Final answer:
Using Boyle's Law, the volume of a gas when pressure changes while maintaining constant temperature can be calculated. Given the initial conditions of 3.00 L at 1 atm and final pressure of 1.45 atm, the new volume is 2.07 L.
Step-by-step explanation:
The question involves the use of the gas law principle, specifically Boyle's Law, to calculate the change in volume of a gas given a change in pressure while keeping the temperature constant. In the given scenario, the initial pressure is 760 torr, which is equivalent to 1 atm, as 760 torr equals 1 atm. The initial volume is 3.00 L.
According to Boyle's Law, the product of pressure and volume for a given amount of gas at constant temperature is constant:
P1V1 = P2V2
By substituting the known values, we can solve for the new volume (V2):
V2 = (P1V1) / P2
Given that P1 = 1 atm (760 torr), V1 = 3.00 L, and P2 = 1.45 atm, we have:
V2 = (1 atm * 3.00 L) / 1.45 atm = 2.07 L
The volume the gas will occupy at 1.45 atm and the same temperature is 2.07 liters.