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Answer :
To solve this problem, we need to use Boyle's Law, which relates the pressure and volume of a gas at constant temperature. Boyle's Law is expressed by the equation:
[tex]P_1 \times V_1 = P_2 \times V_2[/tex]
Where:
- [tex]P_1[/tex] is the initial pressure (4.00 atm).
- [tex]V_1[/tex] is the initial volume (8.00 L).
- [tex]P_2[/tex] is the final pressure (what we're solving for).
- [tex]V_2[/tex] is the final volume (2.00 L).
Using Boyle's Law, we can solve for [tex]P_2[/tex]:
[tex]4.00 \, \text{atm} \times 8.00 \, \text{L} = P_2 \times 2.00 \, \text{L}[/tex]
Simplifying the equation:
[tex]32.00 \, \text{atm} \cdot \text{L} = P_2 \times 2.00 \, \text{L}[/tex]
Divide both sides by 2.00 L to solve for [tex]P_2[/tex]:
[tex]P_2 = \frac{32.00 \, \text{atm} \cdot \text{L}}{2.00 \, \text{L}} = 16.00 \, \text{atm}[/tex]
Therefore, the final pressure after the compression is 16.0 atm. This corresponds to option D in the multiple-choice answers.
So, the correct answer is: D) 16.0
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