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Molecular Speeds - Vrms, Vavg, Vmps

At what tempe...

Question

At what temperature (in $^{\circ} C$ ) is the root mean square velocity of $O_{2}$ gas at $300 K$ equal to the most probable velocity of $N e$ (Given 273 K = 0 $^{\circ} C$ )?

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Solution

According to question
$u_{rms} = u_{mp}$
$\sqrt{\frac{3 R T_{1}}{M_{1}}} = \sqrt{\frac{2 R T_{2}}{M_{2}}}$
$T_{1} = 300 K$
$M_{1} = 32 g / m o l$ , $M_{2} = 20 g / m o l$
$\frac{3 \times 300}{32} = \frac{2 T_{2}}{20}$
$T_{2} = 281.25 K$
Thus, $T_{2} = 281.25 - 273 = {8.25}^{\circ} C$

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Molecular Speeds - Vrms, Vavg, Vmps

Standard XIII Chemistry

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