Write the `K_(C )` value for the equilibrium `N_(2(g))+3H_(2(g)) hArr 2NH_(3(g))` and relate it to the `K_(C )` values for the following equilibria :
`(a) (1)/(2)N_(2(g))+(3)/(2)H_(2(g)) hArr NH_(3(g))`
(b)` 2N_(2(g)) +6H_(2(g)) hArr 4NH_(3(g))`

Explanation

`N_(2)+3H_(2) hArr 2NH_(3)`
`K_(c_(1))=([NH_(3)]^(2))/([N_(2)][H_(2)]^(3))`
`(a) (1)/(2)N_(2(g))+(3)/(2)H_(2(g)) hArr NH`
`K_(c_(2))=([NH_(3)])/([N_(2)]^(1/2)[H_(2)]^(3/2))`
`K_(c_(2))=sqrt(K_(c_(1)))`
(b) `2N_(2(g))+6H_(2(g)) hArr 4NH_(3(g))`
`K_(c_(3))=([NH_(3)]^(4))/([N_(2)]^(2)[H_(2)]^(6))`
`K_(c_(3))=K_(c_(1))^(2)`