Answer:
2.746
Step-by-step explanation:
To find the final pressure of the gas, we can use the ideal gas law equation:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant (8.314 J/(mol·K))
T = temperature
First, let's calculate the initial pressure of the gas. We'll use the initial volume, temperature, and the ideal gas law equation:
P1 * V1 = n * R * T1
Since the number of moles (n) is constant, we can rewrite the equation as:
P1 = (n * R * T1) / V1
Now, let's calculate the final pressure of the gas using the final volume and temperature:
P2 * V2 = n * R * T2
Rearranging the equation:
P2 = (n * R * T2) / V2
Since the number of moles (n) is constant, we can substitute the value from the initial pressure equation:
P2 = (P1 * V1 * T2) / (V2 * T1)
Now we can plug in the given values:
P1 = initial pressure (to be calculated)
V1 = 8.33 L
T1 = 286 K
T2 = 355 K
V2 = 5.72 L
R = 8.314 J/(mol·K)
Calculating P1:
P1 = (P1 * 8.33 L * 355 K) / (5.72 L * 286 K)
To solve for P1, we'll isolate P1 on one side of the equation:
P1 * (5.72 L * 286 K) = P1 * 8.33 L * 355 K
Canceling out P1 on both sides:
5.72 L * 286 K = 8.33 L * 355 K
Dividing both sides by (5.72 L * 286 K):
P1 = (8.33 L * 355 K) / (5.72 L * 286 K)
Simplifying:
P1 = 2.746
Therefore, the initial pressure of the gas is approximately 2.746 units.
Please note that the units of pressure are not specified in the question, so the final answer will be in the same units as the initial pressure.