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

6.87 atm
6.87 atm

11.7 atm
11.7 atm

8.9 atm
8.9 atm

10 atm
10 atm

Answer 1

To find the new pressure of the gas when the volume is decreased, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature is constant. The equation can be expressed as:

\[ P_1 V_1 = P_2 V_2 \]

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

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

We need to find \( P_2 \). Rearranging the formula gives us:

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

Now, substituting in the values:

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

Calculating:

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

Thus, the new pressure when the volume is decreased to 36 L is **11.7 atm**.