At 400 K,the root mean square (rms) speed of | vedclass

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Question

(B) The formula for root mean square speed is $V_{rms} = \sqrt{\frac{3RT}{M_X}}$.The formula for most probable speed is $V_{mp} = \sqrt{\frac{2RT}{M_Y

Vedclass · Accepted Answer

$4$

Vedclass · Answer

(B) The formula for root mean square speed is $V_{rms} = \sqrt{\frac{3RT}{M_X}}$.The formula for most probable speed is $V_{mp} = \sqrt{\frac{2RT}{M_Y}}$.Given that $V_{rms} (X) = V_{mp} (Y)$,we have:$\sqrt{\frac{3R(400)}{40}} = \sqrt{\frac{2R(60)}{M_Y}}$.Squaring both sides:$\frac{3 	imes 400}{40} = \frac{2 	imes 60}{M_Y}$.$30 = \frac{120}{M_Y}$.$M_Y = \frac{120}{30} = 4$.Thus,the molecular weight of gas $Y$ is $4$. Hence,the correct answer is option $B$.

At $400 \ K$,the root mean square $(rms)$ speed of a gas $X$ (molecular weight $= 40$) is equal to the most probable speed of gas $Y$ at $60 \ K$. The molecular weight of the gas $Y$ is:

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