The rms speed of oxygen is v at a particular | vedclass

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

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$2v$

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(C) The root mean square (rms) speed of a gas is given by the formula $v_{	ext{rms}} = \sqrt{\frac{3RT}{M}}$, where $R$ is the universal gas constant, $T$ is the absolute temperature, and $M$ is the molar mass.From this, we can see that $v_{	ext{rms}} \propto \sqrt{\frac{T}{M}}$.Let the initial state be $T_1 = T$ and $M_1 = M$ (for $O_2$ molecules). Then $v_1 = v \propto \sqrt{\frac{T}{M}}$.In the final state, the temperature is doubled, so $T_2 = 2T$. The oxygen molecules dissociate into atoms, so the molar mass becomes half, $M_2 = M/2$.The new rms speed $v_2$ is proportional to $\sqrt{\frac{T_2}{M_2}} = \sqrt{\frac{2T}{M/2}} = \sqrt{\frac{4T}{M}} = 2 \sqrt{\frac{T}{M}}$.Comparing the two, $v_2 = 2 	imes v_1 = 2v$.

The rms speed of oxygen is $v$ at a particular temperature. If the temperature is doubled and oxygen molecules dissociate into oxygen atoms, the rms speed becomes

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