$NO_{(g)} + \frac{1}{2}{O_2} \rightleftharpoons N{O_2}_{(g)}$
$2N{O_2}_{(g)} \rightleftharpoons 2NO_{(g)} + {O_2}_{(g)}$
\( \Rightarrow \) \(\frac{{{{[N{O_2}]}^2}}}{{{{[NO]}^2}[{O_2}]}} = \frac{1}{{{K_2}}}\)
\( \Rightarrow \) \(\frac{{[N{O_2}]}}{{[NO]\;{{[{O_2}]}^{1/2}}}} = \frac{1}{{\sqrt {{K_2}} }}\)
\( \Rightarrow \) \({K_1} = \frac{1}{{\sqrt {{K_2}} }}\); \({K_2} = \frac{1}{{K_1^2}}\)
$(a) N_2O_4 $ $\rightleftharpoons$ $ 2NO_2$
$(b) 2SO_2 + O_2 $ $\rightleftharpoons$ $ 2SO_3$
$(c) X + Y $ $\rightleftharpoons$ $ 4Z$
$(d) A + 3B $ $\rightleftharpoons$ $ 7C$