consider the following gaseous equilibrium with equilibrium constant `K_(1)` and `K_(2)` respectively
`SO_(2)(g)+ 1//2O_(2)hArrSO_(3)(g)`
`2SO_(3)(g)hArr2SO_(2)(g)+O_(2)(g)`
The equilibrium constants are related as

Options

A. `K_(1)^(2)=(1)/(K_(2))`
B. `2K_(1)=K_(2)^(2)`
C. `K_(2)=(2)/(K_(1)^(2))`
D. `K_(2)^(2)=(1)/(K)`

Answer

A

Explanation

`SO_(2)(g)+1//2O_(2)(g) hArr SO_(3)(g)`
`K_(1)=([SO_(3)])/([SO_(3)][O_(2)]^(1//2))`
`2SO_(3)(g) hArr 2SO_(2)(g) +O_(2)(g)`
`K_(2)=([SO_(2)]^(2)[O_(2)])/([SO_(3)]^(2))`
`K_(2)=(1)/((K_(1))^(2))` or `(K_(1))^(2)=(1)/(K_(2))`