According to Boyle's Law, for an isothermal process, the pressure and volume of a gas are inversely proportional when the temperature remains constant. Mathematically, this can be expressed as:
P1 * V1 = P2 * V2
Where: P1 = Initial pressure V1 = Initial volume P2 = Final pressure V2 = Final volume
In this case, the initial pressure (P1) is 2 ATM, and the initial volume (V1) is not given. However, we know that the gas is compressed to one-third of its initial volume, which means the final volume (V2) is V1/3.
Using the equation mentioned earlier, we can rewrite it as:
2 ATM * V1 = P2 * (V1/3)
Now, let's solve for P2:
2 ATM * V1 = P2 * (V1/3)
2 * 3 = P2
6 ATM = P2
Therefore, the final pressure of the gas after being compressed isothermally to one-third of its initial volume will be 6 ATM.