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JEE Advanced levelSingle correct optionDifficulty 3 of 3ig203

A mixture of $H X_{2}$ (2) and $He$ (4) in the mole ratio $2 : 1$ effuses through a pinhole. The mole fraction of $H X_{2}$ in the gas that effuses out initially is

A $\frac{2 2}{2 2 + 1}$
B $\frac{2}{3}$
C $\frac{2}{2 + 1}$
D $\frac{1}{3}$

Answer: A

Effused amounts

\propto x_{i} / M_{i}

:

H X_{2}

\propto \frac{2/3}{2}

,

He

\propto \frac{1/3}{2}

. Ratio

H X_{2} : He = \frac{2}{2} : \frac{1}{2} = 2 : \frac{1}{2} = 22 : 1

. Mole fraction

= \frac{2 2}{2 2 + 1}

.

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