Answer :
To find the pressure of the gas in a 10.6 L cylinder, we can use Boyle's Law, which states that for a given amount of gas at constant temperature, the product of the initial pressure and volume is equal to the product of the new pressure and volume. The formula is:
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
Let's break down the steps to solve the problem:
1. Identify the given values:
- Initial pressure ([tex]\(P_1\)[/tex]) = 2.54 atm
- Initial volume ([tex]\(V_1\)[/tex]) = 12.4 L
- New volume ([tex]\(V_2\)[/tex]) = 10.6 L
2. Substitute the values into Boyle's Law formula:
[tex]\[
2.54 \, \text{atm} \times 12.4 \, \text{L} = P_2 \times 10.6 \, \text{L}
\][/tex]
3. Solve for the new pressure ([tex]\(P_2\)[/tex]):
[tex]\[
P_2 = \frac{2.54 \, \text{atm} \times 12.4 \, \text{L}}{10.6 \, \text{L}}
\][/tex]
4. Calculate the result:
[tex]\[
P_2 = \frac{31.496}{10.6} \approx 2.97 \, \text{atm}
\][/tex]
Therefore, the pressure of the gas in a 10.6 L cylinder at the same temperature would be approximately 2.97 atm.
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
Let's break down the steps to solve the problem:
1. Identify the given values:
- Initial pressure ([tex]\(P_1\)[/tex]) = 2.54 atm
- Initial volume ([tex]\(V_1\)[/tex]) = 12.4 L
- New volume ([tex]\(V_2\)[/tex]) = 10.6 L
2. Substitute the values into Boyle's Law formula:
[tex]\[
2.54 \, \text{atm} \times 12.4 \, \text{L} = P_2 \times 10.6 \, \text{L}
\][/tex]
3. Solve for the new pressure ([tex]\(P_2\)[/tex]):
[tex]\[
P_2 = \frac{2.54 \, \text{atm} \times 12.4 \, \text{L}}{10.6 \, \text{L}}
\][/tex]
4. Calculate the result:
[tex]\[
P_2 = \frac{31.496}{10.6} \approx 2.97 \, \text{atm}
\][/tex]
Therefore, the pressure of the gas in a 10.6 L cylinder at the same temperature would be approximately 2.97 atm.
