A gas bulb of `1 L` capacity contains `2.0xx10^(11)` molecules of nitrogen exerting a pressure of `7.57xx10^(3)Nm^(-2)`. Calculate the root mean square (rms) speed and the temperature of the gas molecules. If the ratio of the most probable speed to the root mean square is `0.82`, calculate the most probable speed for these molecules at this temperature.

Explanation

`C_(rms)=((3RT)/(M))^(1//2) T=?`
Using, `PV=nRT`, we get
`T=(PV)/(nR)=(7.57xx10^(-3)xx1xx10^(-3))/((2.0xx10^(21))/(6xx10^(23))xx8.314)`
`C_(rms)=sqrt((3xx8.314xx273.15)/(28xx10^(-3)))=493.27 m s^(-1)`
Most probable speed `(C_(MP))` is
`0.82xx493.27=404.45 m s^(-1)`