3 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 6L

Options

A. 370 mm Hg
B. 380 mm Hg
C. 390 mm Hg
D. 400 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 product of pressure and volume is constant. This can be expressed mathematically as:

\[ P_1 V_1 = P_2 V_2 \]

Where:
- \( P_1 \) is the initial pressure,
- \( V_1 \) is the initial volume,
- \( P_2 \) is the final pressure,
- \( V_2 \) is the final volume.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Initial pressure \( P_1 = 760 \, \text{mm Hg} \)
- Initial volume \( V_1 = 3 \, \text{L} \)
- Final volume \( V_2 = 6 \, \text{L} \)
- Final pressure \( P_2 \) is what we need to find.

2. **Use Boyle's Law:**
We can rearrange the equation to solve for \( P_2 \):
\[ P_2 = \frac{P_1 V_1}{V_2} \]

3. **Substitute the Known Values:**
\[ P_2 = \frac{760 \, \text{mm Hg} \times 3 \, \text{L}}{6 \, \text{L}} \]

4. **Calculate the Pressure:**
- First, calculate the numerator:
\[ 760 \times 3 = 2280 \, \text{mm Hg} \cdot \text{L} \]
- Now divide by the final volume:
\[ P_2 = \frac{2280 \, \text{mm Hg} \cdot \text{L}}{6 \, \text{L}} = 380 \, \text{mm Hg} \]

5. **Final Answer:**
The final pressure \( P_2 \) when the volume changes to 6 L is:
\[ P_2 = 380 \, \text{mm Hg} \]