Boyle's Law states that the pressure of a gas is inversely proportional to its volume when the temperature is held constant. This can be represented with the formula:
\[ P_1 V_1 = P_2 V_2 \]
where:
- \( P_1 \) = initial pressure
- \( V_1 \) = initial volume
- \( P_2 \) = final pressure
- \( V_2 \) = final volume
Given:
- \( P_1 = 760 \) mmHg
- \( V_1 = 250 \) mL
- \( V_2 = 150 \) mL
We are solving for \( P_2 \):
First, rearranging the formula to solve for \( P_2 \):
\[ P_2 = \frac{P_1 V_1}{V_2} \]
Now plugging in the known values:
\[ P_2 = \frac{760 , \text{mmHg} \times 250 , \text{mL}}{150 , \text{mL}} \]
Calculating:
\[ P_2 = \frac{190000 , \text{mmHg} \cdot \text{mL}}{150 , \text{mL}} = \frac{190000}{150} \approx 1266.67 , \text{mmHg} \]
Rounding this value gives:
\[ P_2 \approx 1267 , \text{mmHg} \]
Thus, the pressure required to change the volume to 150 mL is approximately 1267 mmHg.
The correct answer is c) 1267 mmHg.