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(D) The root mean square speed $(u_{rms})$ of a gas is given by the formula: $u_{rms} = \sqrt{\frac{3RT}{M}}$.Here,$R$ is the gas constant,$T$ is the

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$Cl_2$

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(D) The root mean square speed $(u_{rms})$ of a gas is given by the formula: $u_{rms} = \sqrt{\frac{3RT}{M}}$.Here,$R$ is the gas constant,$T$ is the temperature in Kelvin,and $M$ is the molar mass of the gas.Since $3$,$R$,and $T$ are constant for all gases at the same temperature,$u_{rms} \propto \frac{1}{\sqrt{M}}$.This means the gas with the highest molar mass will have the lowest root mean square speed.The molar masses are:$M(SO_2) = 32 + 2 	imes 16 = 64 \, g/mol$$M(N_2) = 2 	imes 14 = 28 \, g/mol$$M(O_2) = 2 	imes 16 = 32 \, g/mol$$M(Cl_2) = 2 	imes 35.5 = 71 \, g/mol$Comparing the molar masses,$Cl_2$ has the highest molar mass $(71 \, g/mol)$.Therefore,$Cl_2$ will have the lowest root mean square speed.

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

Which of the following gases will have the lowest root mean square speed at $25\,^{\circ}C$?

Similar Questions

At what temperature $(^oC)$ will the average velocity of oxygen molecules be equal to their $(rms)$ velocity at $27^oC$?

Among the following,identify the gas which has the greatest average speed of its molecules?

Which of the following gases has the maximum $R.M.S.$ velocity at $25,^{\circ}C$?

Match the following (where $U_{rms}$ = root mean square speed,$U_{av}$ = average speed,$U_{mp}$ = most probable speed)
List-$I$ List-$II$
$(a)$ $U_{rms} / U_{av}$ $(i)$ $1.22$
$(b)$ $U_{av} / U_{mp}$ $(ii)$ $1.13$
$(c)$ $U_{rms} / U_{mp}$ $(iii)$ $1.08$

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