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To solve this problem, we can use Boyle's Law, which states that the pressure and volume of a gas are inversely proportional at constant temperature.

Boyle's Law can be mathematically expressed as:

P1 * V1 = P2 * V2

Where P1 and V1 are the initial pressure and volume, respectively, and P2 and V2 are the final pressure and volume, respectively.

Given: P1 = 1 ATM V1 = 10 L V2 = 5 mL = 0.005 L (since 1 mL = 0.001 L)

We need to find P2.

Plugging the values into Boyle's Law equation:

1 ATM * 10 L = P2 * 0.005 L

Simplifying the equation:

10 = P2 * 0.005

Dividing both sides by 0.005:

P2 = 10 / 0.005 P2 = 2000 ATM

Therefore, the pressure that must be applied to reduce the volume to 5 mL (0.005 L) at constant temperature is 2000 ATM.

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