If the most probable speed of CO_2 at 27^{cir | vedclass

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Question

(B) Given,\ Temperature $(T)$ is the same for most probable velocity $(v_{mp})$ and root mean square velocity $(v_{rms})$. \ The formulas are: \ $v

Vedclass · Accepted Answer

$490$

Vedclass · Answer

(B) Given,\ Temperature $(T)$ is the same for most probable velocity $(v_{mp})$ and root mean square velocity $(v_{rms})$. \ The formulas are: \ $v_{mp} = \sqrt{\frac{2RT}{M}}$ and $v_{rms} = \sqrt{\frac{3RT}{M}}$. \ Taking the ratio: \ $\frac{v_{rms}}{v_{mp}} = \sqrt{\frac{3RT/M}{2RT/M}} = \sqrt{\frac{3}{2}} = \sqrt{1.5} \approx 1.2247$. \ Given $v_{mp} = 400 \ ms^{-1}$,then: \ $v_{rms} = 1.2247 	imes 400 \ ms^{-1} \approx 489.88 \ ms^{-1} \approx 490 \ ms^{-1}$. \ Thus,option $(B)$ is the correct answer.

If the most probable speed of $CO_2$ at $27^{\circ} C$ is $400 \ ms^{-1}$,the root mean square velocity of $CO_2$ at the same temperature in $ms^{-1}$ is approximately:

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