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According to Boyle's law, the volume of a gas is inversely proportional to its pressure. Mathematically, this can be expressed as P₁V₁ = P₂V₂, where P₁ and V₁ are the initial pressure and volume, and P₂ and V₂ are the final pressure and volume. Using this formula, we can calculate the volume of the gas in the capsule after compression:
P₁V₁ = P₂V₂
1.00 atm * 0.500 L = 3.25 atm * V₂
V₂ = 0.154 L
Therefore, the volume of the gas in the capsule after compression is 0.154 L.