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Question
Answer in brief:
Compare the rms speed of hydrogen molecules at 127ºC with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.
Solution
Data: M01 (hydrogen) = 2 g/mol,
M02 (oxygen) = 32 g/mol,
T1 (hydrogen) = 273 + 127 = 400 K,
T2 (oxygen) = 273 + 27 = 300 K
The rms speed, `"v"_"rms" = sqrt("3RT"/"M"_0)`,
where M0 denotes the molar mass
`therefore ("v"_"rms1" ("hydrogen"))/("v"_"rms2"("oxygen")) = sqrt(("T"_1/"T"_2)("M"_02/"M"_01))`
`= sqrt((400/300)(32/2)) = sqrt((4/3)(16))`
`= ((2)(4))/sqrt3 = 8/sqrt3`
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