The ratio between the most probable speed of | vedclass

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Question

(C) The formula for the most probable speed $(v_{mp})$ is $v_{mp} = \sqrt{\frac{2RT}{M}}$.Given:Molar mass of $N_2$ $(M_1)$ = $28 \ g \ mol^{-1}$, Tem

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$0.707$

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(C) The formula for the most probable speed $(v_{mp})$ is $v_{mp} = \sqrt{\frac{2RT}{M}}$.Given:Molar mass of $N_2$ $(M_1)$ = $28 \ g \ mol^{-1}$, Temperature $(T_1)$ = $400 \ K$.Molar mass of $CO$ $(M_2)$ = $28 \ g \ mol^{-1}$, Temperature $(T_2)$ = $800 \ K$.The ratio of the most probable speed of $N_2$ to $CO$ is:$\frac{v_{mp(N_2)}}{v_{mp(CO)}} = \frac{\sqrt{\frac{2RT_1}{M_1}}}{\sqrt{\frac{2RT_2}{M_2}}} = \sqrt{\frac{T_1}{T_2} 	imes \frac{M_2}{M_1}}$Substituting the values:$\frac{v_{mp(N_2)}}{v_{mp(CO)}} = \sqrt{\frac{400}{800} 	imes \frac{28}{28}} = \sqrt{\frac{1}{2}} = \sqrt{0.5} \approx 0.707$.

The ratio between the most probable speed of $N_2$ at $400 \ K$ and $CO$ at $800 \ K$ is (molar mass of $N_2 = 28 \ g \ mol^{-1}$, molar mass of $CO = 28 \ g \ mol^{-1}$)

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