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At what temperature will the most probab...

At what temperature will the most probable velocity of `H_(2)` molecule be equal to the root mean square velocity of `O_(2)` molecule at `20^(@)C` ?

Text Solution

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At `20^(@)C` temperature, root mean square velocity of `O_(2)` molecule `=sqrt((3RT)/(M))=sqrt((3xx8.314xx10^(7)xx(273+20))/(32))cm*s^(-1)`
Let at temperature TK the most probable velocity of `H_(2)`
=the rms velocity of `O_(2)` at `20^(@)C`.
At TK, the most probable velocity of `H_(2)`,
`=sqrt(2RT)/(M)=sqrt((2xx8.314xx10^(7)xxT)/(2))cm*s^(-1)`
`therefore sqrt((2xx8.314xx10^(7)xxT)/(2))=sqrt((3xx8.314xx10^(7)xx293)/(32))`
or, `T=(3xx293)/(32)=27.50" "27.5K=27.5-273=-245.5^(@)C`
Therefore at `-245.5^(@)C`, the most probable velocity of `H_(2)`
molecules will be equal to the rms velocity of `O_(2)` at `20^(@)C`.
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