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Relating Translational KE and T

At certain te...

Question

At certain temperature rms velocity of ethane molecules is $5.33 \times 10^{4} c m$ find the rms velocity of $O_{2}$ at temperature.

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Solution

We know,
$U_{R M S} = \sqrt{\frac{3 R T}{M}}$
So,
$\frac{U_{a v g} (C_{2} H_{6})}{U_{a v g} (O_{2})} = \sqrt{\frac{T_{C_{2} H_{6}} \times M_{O_{2}}}{T_{O_{2}} \times M_{C_{2} H_{6}}}}$
$M_{C_{2} H_{6}} = 30$ , $M_{O_{2}} = 32$
Here, $T_{C_{2} H_{6}} = T_{O_{2}}$
Hence,
$\frac{U_{a v g} (C_{2} H_{6})}{U_{a v g} (O_{2})} = 1.038$
Hence,
$U_{R M S} (O_{2}) = \frac{1.038}{5.33 \times 10^{2}} = 0.0019 \frac{m}{s}$

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