At what temperature will the RMS velocity of | vedclass

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(D) The formula for $RMS$ velocity is $v_{rms} = \sqrt{\frac{3RT}{M}}$ ...$(I)$The formula for most probable velocity is $v_{mp} = \sqrt{\frac{2RT}{M}

Vedclass · Accepted Answer

$300$

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(D) The formula for $RMS$ velocity is $v_{rms} = \sqrt{\frac{3RT}{M}}$ ...$(I)$The formula for most probable velocity is $v_{mp} = \sqrt{\frac{2RT}{M}}$ ...$(II)$Given:For $SO_2$: $T_1 = 400 \ K$,$M_1 = 64 \ g/mol$For $O_2$: $T_2 = ?$,$M_2 = 32 \ g/mol$Equating the two velocities:$\sqrt{\frac{3R 	imes 400}{64}} = \sqrt{\frac{2R 	imes T_2}{32}}$Squaring both sides:$\frac{1200}{64} = \frac{2T_2}{32}$$\frac{1200}{64} = \frac{T_2}{16}$$T_2 = \frac{1200 	imes 16}{64} = \frac{1200}{4} = 300 \ K$

At what temperature will the $RMS$ velocity of sulphur dioxide $(SO_2)$ molecules at $400 \ K$ be the same as the most probable velocity of oxygen $(O_2)$ molecules (in $K$)?

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