Question

For the reaction $N_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2NO(g,)$ the equilibrium constant is $K_1.$ The equilibrium constant is $K_2$ for the reaction $2NO\left(g\right)+O_2\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right).$
What is $K$ for the reaction $N{O}_2\left(g\right)\rightleftharpoons \frac{1}{2}{N}_2\left(g\right)+O_2\left(g\right)$?

• A. $\frac{1}{\left(K_1{K}_2\right)}$
• B. $\frac{1}{\left(2K_1{K}_2\right)}$
• C. $\frac{1}{\left(4K_1{K}_2\right)}$
• D. ${\left[\frac{1}{K_1{K}_2}\right]}^{1/2}$

Answer 1

The correct option is D ${\left[\frac{1}{K_1{K}_2}\right]}^{1/2}$

$N_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2NO\left(g\right);K_1$
$2NO\left(g\right)+O_2\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right);K_2$
$------------------$
$N_2\left(g\right)+2O_2\left(g\right)\rightleftharpoons 2N{O}_2\left(g\right);K_3=K_1\times K_2$
$\therefore \text{For}N{O}_2\left(g\right)\rightleftharpoons \frac{1}{2}{N}_2\left(g\right)+O_2\left(g\right);$
$K=\frac{1}{(K_3{)}^{1/2}}=\frac{1}{(K_1\times K_2{)}^{1/2}}$