The compressibility factor for `N_(2)` at 223 K and 81.06 Mpa is 1.95 , and at 373 K and 20 . 265 Mpa , it is 1.10 . A certain mass of `N_(2)` occupies a volume of 1.0 `dm^(3)` at 223 K and 81.06 Mpa . What is the volume occupied by the same quantity of `N_(2)` at 373 K and 20.265 MPa?

Explanation

For `T=223 K`, `P=81.06 MPa`, `Z=1.95` and
`V=1.0 dm^(3)=10^(3) cm^(3)`, we have
`n=(PV)/(nRT)=(81.06xx10^(3))/(1.95xx8.314xx223)=22.42 mol`
Now, at `T=373 K`, `P=20.65 MPa`, `Z=1.10`, the volume occupied will be
`V=(ZnRT)/(P)=(1.10xx22.42xx8.314xx373)/(20.265)=3774.0 cm^(3)`
`:. V=3.774 dm^(3)`