The equilibrium constant for the reaction $ SO_{3(g)} \rightleftharpoons SO_{2(g)} + 1/2 O_{2(g)} Kc = 4.9 \times 10 ^ {-2} $ The value for the $K_C$ of the reaction $2SO_{2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)} $ will be
Equilibrium constant for the reaction $ SO_{ 2 (g) } + { 1 \over 2 } O_{ 2 (g) } \rightleftharpoons SO_{3(g)} $ and for reaction $ 2 SO_{ 2(g)} + O_{2(g)} \rightleftharpoons 2SO_{3(g)} $ $ K_C = ( { 1 \over 4.9 \times 10 ^ {-2} } ) ^ 2 = 416 .49 $