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Question
Compare the rms speed of hydrogen molecules at 227°C with the rms speed of oxygen molecules at 127°C. 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 + 227 = 500 K,
T2 (oxygen) = 273 + 127 = 400 K
Formula:
The rms speed, `"v"_"rms" = sqrt("3RT"/"M"_0)`
where M0 denotes the molar mass
`therefore ("v"_("rms"_1) ("hydrogen"))/("v"_("rms"_2) ("oxygen")) = sqrt(("T"_1/"T"_2)(("M"_(02))/"M"_(01)))`
`= sqrt((500/400)(32/2))`
`= sqrt((5/4)(16))`
`= sqrt(5/cancel(4)_1 xx cancel(16)^4)`
`= sqrt(5 xx4)`
`= sqrt20`
`("v"_("rms"_1) ("hydrogen"))/("v"_("rms"_2) ("oxygen")) = 2 sqrt5 = 2 xx 2.236 = 4.472`
vrms(hydrogen) : vrms(oxygen) = 4.472 : 1
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