If two gases of molecular weights M1 and M2 are at same pressure and temperature, ratio of their r.m.s. speed will be

  • Option 1)

    M_2:M_1

  • Option 2)

    M_1:M_2

  • Option 3)

    \sqrt M_1:\sqrt M_2

  • Option 4)

    \sqrt M_2:\sqrt M_1

 

Answers (1)

As we learnt in 

Root mean square velocity -

V_{rms}= \sqrt{\frac{3RT}{M}}

= \sqrt{\frac{3P}{\rho }}
 

- wherein

R = Universal gas constant

M = molar mass

P = pressure due to gas

\rho = density

 

V_{rms}\propto \frac{1}{\sqrt{M}}

\therefore \frac{V_{1}}{V_{2}}= \frac{\sqrt{M_{2}}}{\sqrt{M_{1}}}

 


Option 1)

M_2:M_1

Incorrect

Option 2)

M_1:M_2

Incorrect

Option 3)

\sqrt M_1:\sqrt M_2

Incorrect

Option 4)

\sqrt M_2:\sqrt M_1

correct

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