The following equilibrium constant are given: … The equilibrium constant for the oxidation of\mathrm{NH}3by oxygen to give\mathrm{NO} is:

Given, $$\begin{aligned} & \mathrm{N}_2+3 \mathrm{H}_2 \rightleftharpoons 2 \mathrm{NH}_3 ; \mathrm{K}_1 \\ & \mathrm{~N}_2+\mathrm{O}_2 \rightleftharpoons 2 \mathrm{NO} ; \mathrm{K}_2 \\ & \mathrm{H}_2+\frac{1}{2} \mathrm{O}_2 \rightleftharpoons \mathrm{H}_2 \mathrm{O} ; \mathrm{K}_3 \end{aligned}$$​N2​+3H2​⇌2NH3​;K1​ N2​+O2​⇌2NO;K2​H2​+21​O2​⇌H2​O;K3​​ We have to calculate $$\begin{aligned} & 4 \mathrm{NH}_3+5 \mathrm{O}_2 \longrightarrow 4 \mathrm{NO}+6 \mathrm{H}_2 \mathrm{O} ; \mathrm{K}=\text { ? } \\ & \text { or } 2 \mathrm{NH}_3+\frac{5}{2} \mathrm{O}_2 \longrightarrow 2 \mathrm{NO}+3 \mathrm{H}_2 \mathrm{O} \end{aligned}$$​4NH3​+5O2​⟶4NO+6H2​O;K= ?  or 2NH3​+25​O2​⟶2NO+3H2​O​ For this equation $\mathrm{K}=\frac{[\mathrm{NO}]^2\left[\mathrm{H}_2 \mathrm{O}\right]^3}{\left[\mathrm{NH}_3\right]^2\left[\mathrm{O}_2\right]^{5 / 2}}$K=[NH3​]2[O2​]5/2[NO]2[H2​O]3​ but $$\begin{aligned} \mathrm{K}_1 & =\frac{\left[\mathrm{NH}_3\right]^2}{\left[\mathrm{~N}_2\right]\left[\mathrm{H}_2\right]^3} \\ \mathrm{~K}_2 & =\frac{[\mathrm{NO}]^2}{\left[\mathrm{~N}_2\right]\left[\mathrm{O}_2\right]} \\ \mathrm{K}_3 & =\frac{\left[\mathrm{H}_2 \mathrm{O}\right]}{\left[\mathrm{H}_2\right]\left[\mathrm{O}_2\right]^{1 / 2}} \\ \mathrm{~K}_3 & =\frac{\left[\mathrm{H}_2 \mathrm{O}^3\right.}{\left[\mathrm{H}_2\right]^3\left[\mathrm{O}_2\right]^{3 / 2}} \end{aligned}$$K1​ K2​K3​ K3​​=[ N2​][H2​]3[NH3​]2​=[ N2​][O2​][NO]2​=[H2​][O2​]1/2[H2​O]​=[H2​]3[O2​]3/2[H2​O3​​ Now $$\begin{aligned} & \frac{\mathrm{K}_2 \cdot \mathrm{K}_3{ }^3}{\mathrm{~K}_1} =\frac{[\mathrm{NO}]^2}{\left[\mathrm{~N}_2\right]\left[\mathrm{O}_2\right]} \times \frac{\left[\mathrm{H}_2 \mathrm{O}\right]^3}{\left[\mathrm{H}_2\right]^3\left[\mathrm{O}_2\right]^{3 / 2}} \times \frac{\left[\mathrm{N}_2\right]\left[\mathrm{H}_2\right]^3}{\left[\mathrm{NH}_3\right]^2} \\ & =\frac{[\mathrm{NO}]^2\left[\mathrm{H}_2 \mathrm{O}\right]^3}{\left[\mathrm{NH}_3\right]^2\left[\mathrm{O}_2\right]^{5 / 2}}=\mathrm{K} \\ & \therefore \mathrm{K}=\frac{\mathrm{K}_2 \cdot \mathrm{K}_3{ }^3}{\mathrm{~K}_1} \end{aligned}$$​ K1​K2​⋅K3​3​=[ N2​][O2​][NO]2​×[H2​]3[O2​]3/2[H2​O]3​×[NH3​]2[N2​][H2​]3​=[NH3​]2[O2​]5/2[NO]2[H2​O]3​=K∴K= K1​K2​⋅K3​3​​