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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)

$\sqrt M_2:\sqrt M_1$

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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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