The correct option is D Ksp×Kf=x2(a−2x)2
Theory:
Complex salt :
Formed due to the combination of simple salts or molecular compounds and they retain their identity in the solution as well as the solid state.
Example - [Ag(NH3)2]Cl,[Co(NH3)4Cl2]Cl
For [Ag(NH3)2]Cl
[Ag(NH3)2]Cl(aq)⇌[Ag(NH3)2]+(aq)+Cl−(aq)
Formation of a complex ion occurs in steps
Example - Formation of [Ag(NH3)2]+ complex ion,
Ag+(aq)+NH3(aq)K1⇌[Ag(NH3)]+(aq)
Where K1 is formation constant or stability constant.
[Ag(NH3)]+(aq)+NH3(aq)K2⇌[Ag(NH3)2]+(aq)
Where K2 is formation constant or stability constant.
Adding above equations we get :
Ag+(aq)+2NH3(aq)Kform⇌[Ag(NH3)2]+(aq)
Kform=K1×K2
where, Kform is the formation constant or the stability constant for [Ag(NH3)2]+ .
Higher the value of the stability constant,more stable will be the complex.
Instability constant Kinst is numerically equal to the inverse of stability constant Kform
Kinst=1Kform
let x be the solubility of AgCl, so
AgCl(s)⇌Ag+(aq)+Cl−(aq)
x−y x
Ag+(aq)+2NH3(aq)⇌[Ag(NH3)2]+(aq)
x a 0
x−y a−2y y
Ksp=(x−y)x
Kf=y(x−y)(a−2y)2
Kf is the formation constant of [Ag(NH3)2]+
If the complex is stable, then Kf will be high (in most of cases Kf is high like in this case) .
∴x−y≈0→x≈y
Adding both the equations, we get :
AgCl(s)+2NH3(aq)⇌[Ag(NH3)2]+(aq)+Cl−(aq)
a−2x x x
Since the equations are added, the equilibrium constant gets multiplied and the new equilibrium constant for this reaction will be (Ksp×Kf):
Ksp×Kf=x2(a−2x)2