At what pressure a quantity of gas will occupy a volume of 60 mL, if it occupies a volume of 100mL at a pressure of 720 mm (while temperature is constant) :

Options

A. 700 mm
B. 800 mm
C. 100 mm
D. 1200 mm

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 a 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, \( P_1 = 720 \, \text{mmHg} \)
- Initial volume, \( V_1 = 100 \, \text{mL} \)
- Final volume, \( V_2 = 60 \, \text{mL} \)
- Final pressure, \( P_2 = ? \)

2. **Use Boyle's Law:**
According to Boyle's Law, we can set up the equation:
\[ P_1 V_1 = P_2 V_2 \]

3. **Substitute the known values into the equation:**
\[ 720 \, \text{mmHg} \times 100 \, \text{mL} = P_2 \times 60 \, \text{mL} \]

4. **Calculate \( P_2 \):**
Rearranging the equation to solve for \( P_2 \):
\[ P_2 = \frac{720 \, \text{mmHg} \times 100 \, \text{mL}}{60 \, \text{mL}} \]

5. **Perform the calculation:**
\[ P_2 = \frac{72000 \, \text{mmHg mL}}{60 \, \text{mL}} = 1200 \, \text{mmHg} \]

6. **Conclusion:**
The final pressure \( P_2 \) is \( 1200 \, \text{mmHg} \).

### Final Answer:
The pressure at which the gas will occupy a volume of 60 mL is **1200 mmHg**.

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