The rms speed of an oxygen molecule at a cert | vedclass

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

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$2 v$

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(C) The root mean square (rms) 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 of the gas.Initially,for oxygen molecules $(O_2)$,the molar mass is $M_1 = 32 	ext{ g/mol}$ and the temperature is $T$. Thus,$v = \sqrt{\frac{3RT}{32}}$.When the temperature is doubled $(T_2 = 2T)$ and oxygen molecules dissociate into atomic oxygen $(O)$,the molar mass becomes $M_2 = 16 	ext{ g/mol}$.The new rms speed $v'$ is given by $v' = \sqrt{\frac{3R(2T)}{16}}$.Simplifying this,$v' = \sqrt{\frac{6RT}{16}} = \sqrt{2} 	imes \sqrt{\frac{3RT}{16}}$.Since $v = \sqrt{\frac{3RT}{32}}$,we have $\sqrt{\frac{3RT}{16}} = \sqrt{2} 	imes v$.Therefore,$v' = \sqrt{2} 	imes (\sqrt{2} v) = 2v$.

The rms speed of an oxygen molecule at a certain absolute temperature is $v$. If the absolute temperature is doubled and the oxygen molecules dissociate into atomic oxygen,then the rms speed would be

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