Question

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

Answer 1

Given, Molar mass of oxygen
`M= 32 g mol^(-1)=0.032kg "mole"^(-1)`
Temperature `T=27^(@)C =(27+273)K=300 K`
Root mean square speed, `v_(rms)=sqrt((3RT)/(M))=sqrt((3(8.314)(300))/((0.032)))=183.6ms^(-1)`
Average speed, `v=sqrt((8RT)/(piM))=sqrt((8(8.314)(300))/((3.14)(0.032)))=445.6ms^(-1)`
Most probable speed, `v_(mp)=sqrt((2RT)/(M))=sqrt((2(8.314)(300))/((0.032)))=394.8ms^(-1)`