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  • The root mean square speed of all molecules in a mixture containing hydrogen and oxygen in the mass ratio is found

The root mean square speed of all molecules in a mixture containing hydrogen and oxygen in the mass ratio 1: 8 is found to be \mathrm{n} times the root mean square speed of oxygen molecules at the same temperature. The value of \mathrm{n} is
 

Option: 1

\sqrt{\frac{8}{3}}
 


Option: 2

\sqrt{\frac{3}{8}}
 


Option: 3

\sqrt{\frac{3}{5}}
 


Option: 4

\sqrt{\frac{5}{8}}


Answers (1)

best_answer

\mathrm{Mass \: ratio\: 1: 8 \Rightarrow\: Mole \: ratio\: 2: 1}

\mathrm{\therefore Mass \: per \: mole =\frac{2 \times \mathrm{M}_{\mathrm{H}}+1 \times \mathrm{M}_{\mathrm{o}}}{3}=\frac{36}{3}=12}

For the mixture, \mathrm{v_1=\sqrt{\frac{3 R T}{12}}}

\mathrm{For \: \mathrm{O}_2, \mathrm{v}_2=\sqrt{\frac{3 \mathrm{RT}}{32}}}

\mathrm{\therefore \mathrm{n}=\frac{v_1}{v_2}=\sqrt{\frac{32}{12}}=\sqrt{8 / 3}}

Hence option 1 is correct.

 

Posted by

shivangi.shekhar

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