Calculate the root mean square, average and most probable speeds of oxygen molecules at `27^(@)C.`

Explanation

Molar mass of oxygen `M=32 g mol^(-1) = 0.032 kg mol^(-1)`
Temperature , `t= 27^@C rArr T= (27 + 273) K = 300 K`
Expressions to be used:
Root mean square speed, `c= sqrt(3RT)/(m)`
Average speed `bar c = sqrt(2RT)/(M)`
Actual calcutations :
Root meant square speed .
`c= sqrt(8RT)/(piM) = sqrt((3(8.314 JK^(-1)mol^(-1))(300K)
)/((0.032 kg mol^(1))))=483.6 ms^(-1)`
Average speed ,
`barc=sqrt((2RT)/(piM))=sqrt((8(8.314 JK^(-1)mol ^(-1))(300K))/((3.14)(0.032 kg mol^(-1))))=445.6ms^(-1)`
Most probable speed,
`C^** = sqrt((2RT)/(M))=sqrt((2.(8.314 JK^(-1)mol^-1)(300K))/((0.0032 kg mol^(-1))))=394.8 ms^(-1)`