At what temperature rms speed of gaseous hydrogen molecule is equal to that of oxygen molecule at 47 degree Celsius?

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At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at 47∘ CA. 80 KB. 73 KC. 3 KD. 20 K

Text Solution

Solution : Molecular weights of oxygen and hydrogen respectively are `M_1=32` and `M_2=2`. <br> rms speed , `c prop sqrt((3RT)/M)` <br> `thereforec_1/c_2=sqrt(T_1/T_2.M_2/M_1)`<br> Here `c_1=c_2` and `T_1=47^@C=320 K` <br> `thereforeT_1/T_2.M_2/M_1=1`<br> or,`T_2=T_1.M_2/M_1=320times2/32`<br> `=20K=(20-273)^@C=-253^@C`

Text Solution

80 K`-73 K`3 K20 K

Answer : D

Solution : `upsilon_(rms) = sqrt((3RT_(H))/(M_H)) = sqrt((3RT_("OXY"))/(M_("OXY"))` <br> `(T_H)/(M_H) = (T_("OXY"))/(M_("OXY"))` <br> or, `T_(H) = T_("OXY") (M_H)/(M_("OXY")) = (47+273) 2/32 = 320/16` <br> `= 20K`.