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Properties of Modulus

For the react...

Question

For the reaction, $N_{2} (g) + O_{2} (g) ⇌ 2 NO (g)$ , equilibrium constant is $K_{c} = 2$ .
Degree of association is:

\frac{1}{1 - \sqrt{2}}

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\frac{1}{1 + \sqrt{2}}

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\frac{2}{1 + \sqrt{2}}

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\frac{2}{1 - \sqrt{2}}

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Solution

The correct option is B $\frac{1}{1 + \sqrt{2}}$
$\begin{matrix} Given, N_{2} (g) + 0_{2} (g) = [k_{c} = 2] t = 01 t=teq (1 - a) (1 - a) 2 a \end{matrix}$

$\begin{matrix} Thus, \frac{(2 a)^{2}}{(1 - a)^{2}} = 2 \Rightarrow \frac{2 a}{1 - a} = \sqrt{2} \Rightarrow 2 a = \sqrt{2} - \sqrt{2} a ∴ a = \frac{1}{1 + \sqrt{2}} so, option (B) is correct. \end{matrix}$

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