(i) $NO (g)+\frac{1}{2} O _{2}(g) \xrightleftharpoons{K_{1}} NO _{2}(g)$
So $K_{1}=\frac{\left[ NO _{2}\right]}{[ NO ]\left[ O _{2}\right]^{\frac{1}{2}}}\,\,\,...(i)$
(ii) $2 NO _{2}(g) \xrightleftharpoons{ R _{2}} 2 NO + O _{2}(g)$
So $K_{3}=\frac{[ NO ]^{2}\left[ O _{2}\right]}{\left[ NO _{2}\right]^{2}}\,\,\,\,...(ii)$
From Eq. (i)
$K_{1}^{2}=\frac{\left[ NO _{2}\right]^{2}}{[ NO ]^{2}\left[ O _{2}\right]} $
or $\frac{1}{K_{1}^{2}}=\frac{[ NO ]^{2}\left[ O _{2}\right]}{\left[ NO _{2}\right]^{2}}\,\,\,\,...(iii)$
From Eqs. (ii) and (iii)
$K_{2}=\frac{1}{K_{1}^{2}}$
