Question

If He(g) has an average kinetic energy of 6670 J/mol under certain conditions, what is the root mean square speed of Cl2(g) molecules under the same conditions?

Answer 1

we know

`V_"rms"=sqrt((RT)/M)`

where

`V_"rms"->"RMS velocity of the gas"`

`T->"Absolute temperature of the gas"`

`M->"Molar mass of the gas"`

`R->"Universal gas constant"`

So average molar kinetic energy of the gas

`E=1/2MV_"rms"^2=1/2RT`

This equation reveals that molar KE is independent of the nature of the gas . It only depends on temperature as ideal behavior is concerned. So both He(g) and `Cl_2(g)` will have same average `KE=6670"J/mol"` .under the same condition of temperature.

So for `Cl_2(g)`

`1/2M_(Cl_2(g))V_(rmsCl_2)^2=6670`

`color(red)("Taking atomic mass of Cl"=35.5"g/mol"=35.5xx10^-3"kg/mol")`

`=>V_(rmsCl_2(g))^2=(6670xx2)/(2xx35.5xx10^-3)`

`=>V_(rmsCl_2(g))=sqrt(6670000/35.5)~~433.5ms^-2`