MCQ
For the reaction ,${N_2} + {O_2} \rightleftharpoons 2NO$  equilibrium constant $K_c = 2.$ Degree of dissociation of $N_2$ and $O_2$ are  (Both have same initial moles)
  • A
    $\frac{1}{{1 + \sqrt 2 }},\frac{1}{{1 - \sqrt 2 }}$
  • B
    $\frac{1}{{1 - \sqrt 2 }},\frac{1}{{1 + \sqrt 2 }}$
  • Both are $\frac{1}{{1 + \sqrt 2 }}$
  • D
    Both are $\frac{1}{{1 - \sqrt 2 }}$

Answer

Correct option: C.
Both are $\frac{1}{{1 + \sqrt 2 }}$
c
$\mathop {\mathop {{N_2}}\limits_1 }\limits_{1 - \alpha }  + \mathop {\mathop {{O_2}}\limits_1 }\limits_{1 - \alpha }  \leftrightarrow \mathop {\mathop {2NO}\limits_0 }\limits_{2\alpha } $

$K=\frac{(2 \alpha)^{2}}{(1-\alpha)^{2}}$

$\sqrt{\mathrm{K}}=\frac{2 \alpha}{1-\alpha}$

$\alpha=\frac{\sqrt{\mathrm{K}}}{2+\sqrt{\mathrm{K}}}=\frac{\sqrt{2}}{2+\sqrt{2}}=\frac{1}{1+\sqrt{2}}$

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