What is the ratio of the volumes occupied by 1 mole of `O_(2)` and 1 mole of `O_(3)` in identical conditions?

Answer

To find the ratio of the volumes occupied by 1 mole of \( O_2 \) (oxygen gas) and 1 mole of \( O_3 \) (ozone) under identical conditions, we can follow these steps:

### Step-by-Step Solution:

1. **Understand the Concept of Molar Volume**:
At standard temperature and pressure (STP), 1 mole of any ideal gas occupies a volume of 22.4 liters.

2. **Calculate the Volume of 1 Mole of \( O_2 \)**:
Since 1 mole of \( O_2 \) is present, the volume occupied by 1 mole of \( O_2 \) is:
\[ \text{Volume of } O_2 = 22.4 \text{ liters} \]

3. **Calculate the Volume of 1 Mole of \( O_3 \)**:
Similarly, for 1 mole of \( O_3 \), the volume occupied is also:
\[ \text{Volume of } O_3 = 22.4 \text{ liters} \]

4. **Determine the Ratio of the Volumes**:
Now, we can find the ratio of the volumes occupied by \( O_2 \) and \( O_3 \):
\[ \text{Ratio} = \frac{\text{Volume of } O_2}{\text{Volume of } O_3} = \frac{22.4 \text{ liters}}{22.4 \text{ liters}} = 1 \]

5. **Final Result**:
Therefore, the ratio of the volumes occupied by 1 mole of \( O_2 \) and 1 mole of \( O_3 \) is:
\[ \text{Ratio} = 1:1 \]