`K_p` for the reaction :
`2SO_2(g) + O_2(g) hArr 2SO_3(g)` is `2.5xx10^10`
Calculate the `K_p` values for the following reactions :
(i)`SO_2(g) + 1/2O_2(g) hArr SO_3(g)`
(ii)`SO_3(g) hArr SO_2(g) +1/2O_2(g)`
(iii) `3SO_2(g) + 3/2 O_2(g) hArr 3SO_3(g)`

Explanation

`2SO_2(g) +O_2(g) hArr 2SO_3(g) " " K_p = 2.5xx10^10`
(i)`SO_2(g) +1/2O_2(g) hArr SO_3(g)`
`K_i=(K_p)^(1//2)`
`=(2.5xx10^10)^(1//2) =1.58xx10^5`
(ii)`SO_3(g)hArr SO_2(g) +1/2O_2(g)`
`K_(ii)=1/K_i`
`=1/(1.58xx10^5)=6.3xx10^(-6)`
(iii)`3SO_2(g) +3/2O_2(g) hArr 3SO_3(g)`
`K_(iii)=(K_p)^(3//2)`
`=(2.5xx10^10)^(3//2)=3.95xx10^15`