Chemistry - Chemical Equilibrium Question with Solution | TestHub

Given, $\begin{array}{rl}& {\mathrm{N}}_2+3{\mathrm{H}}_2\rightleftharpoons 2{\mathrm{NH}}_3;{\mathrm{K}}_1\\ & {\mathrm{N}}_2+{\mathrm{O}}_2\rightleftharpoons 2\mathrm{NO};{\mathrm{K}}_2\\ & {\mathrm{H}}_2+\frac{1}{2}{\mathrm{O}}_2\rightleftharpoons {\mathrm{H}}_2\mathrm{O};{\mathrm{K}}_3\end{array}$ We have to calculate $\begin{array}{rl}& 4{\mathrm{NH}}_3+5{\mathrm{O}}_2⟶4\mathrm{NO}+6{\mathrm{H}}_2\mathrm{O};\mathrm{K}=\text{ ? }\\ & \text{ or }2{\mathrm{NH}}_3+\frac{5}{2}{\mathrm{O}}_2⟶2\mathrm{NO}+3{\mathrm{H}}_2\mathrm{O}\end{array}$ For this equation $\mathrm{K}=\frac{[\mathrm{NO}{]}^2{\left[{\mathrm{H}}_2\mathrm{O}\right]}^3}{{\left[{\mathrm{NH}}_3\right]}^2{\left[{\mathrm{O}}_2\right]}^{5/2}}$ but $\begin{array}{rl}{\mathrm{K}}_1& =\frac{{\left[{\mathrm{NH}}_3\right]}^2}{\left[{\mathrm{N}}_2\right]{\left[{\mathrm{H}}_2\right]}^3}\\ {\mathrm{K}}_2& =\frac{[\mathrm{NO}{]}^2}{\left[{\mathrm{N}}_2\right]\left[{\mathrm{O}}_2\right]}\\ {\mathrm{K}}_3& =\frac{\left[{\mathrm{H}}_2\mathrm{O}\right]}{\left[{\mathrm{H}}_2\right]{\left[{\mathrm{O}}_2\right]}^{1/2}}\\ {\mathrm{K}}_3& =\frac{[{\mathrm{H}}_2{\mathrm{O}}^3}{{\left[{\mathrm{H}}_2\right]}^3{\left[{\mathrm{O}}_2\right]}^{3/2}}\end{array}$ Now $\begin{array}{rl}& \frac{{\mathrm{K}}_2\cdot {\mathrm{K}}_3{}^3}{{\mathrm{K}}_1}=\frac{[\mathrm{NO}{]}^2}{\left[{\mathrm{N}}_2\right]\left[{\mathrm{O}}_2\right]}\times \frac{{\left[{\mathrm{H}}_2\mathrm{O}\right]}^3}{{\left[{\mathrm{H}}_2\right]}^3{\left[{\mathrm{O}}_2\right]}^{3/2}}\times \frac{\left[{\mathrm{N}}_2\right]{\left[{\mathrm{H}}_2\right]}^3}{{\left[{\mathrm{NH}}_3\right]}^2}\\ & =\frac{[\mathrm{NO}{]}^2{\left[{\mathrm{H}}_2\mathrm{O}\right]}^3}{{\left[{\mathrm{NH}}_3\right]}^2{\left[{\mathrm{O}}_2\right]}^{5/2}}=\mathrm{K}\\ & \therefore \mathrm{K}=\frac{{\mathrm{K}}_2\cdot {\mathrm{K}}_3{}^3}{{\mathrm{K}}_1}\end{array}$