Chemistry - Chemical Equilibrium Question with Solution | TestHub

Given,
${\mathrm{N}}_2\left(\mathrm{g}\right)3{\mathrm{H}}_2\left(\mathrm{g}\right)\rightleftharpoons 2{\mathrm{NH}}_3\left(\mathrm{g}\right),{\mathrm{K}}_1=4\times {10}^5 \dots \left(1\right)$

${\mathrm{N}}_2\left(\mathrm{g}\right)+{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{NO}\left(\mathrm{g}\right),{\mathrm{K}}_2=1.6\times {10}^{12} \dots \left(2\right)$

${\mathrm{H}}_2\left(\mathrm{g}\right)+\frac{1}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons {\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right),{\mathrm{K}}_3=1.0\times {10}^{-13} \dots \left(3\right)$
Using properties of equilibrium constant:

$\left(2\right)+3\times \left(3\right)-\left(1\right)$

$2{\mathrm{NH}}_3\left(\mathrm{g}\right)+\frac{5}{2}{\mathrm{O}}_2\left(\mathrm{g}\right)\rightleftharpoons 2\mathrm{NO}\left(\mathrm{g}\right)+3{\mathrm{H}}_2\mathrm{O}\left(\mathrm{g}\right)$

${\mathrm{K}}_{\mathrm{eq}}=\frac{{\mathrm{K}}_2\times {\mathrm{K}}_3^3}{{\mathrm{K}}_1}=\frac{1.6\times {10}^{12}\times {\left({10}^{-13}\right)}^3}{4\times {10}^5}$

$=\frac{1.6}{4}\times {10}^{-32}=4\times {10}^{-33}$