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A flask contains Argon and chloring in t...

A flask contains Argon and chloring in the ratio of `2:1` by mass. The temperature of the mixture is `27^@C` Obtain the ratio of averagae kinetic energy per molecule and root mean square speed `v_(rms)` of the molecules of the two gases. Given atomic mass of argon=39.9 u and molarcular mass of chlorine.=70.9 u.

Text Solution

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Average kinetic energy of a molecule of any ideal gas =`3/2 kT`
(i) As both argon and chlorine have the same temperature the ratio of average kinetic energy per molecule of the gases =1:1.
(ii) Let m be the mass of a molecule of a gas
Now average kinetic energy per molecule
`1/2mv_(rms)^2`
`therefore1/2m_1v_1^2=1/2m_2v_2^2=3/2kT`
or,`v_1^2/v_2^2=m_2/m_1=M_2/M_1=70.9/39.9=1.77`
where M is the atomic or molecular mass of the gas
So, `v_1/v_2=sqrt(1.77)=1.33`
Here, composition of mixture of gases is not relevant since
`v_1/v_2=sqrt(M_2/M_1)=constant`
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