`color{green}("Definition" )` : The stability of a complex in solution refers to the degree of association between the two species involved in the state of equilibrium.
● The magnitude of the (stability or formation) equilibrium constant for the association, quantitatively expresses the stability.
● Thus, if we have a reaction of the type :
`color{red}(M +4L ⇆ ML_4)`
● Then the larger the stability constant, the higher the proportion of `color{red}(ML_4)` that exists in solution.
`=>` Free metal ions rarely exist in the solution so that `color{red}(M)` will usually be surrounded by solvent molecules which will compete with the ligand molecules, `color{red}(L)`, and be successively replaced by them. For simplicity, we generally ignore these solvent molecules and write four stability constants as follows :
`color{red}(tt (( M , + , L , ⇆ , ML , K_1 = [ML]//[M][L] ) , ( ML , + , L , ⇆ , ML_2 , K_2 = [ML_2]//[ML][L] ) , ( ML_2, +, L, ⇆, ML_3 ,K_3 = [ML_3]//[ML_2][L] ), ( ML_3 , + , L ,⇆ , ML_4 ,K_4 = [ML_4]//[ML_3][L]) ))`
where `color{red}(K_1)`, `color{red}(K_2)`, etc., are referred to as `color{green}("stepwise stability constants")`. Alternatively, we can write the `color{green}("overall stability constant")` thus :
` color{red}(M + 4L \ \ \ ML_4 \ \ \ \ \ \ \ β_4 = [ML_4]//[M][L]^4)`
`=>` The stepwise and overall stability constant are therefore related as follows :
`color{red}(β_4 = K_1 xx K_2 xx K_3 xx K_4)` or more generally,
`color{red}(β_n = K_1 xx K_2 xx K_3 xx K_4.............k_n)`
`=>` If we take as an example, the steps involved in the formation of the cuprammonium ion, we have the following :
`color{red}(Cu^(2+) + NH_3 \ \ \ Cu(NH_3)^(2+) \ \ \ K_1 = [Cu (NH_3)^(2+)]//[Cu^(2+) ] [NH_3])`
`color{red}(Cu (NH_3)^(2+) + NH_3 ⇆ Cu(NH_3)_(2)^(2+) \ \ \ K_2 = [Cu ( NH_3)_(2)^(2+) ]//[Cu (NH_3)^(2+)] [NH_3])` etc.
● where `color{red}(K_1)`, `color{red}(K_2)` are the stepwise stability constants and overall stability constant.
● Also `color{red}(β_4 = [Cu (NH_3)_(4)^(2+)]//[Cu^(2+)] [NH_3 ]^4)`
`=>` The addition of the four amine groups to copper shows a pattern found for most formation constants, in that the successive stability constants decrease. In this case, the four constants are :
`color{red}(logK_1 = 4.0, logK_2 = 3.2, logK_3 = 2.7, logK_4 = 2.0)` or `color{red}(log β_4 = 11.9)`
`color{green}("Instability Constant ")` : The instability constant or the dissociation constant of coordination compounds is defined as the reciprocal of the formation constant.
`color{green}("Definition" )` : The stability of a complex in solution refers to the degree of association between the two species involved in the state of equilibrium.
● The magnitude of the (stability or formation) equilibrium constant for the association, quantitatively expresses the stability.
● Thus, if we have a reaction of the type :
`color{red}(M +4L ⇆ ML_4)`
● Then the larger the stability constant, the higher the proportion of `color{red}(ML_4)` that exists in solution.
`=>` Free metal ions rarely exist in the solution so that `color{red}(M)` will usually be surrounded by solvent molecules which will compete with the ligand molecules, `color{red}(L)`, and be successively replaced by them. For simplicity, we generally ignore these solvent molecules and write four stability constants as follows :
`color{red}(tt (( M , + , L , ⇆ , ML , K_1 = [ML]//[M][L] ) , ( ML , + , L , ⇆ , ML_2 , K_2 = [ML_2]//[ML][L] ) , ( ML_2, +, L, ⇆, ML_3 ,K_3 = [ML_3]//[ML_2][L] ), ( ML_3 , + , L ,⇆ , ML_4 ,K_4 = [ML_4]//[ML_3][L]) ))`
where `color{red}(K_1)`, `color{red}(K_2)`, etc., are referred to as `color{green}("stepwise stability constants")`. Alternatively, we can write the `color{green}("overall stability constant")` thus :
` color{red}(M + 4L \ \ \ ML_4 \ \ \ \ \ \ \ β_4 = [ML_4]//[M][L]^4)`
`=>` The stepwise and overall stability constant are therefore related as follows :
`color{red}(β_4 = K_1 xx K_2 xx K_3 xx K_4)` or more generally,
`color{red}(β_n = K_1 xx K_2 xx K_3 xx K_4.............k_n)`
`=>` If we take as an example, the steps involved in the formation of the cuprammonium ion, we have the following :
`color{red}(Cu^(2+) + NH_3 \ \ \ Cu(NH_3)^(2+) \ \ \ K_1 = [Cu (NH_3)^(2+)]//[Cu^(2+) ] [NH_3])`
`color{red}(Cu (NH_3)^(2+) + NH_3 ⇆ Cu(NH_3)_(2)^(2+) \ \ \ K_2 = [Cu ( NH_3)_(2)^(2+) ]//[Cu (NH_3)^(2+)] [NH_3])` etc.
● where `color{red}(K_1)`, `color{red}(K_2)` are the stepwise stability constants and overall stability constant.
● Also `color{red}(β_4 = [Cu (NH_3)_(4)^(2+)]//[Cu^(2+)] [NH_3 ]^4)`
`=>` The addition of the four amine groups to copper shows a pattern found for most formation constants, in that the successive stability constants decrease. In this case, the four constants are :
`color{red}(logK_1 = 4.0, logK_2 = 3.2, logK_3 = 2.7, logK_4 = 2.0)` or `color{red}(log β_4 = 11.9)`
`color{green}("Instability Constant ")` : The instability constant or the dissociation constant of coordination compounds is defined as the reciprocal of the formation constant.