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Match column I(gaseous composition) with column II(ratio)
column I column II(ratio)
A Mixture containing equal masses of H₂ and CH₄ in a vessel of "V" lits at T K I Average K.E = 1:1
B 8 gms of O₂ at 600K and 8 gms of SO₂ at 300K II
RMS velocity
= 1: $\sqrt{2}$
C Mixture containing 4 gms of He and 44 gms of CO₂ at 400K III partial pressure = 8:1
D NO gas at 400K and C₂H₆ at 800K IV K.E = 4:1
V Average velocity = 1:2

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A	B	C	D
III	IV	I	V

A	B	C	D
I	IV	III	II

A	B	C	D
III	IV	I	II

A	B	C	D
III	I	IV	II

answer is C.

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Detailed Solution

$P_{H_{2}} : P_{{CH}_{4}} = n_{H_{2}} : n_{{CH}_{4}} = 8 : 1$

$\frac{{(KE)}_{O_{2}}}{{(KE)}_{{SO}_{2}}} = \frac{T_{O_{2}}}{M_{O_{2}}} \times \frac{M_{S O_{2}}}{M_{O_{2}}} = \frac{600}{32} \times \frac{64}{300} = 4 : 1$

Average kinetic energy remains same at same temperature 1:1

$\frac{{RMS}_{(NO)}}{{RMS}_{(C_{2} H_{6})}} = \sqrt{\frac{T_{N O}}{T_{C_{2} H_{6}}}} = \sqrt{\frac{400}{800}} = 1 : \sqrt{2}$

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