure.
- We need to find the volume of the ozone formed.

The balanced chemical reaction is:
\[ 3O_2(g) \rightarrow 2O_3(g) \]

### Steps to solve:

1. **Calculate moles of \( O_3 \) formed from \( O_2 \):**
   - The ratio of \( O_2 \) to \( O_3 \) from the balanced equation is 3:2.
   - Moles of \( O_3 \) formed = \(\frac{2}{3} \times 0.50 \) mol = \(\frac{2}{3} \times 0.50 = 0.333 \) mol.

2. **Use the Ideal Gas Law to relate volume and moles:**
   - Since pressure and temperature remain constant, volume is directly proportional to the number of moles (\( V_1 / n_1 = V_2 / n_2 \)).

3. **Calculate the volume of \( O_3 \):**
   \[
   V_{O_3} = \frac{n_{O_3}}{n_{O_2}} \times V_{O_2}
   \]
   \[
   V_{O_3} = \frac{0.333}{0.50} \times 12.2 \, L
   \]
   Let's compute this value.

The volume of ozone (\( O_3 \)) formed is approximately **8.13 L**.

Would you like more details on this solution or have any further questions? Here are some related questions you might find interesting:

1. What would happen to the volume if the temperature were increased?
2. How does the ideal gas law apply to this problem?
3. What is the relationship between the molar volumes of gases in a chemical reaction?
4. How would the result change if the initial amount of \( O_2 \) were different?
5. What is the significance of the mole ratio in chemical reactions?

**Tip:** In gas reactions, remember that the volume ratios of gases at the same temperature and pressure are the same as their mole ratios!

Suppose we have a 12.2 L sample containing 0.50 mol of oxygen gas O2 at a pressure of 1.0 atm and a temperature of 25°C. If all of this O2 is converted into ozone O3 at the same temperature and pressure, what will be the volume of the ozone formed?

Solve a gas stoichiometry problem where oxygen gas (O2) is converted to ozone (O3) under constant conditions of temperature and pressure. Learn how the ideal gas law and mole ratios help in calculating the volume of ozone formed. Suitable for chemistry students at the introductory college level.

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