Final answer:
The volume a gas will occupy at a different pressure is found using Boyle's law, P1V1 = P2V2. The new volume is calculated as approximately 0.868 L when the pressure increases from 28.2 kPa to 87.7 kPa, assuming constant temperature and amount of gas.
Step-by-step explanation:
The question involves using the principles of gas laws to determine the volume a gas will occupy at a different pressure. The initial conditions provided are a volume of 2.7 L of gas at 28.2 kPa. The final condition is a pressure of 87.7 kPa, and we need to find the new volume.
For a gas at constant temperature and amount, the relationship between pressure and volume is described by Boyle's law, which can be written as P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume respectively.
Using Boyle's law:
(28.2 kPa) x (2.7 L) = (87.7 kPa) x V2.
Now, we solve for V2:
V2 = (28.2 kPa x 2.7 L) / 87.7 kPa
V2 = 0.868 L (approximately)
Thus, at a pressure of 87.7 kPa, the gas will occupy a volume of approximately 0.868 liters.