6L of gas is enclosed in a vessel at a pressure of 760 mm Hg. If temperature remain constant , calculate pressure when volume changes to 7 L .

Options

A. 606 mm Hg
B. 651 mm Hg
C. 760 mm Hg
D. None of these

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 volume (\( V_1 \)) = 6 L
- Initial pressure (\( P_1 \)) = 760 mm Hg
- Final volume (\( V_2 \)) = 7 L

2. **Use Boyle's Law:**
We need to find the final pressure (\( P_2 \)). According to Boyle's Law:
\[ P_1 V_1 = P_2 V_2 \]

3. **Rearranging the Equation:**
To find \( P_2 \), we rearrange the equation:
\[ P_2 = \frac{P_1 V_1}{V_2} \]

4. **Substituting the Known Values:**
Now, substitute the known values into the equation:
\[ P_2 = \frac{760 \, \text{mm Hg} \times 6 \, \text{L}}{7 \, \text{L}} \]

5. **Calculating the Final Pressure:**
Now, perform the calculation:
\[ P_2 = \frac{4560 \, \text{mm Hg}}{7} \approx 651.43 \, \text{mm Hg} \]

6. **Final Result:**
Therefore, the final pressure when the volume changes to 7 L is approximately:
\[ P_2 \approx 651 \, \text{mm Hg} \]

### Final Answer:
The pressure when the volume changes to 7 L is **651 mm Hg**.

---