If the r.m.s. speed of a chlorine molecule is | vedclass

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(C) The root mean square (r.m.s.) speed of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas cons

Vedclass · Accepted Answer

$651$

Vedclass · Answer

(C) The root mean square (r.m.s.) speed of a gas molecule is given by the formula $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $R$ is the universal gas constant,$T$ is the absolute temperature,and $M$ is the molar mass.Since the temperature $T$ is the same for both gases,we have $v_{rms} \propto \frac{1}{\sqrt{M}}$.Therefore,the ratio of the r.m.s. speeds is $\frac{v_{Ar}}{v_{Cl}} = \sqrt{\frac{M_{Cl}}{M_{Ar}}}$.Given $v_{Cl} = 490\,m/s$,$M_{Cl} = 70.9\,u$,and $M_{Ar} = 39.9\,u$.Substituting the values: $v_{Ar} = 490 	imes \sqrt{\frac{70.9}{39.9}}$.$v_{Ar} = 490 	imes \sqrt{1.7769} \approx 490 	imes 1.333 = 653.17\,m/s$.Rounding to the nearest provided option,we get $651.7\,m/s$.

If the r.m.s. speed of a chlorine molecule is $490\,m/s$ at $27^{\circ}C$,the r.m.s. speed of argon molecules at the same temperature will be $......\,m/s$ (Atomic mass of argon $= 39.9\,u$,molecular mass of chlorine $= 70.9\,u$). (in $.7$)

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