Question

Use Boyles Law

A gas sample has an intial volume of 250ml at 760 mmHg. Calculate the pressure required to change the volume to 150ml.
a
354 mm Hg
b
1567 mm Hg
c
1267 mm Hg
d
456 mm Hg

Answer 1

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**.