An automobile tire has an internal volume of 32 L at 271 kPa and 20 oC. What volume would be the air inside the tire occupy if it escaped?
To find the volume the air inside the tire would occupy if it escaped, we need to use the ideal gas law equation:
PV = nRT
Where:
P = pressure (271 kPa)
V = volume (32 L)
n = number of moles of gas
R = ideal gas constant (8.31 J/(mol*K))
T = temperature (20 oC + 273.15 = 293.15 K)
First, we need to calculate the number of moles of gas in the tire:
n = (P * V) / (R * T)
n = (271 kPa * 32 L) / (8.31 J/(mol*K) * 293.15 K)
n = 0.334 moles
Now that we have the number of moles of gas, we can use the ideal gas law to calculate the new volume if the air escapes:
V_new = n_newRT / P
V_new = (0.334 moles * 8.31 J/(mol*K) * 293.15 K) / 101.325 kPa
V_new = 8.145 L
Therefore, the air inside the tire would occupy a volume of 8.145 L if it escaped.