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

Explanation

`27^(@)C = 300 K`
Root mean square speed `= sqrt((3RT)/(M))`
`R = 8.314 xx 10^(7) " erg" K^(-1) mol^(-1), M = 32 g mol^(-1), T = 300 K`
Substituting the values,
`= sqrt((3 xx 8.314 xx 10^(7) xx 300)/(32))`
`= 48356 cm//sec`
`= 483.56 m//sec`
Average speed `= sqrt((8RT)/(pi M))`
`= sqrt((8 xx 8.314 xx 10^(7) xx 300 xx 7)/(22 xx 32))`
`= 44542 cm//sec`
`= 445.42 m//sec`
Most probable speed `= sqrt((2 xx R xx T)/(M))`
`= sqrt((2 xx 8.314 xx 10^(7) xx 300)/(32))`
`= 39483 cm//sec`
`= 394.83 m//sec`