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Question
At what temperature will oxygen molecules have same rms speed as helium molecules at S.T.P.? (Molecular masses of oxygen and helium are 32 and 4 respectively).
Solution
Given: Standard Temperature Pressure (S.T.P) i.e. T2 = 273 K, M01 (oxygen) = 32 × 10-3 kg/mol, M02 (helium) = 4 × 10-3 kg/mol,
`"v"_"rms" = sqrt("3RT"/"M"_0)`
The rms speed of oxygen molecules, `"v"_1 = sqrt("3RT"_1/"M"_01)` and that of helium molecules,
`"v"_2 = sqrt("3RT"_2/"M"_02)`
when v1 = v2 ,
`sqrt("3RT"_1/"M"_01) = sqrt("3RT"_2/"M"_02)`
`∴ "T"_1/"M"_01 = "T"_2/"M"_02`
∴ Temperature, T1 = `"M"_01/"M"_02. "T"_2`
`= ((32 xx 10^-3)(273))/(4 xx 10^-3)`
= 2184 K
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