At `25^(@)C` and 730 mm pressure, 380 mL of dry oxygen was collected. If the temperature is constant, what volume will be oxygen occupy at `760 mm` pressure ?

Options

A. 365 mL
B. 2 mL
C. 10 mL
D. 20 mL

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 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, \( P_1 = 730 \, \text{mm} \)
- Initial volume, \( V_1 = 380 \, \text{mL} \)
- Final pressure, \( P_2 = 760 \, \text{mm} \)
- Final volume, \( V_2 = ? \)

2. **Apply Boyle's Law**:
Using the formula \( P_1 V_1 = P_2 V_2 \), we can rearrange it to solve for \( V_2 \):
\[ V_2 = \frac{P_1 V_1}{P_2} \]

3. **Substitute the known values into the equation**:
\[ V_2 = \frac{730 \, \text{mm} \times 380 \, \text{mL}}{760 \, \text{mm}} \]

4. **Perform the calculations**:
- First, calculate the numerator:
\[ 730 \times 380 = 277400 \, \text{mm} \cdot \text{mL} \]
- Now divide by the final pressure:
\[ V_2 = \frac{277400}{760} \approx 365.79 \, \text{mL} \]
- Rounding this to three significant figures gives:
\[ V_2 \approx 365 \, \text{mL} \]

5. **Conclusion**:
The volume of oxygen at 760 mm pressure is approximately 365 mL.

### Final Answer:
The volume of oxygen at 760 mm pressure is **365 mL**.

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