What is the volume of a sample of oxygen at a pressure of `3.5"bar"` if its volume at `1`bar is `3.15 L` at the same temperature?

Explanation

To solve the problem, we will use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is a constant. This can be expressed mathematically as:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume

### Step-by-Step Solution:

1. **Identify the given values:**
- Initial pressure \( P_2 = 1 \, \text{bar} \)
- Initial volume \( V_2 = 3.15 \, \text{L} \)
- Final pressure \( P_1 = 3.5 \, \text{bar} \)
- We need to find the final volume \( V_1 \).

2. **Apply Boyle's Law:**
According to Boyle's Law:
\[ P_1 V_1 = P_2 V_2 \]

3. **Rearrange the equation to solve for \( V_1 \):**
\[ V_1 = \frac{P_2 V_2}{P_1} \]

4. **Substitute the known values into the equation:**
\[ V_1 = \frac{(1 \, \text{bar}) \times (3.15 \, \text{L})}{3.5 \, \text{bar}} \]

5. **Calculate \( V_1 \):**
\[ V_1 = \frac{3.15}{3.5} \]
\[ V_1 = 0.90 \, \text{L} \]

### Final Answer:
The volume of the sample of oxygen at a pressure of 3.5 bar is **0.90 L**.