Which one of the following gases has the same RMS velocity at $27^{o} C$ as that of $N_{2}$ with RMS velocity of $5.0 \times 10^{4} c m . s^{- 1} a t 7^{o} C$ ?

C_{4} H_{10}

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C_{2} H_{6}

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C_{3} H_{8}

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C H_{4}

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Solution

The correct option is C $C_{2} H_{6}$
The root mean velocity $u = \sqrt{\frac{3 R T}{M}}$

$500 m / s = \sqrt{\frac{3 \times 8.314 J / m o l . K \times 300 K}{M}}$

$M = 0.03 k g / m o l = 30 g / m o l$

It is equal to the molecular weight of ethane $C_{2} H_{6}$

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