Chemistry - Chemical Equilibrium Question with Solution | TestHub

${\mathrm{N}}_2+3{\mathrm{H}}_2\rightleftharpoons 2\mathrm{N}{\mathrm{H}}_3;{\mathrm{K}}_1$
${\mathrm{K}}_1=\frac{[\mathrm{N}{\mathrm{H}}_3{]}^2}{\left[{\mathrm{N}}_2\right][{\mathrm{H}}_2{]}^3}$
${\mathrm{N}}_2+{\mathrm{O}}_2\rightleftharpoons 2\mathrm{N}\mathrm{O};{\mathrm{K}}_2$
${\mathrm{H}}_2+\frac{1}{2}{\mathrm{O}}_2\rightleftharpoons {\mathrm{H}}_2\mathrm{O};{\mathrm{K}}_3$
${\mathrm{K}}_2=\frac{[\mathrm{N}\mathrm{O}{]}^2}{\left[{\mathrm{N}}_2\right]\left[{\mathrm{O}}_2\right]};{\mathrm{K}}_3=\frac{\left[{\mathrm{H}}_2\mathrm{O}\right]}{\left[{\mathrm{H}}_2\right][{\mathrm{O}}_2{]}^{1/2}}$
Now, oxidation of$\mathrm{N}{\mathrm{H}}_3$takes places as below
$4\mathrm{N}{\mathrm{H}}_3+5{\mathrm{O}}_2\rightleftharpoons 4\mathrm{N}\mathrm{O}+6{\mathrm{H}}_2\mathrm{O}$
or$2\mathrm{N}{\mathrm{H}}_3+\frac{5}{2}{\mathrm{O}}_2\rightleftharpoons 2\mathrm{N}\mathrm{O}+3{\mathrm{H}}_2\mathrm{O}$
$\mathrm{K}=\frac{\left[\mathrm{N}\mathrm{O}{]}^2\right[{\mathrm{H}}_2\mathrm{O}{]}^3}{\left[\mathrm{N}{\mathrm{H}}_3{]}^2\right[{\mathrm{O}}_2{]}^{5/2}}$
$\mathrm{K}=\frac{[\mathrm{N}\mathrm{O}{]}^2}{\left[{\mathrm{N}}_2\right]\left[{\mathrm{O}}_2\right]}.\frac{\left[{\mathrm{N}}_2\right]\left[{\mathrm{O}}_2\right]}{[\mathrm{N}{\mathrm{H}}_3{]}^2}.\frac{\left[{\mathrm{N}}_2\right][{\mathrm{H}}_2{]}^3}{\left[{\mathrm{N}}_2\right][{\mathrm{H}}_2{]}^3}.\frac{[{\mathrm{H}}_2\mathrm{O}{]}^3}{\left[{\mathrm{H}}_2{]}^3\right[{\mathrm{O}}_2{]}^{3/2}}.\frac{\left[{\mathrm{H}}_2{]}^3\right[{\mathrm{O}}_2{]}^{3/2}}{[{\mathrm{O}}_2{]}^{5/2}}$
$=\left\{\frac{[\mathrm{N}\mathrm{O}{]}^2}{\left[{\mathrm{N}}_2\right]\left[{\mathrm{O}}_2\right]}\right\}\left\{\frac{\left[{\mathrm{N}}_2\right][{\mathrm{H}}_2{]}^3}{[\mathrm{N}{\mathrm{H}}_3{]}^2}\right\}.\left\{\frac{[{\mathrm{H}}_2\mathrm{O}{]}^3}{\left[{\mathrm{H}}_2{]}^3\right[{\mathrm{O}}_2{]}^{3/2}}\right\}$
$={\mathrm{K}}_2.\frac{1}{{\mathrm{K}}_1}.{\mathrm{K}}_3^3=\frac{{\mathrm{K}}_3^3{\mathrm{K}}_2}{{\mathrm{K}}_1}$