2 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. 370 mm Hg
B. 480 mm Hg
C. 304 mm Hg
D. 470 mm Hg

Explanation

To solve the problem step by step, 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:

\[ P_1 V_1 = P_2 V_2 \]

### Step 1: Identify the given values
- Initial pressure (\( P_1 \)) = 760 mm Hg
- Initial volume (\( V_1 \)) = 2 L
- Final volume (\( V_2 \)) = 5 L
- Final pressure (\( P_2 \)) = ?

### Step 2: Rearrange the formula to solve for \( P_2 \)
Using Boyle's Law, we can rearrange the equation to find \( P_2 \):

\[ P_2 = \frac{P_1 V_1}{V_2} \]

### Step 3: Substitute the known values into the equation
Now we will substitute the values we have into the equation:

\[ P_2 = \frac{760 \, \text{mm Hg} \times 2 \, \text{L}}{5 \, \text{L}} \]

### Step 4: Perform the calculation
Now we will calculate \( P_2 \):

\[ P_2 = \frac{1520 \, \text{mm Hg}}{5} \]

\[ P_2 = 304 \, \text{mm Hg} \]

### Step 5: State the final answer
The final pressure when the volume changes to 5 L is:

\[ P_2 = 304 \, \text{mm Hg} \]

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