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This problem involves Boyle's Law, which states that the product of pressure and volume is constant for a fixed amount of gas at a constant temperature. Mathematically, this is expressed as P₁V₁ = P₂V₂.
Here's how to solve the problem:
Given:
Initial volume (V₁) = 24.0 L
Initial pressure (P₁) = 565 mmHg
Final volume (V₂) = 16.0 L
To find: Final pressure (P₂)
Using Boyle's Law:
P₁V₁ = P₂V₂
(565 mmHg)(24.0 L) = P₂(16.0 L)
P₂ = (565 mmHg)(24.0 L) / (16.0 L)
P₂ = 847.5 mmHg
Therefore, the final pressure of the gas is 847.5 mmHg.