To determine the pressure required to compress a gas at constant temperature, we can use Boyle's law, which states that the pressure and volume of a gas are inversely proportional, assuming constant temperature.
Boyle's law equation:
P1 * V1 = P2 * V2
Where: P1 = initial pressure V1 = initial volume P2 = final pressure V2 = final volume
Let's plug in the given values into the equation:
P1 * V1 = P2 * V2
(2.09 ATM) * (206 L) = P2 * (55 L)
Now, let's rearrange the equation to solve for P2:
P2 = (P1 * V1) / V2
P2 = (2.09 ATM * 206 L) / 55 L
P2 ≈ 7.82 ATM
Therefore, approximately 7.82 ATM of pressure would be required to compress 206 L of gas at 2.09 ATM to 55 L at constant temperature.