To determine the pressure required to compress a gas at a constant temperature, you can use Boyle's Law, which states that the product of pressure and volume is constant for a given amount of gas at a constant temperature. Mathematically, it can be expressed as P1V1 = P2V2.
Let's assign the following values: P1 = 2.00 ATM (initial pressure) V1 = 106 L (initial volume) V2 = 55 L (final volume)
Using Boyle's Law, we can rearrange the formula to solve for the final pressure (P2):
P2 = (P1 × V1) / V2 = (2.00 ATM × 106 L) / 55 L = 3.6545 ATM (rounded to four decimal places)
Therefore, to compress 106 L of gas at 2.00 ATM pressure to 55 L at a constant temperature, a pressure of approximately 3.6545 ATM is required.