Question

Given:
$N_2\left(g\right)+3H_2\left(g\right)\rightleftharpoons 2N{H}_3\left(g\right);K_1$
$N_2\left(g\right)+O_2\left(g\right)\rightleftharpoons 2NO\left(g\right),K_2$
$H_2\left(g\right)+\frac{1}{2}{O}_2\left(g\right)\rightleftharpoons H_{2}O\left(g\right);K_3$
The equilibrium constant for,
$2N{H}_3\left(g\right)+\frac{5}{2}{O}_2\left(g\right)\rightleftharpoons 2NO\left(g\right)+3H_{2}O\left(g\right)$
will be:

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

Answer 1

The correct option is D

$\frac{K_2{K}_3^3}{K_1}$
$K_1=\frac{[N{H}_3{]}^2}{\left[N_2\right][H_2{]}^3};K_2=\frac{[NO{]}^2}{\left[N_2\right]\left[O_2\right]};K_3=\frac{\left[H_{2}O\right]}{\left[H_2\right][O_2{]}^{1/2};}$
The equilibrium constant for
$2N{H}_3\left(g\right)+\frac{5}{2}{O}_2\left(g\right)\rightleftharpoons 2NO\left(g\right)+3H_{2}O\left(g\right)$
will be: $\frac{\left[NO{]}^2\right[H_{2}O{]}^3}{\left[N{H}_3{]}^2\right[O_2{]}^{5/2}}=\frac{K_2\times K_3^3}{K_1}$