Question

At ${25}^o$C, the equilibrium constants $K_1,K_2$ and $K_3$ of three reactions are:
$N_2+3H_2\rightleftharpoons 2N{H}_3;K_1$
$N_2+O_2\rightleftharpoons 2NO;K_2$
$H_2+\frac{1}{2}{O}_2\rightleftharpoons H_{2}O;K_3$
The equilibrium constants for the oxidation of $N{H}_3$ by oxygen to given $NO$ is:

• A. $K_3^2/K_1$
• B. $K_2^2{K}_3/K_1$
• C. $K_1{K}_2/K_3$
• D. $K_2{K}_3^3/K_1$

Answer 1

The correct option is D $K_2{K}_3^3/K_1$

$K_1=\frac{{\left[N{H}_3\right]}^2}{\left[N_2\right]{\left[H_2\right]}^3}$

$K_2=\frac{{\left[NO\right]}^2}{\left[N_2\right]\left[O_2\right]}$

$K_3=\frac{\left[H_{2}O\right]}{\left[H_2\right]{\left[O_2\right]}^{\frac{1}{2}}}$

For the reaction

$N{H}_3+\frac{5}{3}{O}_2\to 2NO+H_{2}O$

$K=\frac{{\left[NO\right]}^2{\left[H_{2}O\right]}^3}{{\left[N{H}_3\right]}^2{\left[O_2\right]}^{\frac{5}{2}}}$

$=\frac{K_2{K}_3^3}{K_1}$