The root mean square speeds at STP for the ga | vedclass

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(B) The root mean square speed $(V_{rms})$ is given by the formula $V_{rms} = \sqrt{\frac{3RT}{M}}$,where $M$ is the molar mass of the gas.Since $V_{r

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$HBr < O_2 < N_2 < H_2$

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(B) The root mean square speed $(V_{rms})$ is given by the formula $V_{rms} = \sqrt{\frac{3RT}{M}}$,where $M$ is the molar mass of the gas.Since $V_{rms} \propto \frac{1}{\sqrt{M}}$,the gas with the lowest molar mass will have the highest $V_{rms}$.The molar masses are: $M(H_2) = 2 \ g/mol$,$M(N_2) = 28 \ g/mol$,$M(O_2) = 32 \ g/mol$,and $M(HBr) = 81 \ g/mol$.Comparing the values: $\frac{1}{\sqrt{2}} > \frac{1}{\sqrt{28}} > \frac{1}{\sqrt{32}} > \frac{1}{\sqrt{81}}$.Therefore,the order of $V_{rms}$ is $HBr < O_2 < N_2 < H_2$.

List-$I$	List-$II$
$(a)$ $U_{rms} / U_{av}$	$(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$	$(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$	$(iii)$ $1.08$

The root mean square speeds at $STP$ for the gases $H_2, N_2, O_2$ and $HBr$ are in the order

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