Question

For the reaction, $N _{2}( g )+ O _{2}( g ) \rightleftharpoons 2 NO ( g )$
Equilibrium constant $K _{ c }=2$
Degree of association is

• A. $\frac{1}{1-\sqrt{2}}$
• B. $\frac{1}{1+\sqrt{2}}$
• C. $\frac{2}{1+\sqrt{2}}$
• D. $\frac{2}{1-\sqrt{2}}$

Answer 1

Answer: (B)

Degree of association $=\frac{\text { Number of moles associated }}{\text { Number of moles taken }}$

$\therefore K_{c}=\frac{(2 x)^{2}}{(1-x)^{2}}=2$
or, $\frac{2 x}{1-x}=\sqrt{2}$
or, $2 x =\sqrt{2}-\sqrt{2} x$
or, $x (2+\sqrt{2})=\sqrt{2}$
$\Rightarrow x =\frac{\sqrt{2}}{2+\sqrt{2}}=\frac{1}{1+\sqrt{2}}$