The equilibrium constant of the reaction,`SO_(2)(g) + 1/2 O_(2)(g) hArr 2SO_(3)(g)` is `5 xx 10^(-2)atm`. The equilibrium constant of the reaction,`2SO_(3)(g) hArr 2SO_(2)(g) + O_(2)(g)`

Explanation

`SO_(2)+1/2 O_(2) Leftrightarrow SO_(3), K_(1)=P_(SO_(3))/(P_(SO_(2))P_(O_(2))^(1//2)) ................(i)`
`2SO_(3) Leftrightarrow 2SO_(2)+O_(2), K_(2)=P_(SO_(2))^(2) P_(O_(2))/(P_(SO_(3))^(2)) .........(ii)`
From Eqa. (i) and (ii)
`K_(2)=(1)/(K_(1)^(2)), K_(2) =(1)/((5 xx 10^(-2))^(2))=(1)/(25 xx 10^(-4))`
`=(100)/(25)=4 xx 10^(2)" atm"`