Question

For the reaction, $N_2+O_2\rightleftharpoons 2NO$ equilibrium constant $K_c=2$. Degrees of dissociation of $N_2$ and $O_2$ are:

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

Answer 1

The correct option is C Both are $\frac{1}{1+\sqrt{2}}$

Let V L be the total volume.
Let 1 mole of $N_2$ and 1 mole of $O_2$ are present initially.
Let x mole of $N_2$ and x mole of $O_2$ combine to form 2x moles of NO.
$1-x$ mole of $N_2$ and $1-x$ mole of $O_2$ will remain at equilibrium.
The equilibrium constant
$K_c=\frac{[NO{]}^2}{\left[N_2\right]\left[O_2\right]}$
$2=\frac{(2x/V{)}^2}{(1-x)/V\times (1-x)/V}$
$\sqrt{2}=\frac{(2x}{(1-x)/}$
$1-x=\sqrt{2}x$
$1=x(1+\sqrt{2})$
$x=\frac{1}{1+\sqrt{2}}$
The degree of dissociation of $N_2=x=\frac{1}{1+\sqrt{2}}$
The degree of dissociation of $O_2=x=\frac{1}{1+\sqrt{2}}$