Question

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. 

Answer 1

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
n_i = P V/ RT
n_i = 7 x 10⁵ Pa x (2.0 x 10^-3 m³) / 8.314 x (17 + 273.16 )
n_i = 0.5803 moles.
Now we have to find the number of moles in the leaked out air.
n_o = 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
n_o = 1.01 x 10⁵ Pa x 120 x 10^-6 m³ / 8.314 x 290.16 K
n_o =  0.005024 mol
The number of molecules remaining must be equal to
n_r = n_i - n_o
n_r = 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