Answer :
To solve this problem, we will use Boyle's Law, which states that for a given amount of gas at constant temperature, the pressure of the gas is inversely proportional to its volume. Mathematically, this is expressed as:
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
where:
- [tex]\( P_1 \)[/tex] is the initial pressure,
- [tex]\( V_1 \)[/tex] is the initial volume,
- [tex]\( P_2 \)[/tex] is the final pressure,
- [tex]\( V_2 \)[/tex] is the final volume.
We are given the following values:
- [tex]\( P_1 = 735 \)[/tex] mm Hg
- [tex]\( V_1 = 50.0 \)[/tex] mL
- [tex]\( P_2 = 925 \)[/tex] mm Hg
We need to find the final volume, [tex]\( V_2 \)[/tex].
Using the formula, we can rearrange it to solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{P_1 \times V_1}{P_2} \][/tex]
Now, plug in the given values:
[tex]\[ V_2 = \frac{735 \, \text{mm Hg} \times 50.0 \, \text{mL}}{925 \, \text{mm Hg}} \][/tex]
Calculating this gives:
[tex]\[ V_2 \approx 39.7 \, \text{mL} \][/tex]
Therefore, the final volume of the oxygen gas is approximately [tex]\( 39.7 \, \text{mL} \)[/tex].
[tex]\[ P_1 \times V_1 = P_2 \times V_2 \][/tex]
where:
- [tex]\( P_1 \)[/tex] is the initial pressure,
- [tex]\( V_1 \)[/tex] is the initial volume,
- [tex]\( P_2 \)[/tex] is the final pressure,
- [tex]\( V_2 \)[/tex] is the final volume.
We are given the following values:
- [tex]\( P_1 = 735 \)[/tex] mm Hg
- [tex]\( V_1 = 50.0 \)[/tex] mL
- [tex]\( P_2 = 925 \)[/tex] mm Hg
We need to find the final volume, [tex]\( V_2 \)[/tex].
Using the formula, we can rearrange it to solve for [tex]\( V_2 \)[/tex]:
[tex]\[ V_2 = \frac{P_1 \times V_1}{P_2} \][/tex]
Now, plug in the given values:
[tex]\[ V_2 = \frac{735 \, \text{mm Hg} \times 50.0 \, \text{mL}}{925 \, \text{mm Hg}} \][/tex]
Calculating this gives:
[tex]\[ V_2 \approx 39.7 \, \text{mL} \][/tex]
Therefore, the final volume of the oxygen gas is approximately [tex]\( 39.7 \, \text{mL} \)[/tex].
