An automobile tire has an internal volume of 28 L at 268 kPa and 25 oC. What volume would be the air inside the tire occupy if it escaped? (Atmospheric pressure at the time is 98 kPa and the temperature remains the same)
To solve this problem, we can use the ideal gas law:
PV = nRT
Where:
P = pressure
V = volume
n = number of moles
R = ideal gas constant
T = temperature
First, we calculate the number of moles of air inside the tire using the initial conditions:
P1 = 268 kPa
V1 = 28 L
T1 = 25 oC = 25 + 273 = 298 K
We need to convert temperature to Kelvin for the calculation.
Using the ideal gas law:
n = P1V1 / RT1
n = (268 kPa * 28 L) / (8.31 L*kPa/mol*K * 298 K)
n = 3.72 moles
Now, we can calculate the final volume of air when the pressure is 98 kPa and the temperature remains the same:
P2 = 98 kPa
Using the ideal gas law:
V2 = nRT2 / P2
V2 = (3.72 moles * 8.31 L*kPa/mol*K * 298 K) / 98 kPa
V2 = 90.43 L
Therefore, the volume of air inside the tire would occupy 90.43 L if it escaped at a pressure of 98 kPa.