If the most probable speed of methane (CH_4) | vedclass

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(D) The most probable speed $(u_{mp})$ is given by the formula: $u_{mp} = \sqrt{\frac{2RT}{M}}$.Given $u_{mp} = 400 \ ms^{-1}$ and molar mass of metha

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$1920$

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(D) The most probable speed $(u_{mp})$ is given by the formula: $u_{mp} = \sqrt{\frac{2RT}{M}}$.Given $u_{mp} = 400 \ ms^{-1}$ and molar mass of methane $(M)$ = $16 \ g \ mol^{-1} = 0.016 \ kg \ mol^{-1}$.Squaring both sides: $u_{mp}^2 = \frac{2RT}{M} \Rightarrow \frac{RT}{M} = \frac{u_{mp}^2}{2}$.Substituting the values: $\frac{RT}{0.016} = \frac{400^2}{2} = \frac{160000}{2} = 80000$.Thus,$RT = 80000 	imes 0.016 = 1280 \ J \ mol^{-1}$.The kinetic energy $(KE)$ of one mole of an ideal gas is given by: $KE = \frac{3}{2} RT$.$KE = \frac{3}{2} 	imes 1280 = 3 	imes 640 = 1920 \ J$.

If the most probable speed of methane $(CH_4)$ at a certain temperature is $400 \ ms^{-1}$,what is the kinetic energy of one mole of methane at the same temperature in $J$?

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