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

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)
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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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