Question

For the reaction, $N_2(g)+O_2(g)\rightleftharpoons 2NO(g)$
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 $=\frac{\text{ Number of moles associated }}{\text{ Number of moles taken }}$

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