Find RMS speed , average speed and most probable speed of `CO_2` gas at `27^@C`.

Explanation

T=27+273=330K,
R=8.314 J `mol^-1K^-1`
M=Gram Molecular mass of `CO_2=44g mol^-1`
RMS speed `(u_(rms))=u_(rms)=sqrt((3RT)/M`
T=`27^@C +273=300 K, R=8.314 J Mol^-1K^-1`
M=gram molecular mass of `CO_2=44g mol^-1`
`(IJ=kg m^2s^-2)`
`sqrt((3times8.314kgm^2s^-2K^-1mol^-1times300K)/(0.044kg mol^-1))`
`=4.12times10^2ms^-1`
Average speed `(u_(rms))=0.9123 times `RMS Speed
=`0.9212 times 4.12 times 10^2 ms^-1`
`=3.8 times 10^2 ms^-1`
Most probable speed
`(u_(mp))=0.8166 times 4.12 times 10^2 ms^-1`
`=3.36 times 10^2 ms^-1`