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 equlibrium constant for the given reaction will be:
$2N{H}_2\left(g\right)+\frac{5}{2}{O}_2\left(g\right)\rightleftharpoons 2NO\left(g\right)+3H_{2}O\left(g\right)$

• A. $K_1{K}_2{K}_3$
• B. $\frac{K_1{K}_2}{K_3}$
• C. $\frac{K_1{K}_2^2}{K_3}$
• D. $\frac{K_2{K}_1^2}{K_3}$

Answer 1

The correct option is A $K_1{K}_2{K}_3$

$N_2+{3H}_2\rightleftharpoons {2NH}_3{K}_1\to \left(1\right)$

$N_2+O_2\rightleftharpoons 2NO{K}_2\to \left(2\right)$

$H_2+1/2O_2\rightleftharpoons H_{2}O{K}_3\to \left(3\right)$

$2{NH}_3+5/2O_2\rightleftharpoons 2NO+3H_{2}O\to \left(4\right)$

Reaction $\left(4\right)=$ Inverse of reaction $\left(1\right)$ $+$ reaction $\left(2\right)$ $+$ $3$ $\times$ reaction $\left(3\right)$

$K=K_1^{-1}\times K_2\times K_3^3$

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