A vessel of volume `8.0xx10^(-3) m^(3)` contains an ideal gas at 300K and 200kPa. The gas is allowed to leak till the pressure falls to 125kPa. Calculate the amount of the gas (in moles) leaked assuming that the temperature remains constant.

Explanation

As the gas leaks out, the volume and the temperature of the remaining gas do not change. The number of moles in the vessel is given by `n=(pV)/(RT)`. The number of moles in the vessel before the leakage is
`n_(2)=(p_(1)V)/(RT)`
and that after the leakage is `n_(2)=(p_(2)V)/(RT)`.`Thus, the amount leaked is `n_(1)-n_(2)=((p_(1)-p_(2))V)/(RT)` ltbgt `=((200-125)xx10^(3) N m^(-2)xx8.0xx10^(-3)m^(3))/((8.3JK^(-1)mol^(-1))xx(300K))`
`=0.24mol^(-1).`