$C l_{2} O_{7}$ gas decomposes as
$C l_{2} O_{7} \overset{}{\to} C l_{2} + O_{2}$
A partially decomposed gaseous mixture is allowed to effuse through a pin-hole and the gas coming out initially was analyzed. The mole fraction of the $O_{2}$ was found to be 0.60. If the degree of dissociation of $C l_{2} O_{7}$ is $α$ , the value of $10 α$ is
[Atomic weights: $O = 16, C l = 35.5$ ]

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Detailed Solution

$\underset{1 - α}{C l_{2} O_{7}} \overset{}{\to} \underset{α}{C l_{2}} + \underset{3.5 α}{3.5 O_{2}}$ Now, let x be the mole fraction of $C l_{2}$ in the gaseous mixture being analyzed

$\Rightarrow \frac{r_{O_{2}}}{r_{C l_{2}}} = 3.5 \sqrt{\frac{71}{32}} = \frac{0.6}{x} \Rightarrow x = 0.115$ $\Rightarrow M o l e f r a c t i o n o f C l_{2} O_{7} = 0.285$