The root mean square (rms) speed of X_2 gas i | vedclass

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(C) The formula for root mean square speed is $C_{rms} = \sqrt{\frac{3RT}{M}}$.Initially, for $X_2$ gas at temperature $T$, $C_1 = x = \sqrt{\frac{3RT

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$2x$

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(C) The formula for root mean square speed is $C_{rms} = \sqrt{\frac{3RT}{M}}$.Initially, for $X_2$ gas at temperature $T$, $C_1 = x = \sqrt{\frac{3RT}{M_{X_2}}}$.When temperature is doubled $(T_2 = 2T)$ and $X_2$ dissociates into $2X$, the molar mass becomes $M_2 = \frac{M_{X_2}}{2}$.The new rms speed $C_2$ is given by $C_2 = \sqrt{\frac{3R(2T)}{M_{X_2}/2}} = \sqrt{4 	imes \frac{3RT}{M_{X_2}}} = 2 	imes \sqrt{\frac{3RT}{M_{X_2}}}$.Substituting $x$ for the initial speed, we get $C_2 = 2x \ m/s$.

The root mean square (rms) speed of $X_2$ gas is $x \ m/s$ at a given temperature. When the temperature is doubled, the $X_2$ molecules dissociate completely into atoms. The root mean square speed of the sample of gas then becomes (in $m/s$):

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