${Cl}_{2} O_{7}$ gas decomposes as:
${Cl}_{2} O_{7} ⟶ {Cl}_{2} + O_{2}$
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. The degree of dissociation of ${Cl}_{2} O_{7}$ will be

see full answer

21% of IItians & 23% of AIIMS delhi doctors are from Sri Chaitanya institute !!

An Intiative by Sri Chaitanya

0.6

0.1

0.2

0.4

answer is B.

(Unlock A.I Detailed Solution for FREE)

Ready to Test Your Skills?

Check your Performance Today with our Free Mock Test used by Toppers!

Take Free Test

Detailed Solution

In the given reaction we have;

$\begin{aligned} {Cl}_{2} O_{7} (g) ⟶ {Cl}_{2} (g) + \frac{7}{2} O_{2} (g) \\ 1 - α α 7 \frac{α}{2} \end{aligned}$

$X_{O_{2}}$ coming out= 0.6

$X_{{Cl}_{2}}$ coming out = x

$X_{{Cl}_{2} O_{74}}$ coming out= 0.4-x

Now,

$\frac{0.6}{x} = \frac{\frac{7 α}{2}}{α} \sqrt{\frac{71}{32}}$

$\begin{array}{l} \Rightarrow x = 0.115 \\ \frac{0.115}{0.285} = \frac{α}{1 - α} (\sqrt{\frac{183}{71}}) \\ \Rightarrow α = 0.2 \end{array}$

Watch 3-min video & get full concept clarity