For $2S{O}_2+O_2\rightleftharpoons 2S{O}_3$ , equilibrium pressures of $S{O}_3$  & $O_2$  are 0.4 atm & 0.2 atm respectively. If the total pressure is 1 atm, $K_p$ for $2S{O}_3\rightleftharpoons 2S{O}_2+O_2$ is

$Given,P_{S{O}_3}=0.4atm{P}_{eq}=P_{S{O}_2}+P_{S{O}_3}+P_{O_2}$  $P_{O_2}=0.2atm\Rightarrow P_{S{o}_2}=1-0.6=0.4atm$  

$P_{S{O}_2}=?$

                     $2S{O}_3\rightleftharpoons 2S{O}_2+O_2$

       $K_p=\frac{{\left(0.4\right)}^2\left(0.2\right)}{{\left(0.4\right)}^2}$

              $=\frac{0.4\times 0.4\times 0.2}{0.4\times 0.4}$   

              $=0.2atm$