Final answer:
Using Boyle's Law, the volume of the gas sample at 5.45 atm pressure is calculated to be 2.71 liters, given the initial conditions of 2.59 atm pressure and 5.64 L volume.
Step-by-step explanation:
To determine the volume of a gas sample at a different pressure while keeping the temperature and amount constant, we use Boyle's Law. Boyle's Law states that the pressure of a gas is inversely proportional to its volume when temperature and amount of gas are held constant. In mathematical terms, P1V1 = P2V2 where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume respectively.
Given the initial condition of the gas at 2.59 atm occupying 5.64 L, and the final pressure of 5.45 atm, we can rearrange Boyle's Law to solve for V2:
(2.59 atm)(5.64 L) = (5.45 atm)V2
To find V2, the final volume, divide both sides by the final pressure:
V2 = (2.59 atm)(5.64 L) / 5.45 atm
V2 = 2.71 L
So the volume of the gas sample at 5.45 atm would be 2.71 liters.