The volume of a sample of a gas is 41.5 L at 8.28 atm and 467 K. What volume in L will it occupy at 3.03 atm at the same temperature?

To solve this problem, we can use the combined gas law, which states that the ratio of the initial pressure, volume, and temperature of a gas to the final pressure, volume, and temperature is a constant.

The formula for the combined gas law is:

(P1 * V1) / T1 = (P2 * V2) / T2

Where:
P1 = initial pressure
V1 = initial volume
T1 = initial temperature
P2 = final pressure
V2 = final volume
T2 = final temperature

In this case, we are given:
P1 = 8.28 atm
V1 = 41.5 L
T1 = 467 K
P2 = 3.03 atm
T2 = 467 K (same temperature)

Let's substitute the values into the formula:

(8.28 atm * 41.5 L) / 467 K = (3.03 atm * V2) / 467 K

Now, solve for V2 by multiplying both sides of the equation by (467 K / 3.03 atm):

(8.28 atm * 41.5 L) / 467 K * (467 K / 3.03 atm) = V2

Cancel out the units and calculate:

(8.28 atm * 41.5 L) / 3.03 = V2

V2 ≈ 113.1 L

Therefore, the volume of the gas will be approximately 113.1 L when the pressure is 3.03 atm at the same temperature.