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(A) Given:Temperature $T = 27^{\circ} C = 27 + 273 = 300 \ K$.Root mean square velocity $v_{rms} = 61 \ m/s$.Gas constant $R = 8.31 \ J \ mol^{-1} \ K

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(A) Given:Temperature $T = 27^{\circ} C = 27 + 273 = 300 \ K$.Root mean square velocity $v_{rms} = 61 \ m/s$.Gas constant $R = 8.31 \ J \ mol^{-1} \ K^{-1}$.The formula for $v_{rms}$ is given by $v_{rms} = \sqrt{\frac{3RT}{M}}$,where $M$ is the molar mass in $kg/mol$.Squaring both sides,we get $v_{rms}^2 = \frac{3RT}{M}$.Rearranging for $M$,we get $M = \frac{3RT}{v_{rms}^2}$.Substituting the values: $M = \frac{3 	imes 8.31 	imes 300}{61 	imes 61}$.$M = \frac{7479}{3721} \approx 2.01 \ kg/mol$.Since the molar mass is approximately $2 \ kg/mol$,the molecular weight is $2 \ g/mol$.

The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} C$ in a vessel is $61 \ m/s$. The molecular weight of the gas is nearly:
$[R = 8.31 \ J \ mol^{-1} \ K^{-1}]$

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The r.m.s. velocity of gas molecules kept at temperature $27^{\circ} C$ in a vessel is $61 \ m/s$. The molecular weight of the gas is nearly:$[R = 8.31 \ J \ mol^{-1} \ K^{-1}]$