For `N_(2)(g)+3H_(2)(g)hArr2NH_(3)(g)`, show that `K_(c)=K_(p)(RT)^(2)`.

Explanation

For `N_(2)(g)+3H_(2)(g)hArr2NH_(3)(g)`
But PV = nRT, `P=(n/v)RT`, i.e., P = Concentration `xx` RT
`P_(NH_(3))=[NH_(3)]RT," "p_(n_(2))=[N_(2)]RT," "p_(H_(2))=[H_(2)]RT," "K_(p)=(p_(NH_(3))^(2))/(p_(N_(2))*p_(H_(2))^(3))`
`thereforeK_(p)=({[NH_(3)]RT}^(2))/({[N_(2)]RT}{[H_(2)]RT}^(3))=([NH_(3)]^(2))/([N_(2)][H_(2)]^(3))xx((RT)^(2))/((RT)(RT)^(3))`
`K_(p)=K_(c)*(RT)^(-2)" "thereforeK_(c)=K_(p)(RT)^(2)`.