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.