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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 when the temperature is constant.

Boyle's Law formula: P1V1 = P2V2

Where: P1 = Initial pressure V1 = Initial volume P2 = Final pressure (what we're trying to find) V2 = Final volume

Given: P1 = 4 atmospheres V1 = 10 liters V2 = 5 liters

Using the formula, we can plug in the values and solve for P2:

P1V1 = P2V2

(4 atm)(10 L) = P2(5 L)

40 atm·L = 5P2

Dividing both sides of the equation by 5 L:

40 atm·L / 5 L = P2

8 atm = P2

Therefore, the new pressure of the gas when the volume is reduced to 5 liters while keeping the temperature constant will be 8 atmospheres.

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