A vessel of volume `8.0 xx 10^(-3)m^(3)` contains an ideal gas at `300 K` and pressure `200 kPa`. The gas is allowed to leak till the pressure falls to `125 k Pa`. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constants.

Explanation

As the gas leaks out , the volume and the temperature of the remaining gas do not change. The number of moles of the gas in the vessel In given by n =`(PV)/(RT)`.
The number of moles in the vessel before the leakage in `n_(1) = (P_(1)V)/(RT)` and that after the leakage is`n_(2) = (P_(2)V)/(RT)`.
The amount leaked is `n_(1) - n_(2) = ((P_(1)-P_(2))V)/(RT) = ((200-125) xx 10^(3) xx 8.0 xx 10^(-3))/(8.3 xx 300) = 0.24` mole