A certain mass of the oxygen gas occupies 7 L volume under a pressure of 380 mm Hg . The volume of the same mass of the gas at standard pressure , with temperature remaining constant , shall be

Options

A. `26.60` L
B. `54.28 L`
C. `3.5 L`
D. `7` L

Explanation

To solve the problem of finding the volume of a certain mass of oxygen gas at standard pressure while keeping the temperature constant, we can use Boyle's Law, which states that for a given mass of gas at constant temperature, the product of pressure and volume is constant.

### Step-by-Step Solution:

1. **Identify Given Values**:
- Initial Pressure (P1) = 380 mm Hg
- Initial Volume (V1) = 7 L
- Final Pressure (P2) = Standard pressure = 760 mm Hg (1 atm)

2. **Use Boyle's Law**:
According to Boyle's Law:
\[ P1 \times V1 = P2 \times V2 \]
Where:
- P1 = Initial pressure
- V1 = Initial volume
- P2 = Final pressure
- V2 = Final volume (which we need to find)

3. **Rearranging the Equation**:
To find V2, we can rearrange the equation:
\[ V2 = \frac{P1 \times V1}{P2} \]

4. **Substituting the Values**:
Now, substitute the known values into the equation:
\[ V2 = \frac{380 \, \text{mm Hg} \times 7 \, \text{L}}{760 \, \text{mm Hg}} \]

5. **Calculating V2**:
Perform the calculation:
\[ V2 = \frac{2660}{760} \approx 3.5 \, \text{L} \]

6. **Conclusion**:
Therefore, the volume of the same mass of gas at standard pressure (760 mm Hg) is approximately **3.5 L**.