The most probable speed (u_{mp}) of 8 g of H | vedclass

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Question

(B) The most probable speed is given by the formula $u_{mp} = \sqrt{\frac{2RT}{M}}$.Given $u_{mp} = 200 \ ms^{-1}$ and molar mass $M = 2 	imes 10^{-3

Vedclass · Accepted Answer

$240$

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(B) The most probable speed is given by the formula $u_{mp} = \sqrt{\frac{2RT}{M}}$.Given $u_{mp} = 200 \ ms^{-1}$ and molar mass $M = 2 	imes 10^{-3} \ kg \ mol^{-1}$.$200 = \sqrt{\frac{2RT}{2 	imes 10^{-3}}} \implies 40000 = \frac{2RT}{2 	imes 10^{-3}} \implies RT = 40 \ J \ mol^{-1}$.The kinetic energy of an ideal gas is given by $KE = \frac{3}{2} nRT$.Number of moles $n = \frac{	ext{mass}}{	ext{molar mass}} = \frac{8 \ g}{2 \ g \ mol^{-1}} = 4 \ mol$.$KE = \frac{3}{2} 	imes 4 	imes 40 = 6 	imes 40 = 240 \ J$.

The most probable speed $(u_{mp})$ of $8 \ g$ of $H_2$ is $2 \times 10^2 \ ms^{-1}$. The kinetic energy (in $J$) of the same amount of $H_2$ gas is:

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