A gas bulb of 1 litre capacity contains `2.0xx10^(21)` molecules of nitrogen exerting a pressure of `7.57xx10^(3)" N "m^(-2)`. Calculate the root mean square (r.m.s) speed and the temperature of the gas molecules.

Explanation

Volume of gas =1 litre `=10^(-3)m^(-3)`
Pressure `=7.57xx10^(3)" N "m^(-2)`
No. of moles of the gas `=(2.0xx10^(21))//(6.02xx10^(23))=0.00332`
Applying ` " "` PV=nRT
`(7.57xx10^(3))xx10^(-3)=0.00332xx8.314xxT" or " T=274.25" K"`
Root Mean Square speed `=sqrt((2RT)/(M))=sqrt((3xx8.314xx10^(7)xx274.25)/(28))=49426.5" cm "s^(-1)`