States of Matter - Result Question 22
22.
The rms velocity of hydrogen is $\sqrt{7}$ times the rms velocity of nitrogen. If $T$ is the temperature of the gas
(2000, 1M)
(a) $T\left(H _2\right)=T\left(N _2\right)$
(b) $T\left(H _2\right)>T\left(N _2\right)$
(c) $T \left(H _ 2\right) < T\left(N _2\right)$
(d) $ T \left ( H _ 2 \right ) = \sqrt {7} T \left ( N _ 2 \right ) $
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Answer:
Correct Answer: 22. (c)
Solution:
Root mean square speed $u _{rms}=\sqrt{\frac{3 R T}{M}}$
$ \Rightarrow \quad \frac{u _{rms}\left(H _2\right)}{u _{rms}\left(N _2\right)}=\sqrt{7}=\sqrt{\frac{T\left(H _2\right)}{2} \times \frac{28}{T\left(N _2\right)}} $
$7 =\frac{14 T(\mathrm{H}_2)}{T(\mathrm{~N}_2)} $
$T( \mathrm {N} _ 2) = 2 T ( \mathrm {H} _ 2) \text { i.e. } T(\mathrm {H} _ 2) < T(\mathrm {N} _ 2)$
BETA
