4 L of gas is enclosed in a vessel at a pressure of 760 mm Hg. If temperature remain constant , calculate pressure when volume changes to 5L

Options

A. 380 mm Hg
B. 608 mm Hg
C. 840 mm Hg
D. 420 mm Hg

Explanation

To solve the problem, we will use Boyle's Law, which states that for a given mass of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. The formula for Boyle's Law can be expressed 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 (\( P_1 \)) = 760 mm Hg
- Initial volume (\( V_1 \)) = 4 L
- Final volume (\( V_2 \)) = 5 L

2. **Set up the equation using Boyle's Law:**
\[ P_1 V_1 = P_2 V_2 \]

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

4. **Substitute the known values into the equation:**
\[ P_2 = \frac{760 \, \text{mm Hg} \times 4 \, \text{L}}{5 \, \text{L}} \]

5. **Calculate the value:**
\[ P_2 = \frac{3040 \, \text{mm Hg}}{5} = 608 \, \text{mm Hg} \]

6. **Conclusion:**
The final pressure (\( P_2 \)) when the volume changes to 5 L is 608 mm Hg.

### Final Answer:
The pressure when the volume changes to 5 L is **608 mm Hg**.