Final answer:
Using Boyle's Law, which states that the pressure and volume of a gas are inversely proportional, the new volume when the pressure is increased from 102.2 kPa to 116.8 kPa is found to be approximately 3.50 L, corresponding to answer choice A, 3.52 L.
Step-by-step explanation:
To solve the problem of finding the new volume of a gas when the pressure is increased, we can use Boyle's Law, which states that the pressure of a gas is inversely proportional to its volume when the temperature and amount of gas are held constant.
The formula for Boyle's Law is P1V1 = P2V2, where P1 and V1 are the initial pressure and volume, and P2 and V2 are the final pressure and volume, respectively.
In this case, the initial pressure P1 is 102.2 kPa and the initial volume V1 is 4.0 L.
The final pressure, P2, is 116.8 kPa. We want to solve for the final volume, V2. Using Boyle's Law:
P1V1 = P2V2
(102.2 kPa)(4.0 L) = (116.8 kPa)(V2)
To find V2, divide both sides of the equation by P2:
V2 = (102.2 kPa * 4.0 L) / 116.8 kPa
V2 = 3.50 L
The new volume, approximated to two decimal places, is 3.50 L, which is closest to answer A, 3.52 L.