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Question
Compare the rms speed of hydrogen molecules at 127°C with rms speed of oxygen molecules at 27ºC given that molecular masses of hydrogen and oxygen are 2 and 32 respectively.
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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 r.m.s. speed, `(v_(r.m.s.)) = sqrt((3 R T)/M_0)`,
Where M0 denotes the molar mass.
∴ `(v_(r.m.s._1) ("hydrogen"))/(v_(r.m.s._2) ("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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