Chemistry - Chemical Equilibrium Question with Solution | TestHub

$$\begin{array}{l}{\mathrm{N}}_2+2{\mathrm{O}}_2\rightleftharpoons 2{\mathrm{NO}}_2\\ K_1=\frac{{\left[{\mathrm{NO}}_2\right]}^2}{\left[{\mathrm{N}}_2\right]{\left[{\mathrm{O}}_2\right]}^2}\\ \text{ or }100=\frac{{\left[{\mathrm{NO}}_2\right]}^2}{\left[{\mathrm{N}}_2\right]{\left[{\mathrm{O}}_2\right]}^2}...(i)\end{array}$$ $$\begin{array}{l}\text{ Again, }\left[{\mathrm{NO}}_2\right]\rightleftharpoons \frac{1}{2}{\mathrm{N}}_2+{\mathrm{O}}_2\\ K_2=\frac{{\left[{\mathrm{N}}_2\right]}^{1/2}\left[{\mathrm{O}}_2\right]}{\left[{\mathrm{NO}}_2\right]}\\ \text{ or }{K}_2^2=\frac{\left[{\mathrm{N}}_2\right]{\left[{\mathrm{O}}_2\right]}^2}{{\left[{\mathrm{NO}}_2\right]}^2}...(ii)\end{array}$$ Eqs. (i) $\times ($ ii $)$, we get $100\times K_2^2=1$ $$\Rightarrow K_2^2=\frac{1}{100}\text{ or }{K}_2=\frac{1}{10}=0.1$$