The initial volume of a gas cylinder is 750.0 mL. If the pressure of gas inside the cylinder changes from 840.0 mm Hg to 360.0 mm Hg, the final volume the gas will be:

Options

A. 1.750 L
B. 3.60 L
C. 4.032 L
D. 7.50 L

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:
- \( P_1 \) = 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 (\( V_1 \)) = 750.0 mL
- Initial Pressure (\( P_1 \)) = 840.0 mm Hg
- Final Pressure (\( P_2 \)) = 360.0 mm Hg

2. **Set Up the Equation Using Boyle's Law:**
\[ P_1 V_1 = P_2 V_2 \]

3. **Rearranging the Equation to Solve for \( V_2 \):**
\[ V_2 = \frac{P_1 V_1}{P_2} \]

4. **Substituting the Known Values into the Equation:**
\[ V_2 = \frac{840.0 \, \text{mm Hg} \times 750.0 \, \text{mL}}{360.0 \, \text{mm Hg}} \]

5. **Calculating \( V_2 \):**
- First, calculate the numerator:
\[ 840.0 \times 750.0 = 630000.0 \, \text{mm Hg mL} \]
- Now divide by \( P_2 \):
\[ V_2 = \frac{630000.0 \, \text{mm Hg mL}}{360.0 \, \text{mm Hg}} \approx 1750.0 \, \text{mL} \]

6. **Convert the Final Volume to Liters:**
- Since \( 1000 \, \text{mL} = 1 \, \text{L} \):
\[ V_2 = 1.750 \, \text{L} \]

### Final Answer:
The final volume of the gas will be **1.750 liters**.

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