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The density of O(2) gas at 1 atm pressur...

The density of `O_(2)` gas at 1 atm pressure and 273 K is 1.429 `g*dm^(-3)`. Calculate the root mean square velocity of `O_(2)` molecule at 273 K?

Text Solution

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The root mean square velocity,
`c_(rms)=sqrt((3RT)/(M))=sqrt((3PV)/(M))=sqrt((3P)/(d))" "[becausePV=RT and d=(M)/(V)]`
Given, P=1 atm and d=1.429` g*dm^(-3)`
`P=1atm=1.013xx10^(6)"dyn"*cm^(-2)`
`=1.013xx10^(6)d*cm*s^(-2)*cm^(-2)=1.013xx10^(6)g*cm^(-1)*s^(-2)`
and `d=1.429g*dm^(-3)=1.429xx10^(-3)g*cm^(-3)`
`therefore c_(rms)=sqrt((3xx1.013xx10^(6)g*cm^(_1)*s^(-2))/(1.429xx10^(4)cm*s^(-1)`
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