Three vessels of equal volume contain gases at the same temperatu… - Vidyadip

MCQ

Three vessels of equal volume contain gases at the same temperature and pressure. The first vessel contains neon (monoatomic), the second contains chlorine (diatomic) and third contains uranium hexafloride (polyatomic). Arrange these on the basis of their root mean square speed $\left(v_{ ms }\right)$ and choose the correct answer from the options given below:

A
$v _{ rms }($ mono $)= v _{ rms }($ dia $)= v _{rms}($ poly $)$
✓
$v _{rms}($ mono $) > v _{rms}($ dia $) > v _{rms}$ (poly)
C
$v _{rms}($ dia $) < v _{rms}($ poly $) < v _{rms}($ mono $)$
D
$v _{ rms }( mono ) < v _{rms}( dia ) < v _{ rms }$ (poly $)$

✓

Answer

Correct option: B.

$v _{rms}($ mono $) > v _{rms}($ dia $) > v _{rms}$ (poly)

b
$v _{ rms }(\text { mono })=\sqrt{\frac{3 RT }{4 \times 10^{-3}}}$

$v _{ rms }(\text { dia })=\sqrt{\frac{3 RT }{71 \times 10^{-3}}}$

$v _{ rms }( ply )=\sqrt{\frac{3 RT }{146 \times 10^{-3}}}$

So correct relation is

$v _{ rms }(\text { mono }) > v _{ rms }(\text { dia }) > v _{ rms }(\text { poly })$

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