Question

The initial pressure and volume of a gas in a container is 5.4 atm and 78 L. Calculate the new pressure when the volume is decreased to 36 L.
Responses

8.9 atm
8.9 atm

10 atm
10 atm

11.7 atm
11.7 atm

6.87 atm

Answer 1

To calculate the new pressure when the volume of the gas is decreased, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when temperature remains constant. The formula is:

\[ P_1 \times V_1 = P_2 \times V_2 \]

Where:
- \( P_1 \) is the initial pressure
- \( V_1 \) is the initial volume
- \( P_2 \) is the new pressure
- \( V_2 \) is the new volume

Given:
- \( P_1 = 5.4 \, \text{atm} \)
- \( V_1 = 78 \, \text{L} \)
- \( V_2 = 36 \, \text{L} \)

We want to find \( P_2 \).

Rearranging the formula gives:

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

Plugging in the values:

\[ P_2 = \frac{5.4 \, \text{atm} \times 78 \, \text{L}}{36 \, \text{L}} \]

Calculating it step-by-step:

1. Calculate \( 5.4 \times 78 = 421.2 \).
2. Divide that by 36:

\[ P_2 = \frac{421.2}{36} \approx 11.7 \, \text{atm} \]

So the new pressure \( P_2 \) is approximately **11.7 atm**.

The correct response is **11.7 atm**.