Chemistry - Chemical Equilibrium Question with Solution | TestHub

${\text{N}}_2+3{\text{H}}_{\text{2}}\rightleftharpoons {\text{2NH}}_{\text{3}}$

${\text{K}}_1=\frac{{\left[{\text{NH}}_3\right]}^2}{\left[{\text{N}}_2\right]{\left[{\text{H}}_2\right]}^3}\dots \left(\text{i}\right)$

${\text{N}}_{\text{2}}{\text{+O}}_{\text{2}}\rightleftharpoons 2\text{NO}\text{;}{\text{K}}_{\text{2}}=\frac{{\left[\text{NO}\right]}^2}{\left[{\text{N}}_2\right]\left[{\text{O}}_2\right]}\dots \left(\text{ii}\right)$

${\text{H}}_2+1/2{\text{O}}_2\rightleftharpoons {\text{H}}_2\text{O}\text{;}{\text{K}}_{\text{3}}=\frac{\left[{\text{H}}_2\text{O}\right]}{\left[{\text{H}}_2\right]{\left[{\text{O}}_2\right]}^{1/2}}\dots \left(\text{iii}\right)$

For the reaction,$2{\text{NH}}_3+\frac{5}{2}{\text{O}}_2\rightleftharpoons 2\text{NO}+3{\text{H}}_2\text{O}$

$\text{K}=\frac{{\left[\text{NO}\right]}^2{\left[{\text{H}}_2\text{O}\right]}^3}{{\left[{\text{NH}}_3\right]}^2{\left[{\text{O}}_2\right]}^{5/2}}$

$=\frac{{\left[\text{NO}\right]}^2}{\left[{\text{N}}_2\right]\left[{\text{O}}_2\right]}\times \frac{{\left[{\text{H}}_2\text{O}\right]}^3}{{\left[{\text{H}}_2\right]}^3{\left[{\text{O}}_2\right]}^{3/2}}\times \frac{\left[{\text{N}}_2\right]{\left[{\text{H}}_2\right]}^3}{{\left[{\text{NH}}_3\right]}^2}$

$=\frac{{\text{K}}_{\text{2}}\times {\text{K}}_{\text{3}}^{\text{3}}}{{\text{K}}_{\text{1}}}$