Question

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?

Answer 1

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.