Oxygen is filled in a closed metal jar of volume `1.0xx10^(-3)m^(3)` at a pressure of `1.5xx10^(5)Pa.` and temperature `400K`. The jar has a small leak in it. The atmospheric pressure is `1.0xx10^(5)Pa` and the atmospheric temperature is `300K`. Find the mass of the gas that leaks out by time the pressure and the temperature inside the jar equalise with the surrounding.

Explanation

`P_(1) V = n_(1) R T`
`n_(1) = (P_(1)V)/(R T_(1))`
Number of moles leaked
`Deltan = n_(1) - n_(2)`
`= ((P_(1))/(T_(1)) - (P_(2))/(T_(2))) (V)/(R ) = ((1.5)/(400) - (1)/(300)) xx (10^(5) xx 10^(-3))/(8.3)`
`= 5.02 xx 10^(-3)`
Mass of gas leaked `= Delta n M_(0) = 5.02 xx 10^(-3) xx 32`
`= 0.16 g`