What will be the volume of a given mass of a pressure of 50 cm of Hg., if the occupics 260 mL at a pressure of 98 cm of Hg keeping the temperature constant.

Options

A. 520ml
B. 620ml
C. 510ml
D. 610ml

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 pressure, \( P_1 = 98 \, \text{cm of Hg} \)
- Initial volume, \( V_1 = 260 \, \text{mL} \)
- Final pressure, \( P_2 = 50 \, \text{cm of Hg} \)
- Final volume, \( V_2 = ? \)

2. **Apply Boyle's Law:**
Using the formula \( P_1 V_1 = P_2 V_2 \), we can rearrange it to solve for \( V_2 \):

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

3. **Substitute the known values into the equation:**
\[ V_2 = \frac{98 \, \text{cm of Hg} \times 260 \, \text{mL}}{50 \, \text{cm of Hg}} \]

4. **Calculate \( V_2 \):**
\[ V_2 = \frac{25480 \, \text{cm of Hg} \cdot \text{mL}}{50 \, \text{cm of Hg}} = 509.6 \, \text{mL} \]

5. **Conclusion:**
The volume of the gas at a pressure of 50 cm of Hg is approximately **509.6 mL**.