A bicycle tire has a pressure of 7.05 x 105 Pa at a temperature of 17°C and contains 2.00 L of gas.
What will its pressure be, in pascals, if you let out an amount of air that has a volume of 120 cm3 at atmospheric pressure and at the temperature of the tire? Assume tire temperature and volume remain constant.
The temperature inside the tyre and the volume of the tyre
remains constant.
We can use the ideal gas equation, P V = n R T --------------------
1
We first find the number of molecules were present in the tyre
before we let some amount of air to leak out.
Rearranging equation 1 to get the n
ni = P V/ RT
ni = 7 x 105 Pa x (2.0 x 10-3
m3) / 8.314 x (17 + 273.16 )
ni = 0.5803 moles.
Now we have to find the number of moles in the leaked out
air.
no = P V/ R T
This time the pressure is atmospheric pressure and the volume of
the air leaked is V = 120 cm3 = 120 x 10-6
m3
no = 1.01 x 105 Pa x 120 x 10-6
m3 / 8.314 x 290.16 K
no = 0.005024 mol
The number of molecules remaining must be equal to
nr = ni - no
nr = 0.5803 moles - 0.005024 mol = 0.575276 mol.
Finally we can find the pressure inside the tyre when 120
cm3 of air is leaked out.
P = n RT / V
We have given that the temperature and the volume of the tyre does
not change.
P = 0.575276 mol x 8.314 x 290.16 K / 2.0 x 10-3
m3
P = 6.939 x 105 Pa
A bicycle tire has a pressure of 7.05 x 105 Pa at a temperature of 17°C and contains 2.00 L of gas.
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