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At 400 K, the root mean square (rms) spe...

At `400 K`, the root mean square `(rms)` speed of a gas `X` (molecular weight`=40`) is equal to the most probable speed of gas `Y` at `60 K`. Calculate the molecular weight of the gas `Y`.

Text Solution

Verified by Experts

`v_(rms)(X)=sqrt((3RT)/(M))=sqrt((3Rxx400)/(40))=sqrt(30R)`
`v_(most probable)(Y)=sqrt((2RT)/(M))=sqrt((2Rxx60)/(M))`
Given `v_(rms)(X)=V_("most probable")(Y)`
`:. Sqrt(30R)=sqrt((2Rxx60)/(M))`
or `M=4`
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Knowledge Check

  • The root mean square speed of gas molecules

    A
    is same for all gases at the same temperature
    B
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    independent of its pressure but directly proportional to its Kelvin temperature
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    directly proportional to two square root of both its pressure and its Kelvin temperature
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    indepdent of its pressure but directly proportional to the square root of its Kelvin temperature.
    D
    directly proportional to its pressure and its Kelvin temperature.

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