An oxygen cylinder of volume 30 litres has an intial gauge pressure of 15 atm and a temperature of `27^(@)C`. After some oxygen is withdraw from the cylinder, the gauge pressure drops to 11 atm and its temperature drops to `17^(@)C` Estimate the mass of oxygen taken out of the cylinder `(R=8.31"Jmole"^(-1)K^(-1),"molecular mass of" O_(2)=32 "unit").`

Explanation

Give `P_(1)=15atm, V_(1)=30 "litres," T_(1)=300K`
and `P_(2) = 11 atm, V_(2)=?,T_(2)=290K`
Applying `(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
We get `V_(2)((P_(1)V_(1))/(T_(1)))((T_(2))/(P_(2)))=((15xx30)/(300))((290)/(11))=39.545"litres"`
`V_(2)-V_(1)=9.545xx10^(-3)m^(3).`
Applying `PV = muRT`
We get `mu=(PV)/(RT)=(11xx1.013xx10^(5)xx9.545xx10^(-5))/(8.314xx290)`
`=0.0441 xx 100`
`mu = 4.41` moles
i.e. `mu=(m)/(M)=4.41`
`therefore "Mass of gas expelled" = 4.41xx32=141.16g=0.141kg.`