For the reaction
`N_(2)+3H_(2)hArr2NH_(3)`
and `(1)/(2)N_(2)+(3)/(2)H_(2)hArrNH_(3)`
write down the expression for equilibrium constants `K_(c )` and `K_(c )^(')`. How is `K_(c )` related to `K_(c )^(')`?

Explanation

For equation `N_(2)+3H_(2)hArr2NH_(3),`
`K_(c )=([NH_(3)]^(2))/([N_(2)][H_(2)]^(3))`
and for equation, `(1)/(2)N_(2)+(3)/(2)H_(2)hArrNH_(3),`
`K_(c )^(') =([NH_(3)])/([N_(2)]^(1//2)[H_(2)]^(3//2))..(ii)`
Squaring equation `(ii)`,
`(K_(c )^('))^(2)=([NH_(3)]^(2))/([N_(2)][H_(2)]^(3)) …(iii)`
Equation `(i)` and `(iii)` are same
Thus, `K_(c )=(K_(c )^('))^(2)`
or `sqrt(K_(c ))=K_(c )^(')`