Calculate the `RMS` velocity of chlorine molecules at `17^(@)C` and `800 mm` pressure.

Explanation

We know,
`(P_(1)V_(1))/(T_(1))=(P_(2)V_(2))/(T_(2))`
Here `P_(1)=760 mm Hg`, `P_(2)=800 mm Hg`
`V_(1)=22,400 mL`, `V_(2)=?`
`T_(1)=273 K`, `T_(2)=290 K`
`:. V_(2)=(P_(1)V_(1))/(T_(1))xx(T_(2))/(P_(2))=(760xx22,400)/(273)xx(290)/(800)=22600 mL`
`u_(rms)=((3PV)/(M))^(1//2)`
Here, `P=800 mm=80 cm`
`=80xx13.6xx981 dyn cm^(-2)`
`V=22,600 mL`
`M=71 g mol^(-1)`
`:. u_(rms)=((3xx80xx13.6xx981xx22,600)/(71))^(1//2)`
`=sqrt(0.1018)xx10^(5) cm s^(-1)`