The equilibrium constant of the following equilibria `SO_(2)(g)+(1)/(2)O_(2)(g)hArr SO_(3)(g)`
`2SO_(3)(g)hArr 2SO_(2)(g)+O_(2)(g)` are given by `K_(1) and K_(2)` respectively. Find the relation between `K_(1) and K_(2)`.

Explanation

`K_(1)=([SO_(3)])/([SO_(2)]^(2)[O_(2)]) and K_(2)=([SO_(2)]^(2)[O_(2)])/([SO_(3)]^(2))`
`therefore K_(1)^(2)=([SO_(3)]^(2))/([SO_(2)]^(2)[O_(2)])=(1)/(K_(2)) or, K_(1)=(1)/(sqrt(K_(2)))`.