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

Given, volume `V =10^(-3) m^(3)`,
Pressure `P_(1)=1.5xx10^(5)Pa,P_(2)=10^(5)Pa`
Temperature `T_(1)=400 K, T_(2)=300K,`
From ideal gas equation, `p_(1)V=n_(1)RT_(1)`
`Rightarrow" " n_(1)=p_(1)/(RT_(1))`
Similarly,`Similarly" " p_(2)V=n_(2)RT_(2)Rightarrown_(2)=(P_(2)V)/(RT_(2))`
`therefore` Number of mole leaked
`Delta=n_(1)n_(2)=(P_(1)/T_(1)-P_(2)/T_(2))(V)/(R)=((1.5)/(400)-(1)/(300))xx(10^(5)xx10^(-3))/(8.3)=5.02xx10^(-3)`
Mass of gas leaked =`Deltan M_(o)=5.02xx 10^(-3)xx32=0.16 g`