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**Stability Of Coordination compounds in Solution**

The stability of a complex in solution means the degree of association between the metal ion and the ligands involved in the state of equilibrium.

The magnitude of the (stability or formation) equilibrium constant for the association express quantitatively the stability.

** For ****example:** The formation of [Cu(NH_{3})_{4}]^{2+ }complex may be expressed as :

Cu^{2+} (aq) +4NH_{3} (aq) ⇔ [Cu(NH_{3})_{4}]^{2+} (aq)

The equilibrium constant for the reaction, is therefore, called the stability constant and is represented by K_{s} as

\begin{equation}

\text { Stability constant, } K_{s}=\frac{\left[\mathrm{Cu}\left(\mathrm{NH}_{3}\right)_{4}\right]^{2+}}{\left[\mathrm{Cu}^{2+}\right]\left[\mathrm{NH}_{3}\right]^{4}}

\end{equation}

The interaction between metal ion and ligand may be regarded as Lewis acid-base reaction. If the interaction is strong, the complex formed would be thermodynamically more stable and the value of stability constant (K_{s}) will be large.

The larger the numerical value of K_{s}, the more thermodynamically stable is the complex.

Let us consider a general reaction:

M+4L ⇔ ML_{4}

The stability constant may be written as:

\begin{equation}

K_{B}=\frac{\left[\mathrm{ML}_{4}\right]}{[\mathrm{M}][\mathrm{L}]^{4}}

\end{equation}

Larger the stability constant, the higher the proportion of ML_{4} that exists in solution. Since free metal ions rarely exist in the solution so that metal ion (M) will usually be surrounded by solvent molecules which will complete with the ligand molecules, L and be successively represented as :

[M(H_{2}O)_{n}] + 4L ⇔ [ML_{4}] +nH_{2}O

The above overall reaction proceeds in steps with formation constant K_{1}, K_{2}, K_{3} and K_{4}, for each step as represented below:

where K_{1}, K_{2}, K_{3} and K_{4} are called **stepwise stability constants**

Alternatively, we may write the overall stability constant as

M+ 4L ⇔ ML_{4}

β_{4} = [ML_{4}] /[M] [L]^{4}

The stepwise and overall stability constants are therefore, related as:

β_{4} = K_{1} x K_{2} x K_{3} x K_{4}

β_{n} = K_{1} x K_{2} x K_{3} x K_{4……………..}K_{n}

**For example:** The steps involved in the formation of the complex ion, tetraamminecopper(III) ion, we have the following:

β_{4} =[Cu(NH_{3})_{4}]^{2+}/[Cu^{2+}][NH_{3}]^{4}

Then, logβ may be used as a measure of stability of the complex.

For example:For [Cu(NH_{3})_{4}]^{2+}, the four constants are :

log β_{4 }= logK_{1} + logK_{2} + logK_{3} + logK_{4}

= 4.0 + 3.2 +2.7 + 2.0

log β_{4}= 11.9

For example: for [Cd(NH_{3})_{4}]^{2+}

log β_{4} = 2.6 +2.1 + 1.4 + 0.9 = 7.0

Thus, the log β_{4} value of [Cu(NH_{3})_{4}]^{2+} and [Cd(NH_{3})_{4}]^{2+} complexes indicate that [Cd(NH_{3})_{4}]^{2+} is more stable than [Cd(NH_{3})_{4}]^{2+} complex.

In the second group of qualitative analysis of basic radicals, Cu^{2+} does not form precipitate as CuS when H_{2}S is passed through the solution containing [Cd(NH_{3})_{4}]^{2+} complex, while Cd^{2+} ions form precipitate as CdS because of instability of [Cd(NH_{3})_{4}]^{2+} complex ion.

The reciprocal of stability constant gives the instability constant or dissociation constant of coordination compound, Thus,

Dissociation constant of complex = 1 / Stability constant

The overall stability constant, β_{n} is related to thermodynamic stability when the system has reached equilibrium. Most of the measurements are made from aqueous solutions, which means that the complex is formed by the ligand displacing water molecules from the aqua complex of the metal ion.

_{3}molecule because the stability constants for cyanide complexes are very large in comparison to corresponding ammine complexes.

Ni

^{2+}+ 6 NH

_{3}→ [Ni(NH

_{3})

_{6}]

^{2+}K= 6.1 × 10

^{8}

^{2+}+ 3 en → [Ni(en)

_{3}]

^{2+}K= 4.6 × 10

^{18}

The K values indicate that the bidentate ligand NH

_{2}CH

_{2}CH

_{2}NH

_{2 }forms a considerably more stable complex than ammonia.

**Factors affecting the stability of a complex ion**

**(1) The nature of the central ion**

**(i) Charge on the central metal ion:**In general, the greater the charge density on the central ion, the greater is the stability of its complexes.

The greater the charge and the smaller the size of an ion, i.e., (the larger the charge/radius ratio of an ion), the greater is the stability of its complex. Fe

^{3+}ion carries higher charge than Fe

^{2+}ion but their size is about the same.

Hence charge density is higher on Fe

^{3+}than on Fe

^{2+}ion. The complexes of Fe

^{3+}ion are, therefore more stable.

^{3+}+ 6CN¯ → [Fe(CN)

_{6}]

^{3– }

^{31}

^{2+}+ 6CN¯ → [Fe(CN)

_{6}]

^{4– }

^{6}

**(ii) Size of metal ion:**As the size of the metal ion decreases, the stability of the complex increases. If we consider the bivalent metal ions, than the stability of their complexes (irrespective of the ligands) increases with increase in the ionic radius of the central metal ion as:

Ion | Mn^{2+} |
Fe^{2+} |
Co^{2+} |
Ni^{2+} |
Cu^{2+} |
Zn^{2+} |

Ionic Radius | 91 | 83 | 82 | 78 | 69 | 64 |

Therefore, the order of stability is

^{2+}< Fe

^{2+}< Co

^{2+}< Ni

^{2+}< Cu

^{2+}< Zn

^{2+}

This order is called Irving William’s order of stability.

**The stability of complex ion is also related to the electron charge distribution on the metalion.**

(iii) Electronegativity or charge distribution of metal ion:

(iii) Electronegativity or charge distribution of metal ion:

Metal ions may be classified into two types:

**These are fairly electropositive metals and include the metals of groups 1 and 2, inner transition metals and the early members of the transition series (groups 3 to 6) which have relatively a few electrons beyond an inert gas core. These form most stable coordination entities with ligands containing N, O or F donor atoms.**

(a) Class ‘a’ acceptors:

(a) Class ‘a’ acceptors:

**These are much less electropositive and include heavy metals such as Rh, Pd, Ag, Ir, Pt, Au, Hg, Pb, etc. having relatively full d-orbitals. These form most stable complexes with ligands whose donor atoms are the heavier members of the N, O and F groups.**

(b) Class ‘b’ acceptors:

(b) Class ‘b’ acceptors:

**The stability also depends upon the formation of chelate rings. If L is an unidentate ligand and L-L, a bidentate ligand and if the donor atoms of L and L-L are the same element, then L-L will replace L.**

(iv) Chelate effect:

(iv) Chelate effect:

**chelate effect.**The enhanced stability of complexes containing chelating ligands is of great importance in biological systems and analytical chemistry.

**If a multidentate ligand is cyclic and there are no unfavourable stearic effects, the complexes formed are more stable than corresponding complexes without cyclic ligands. This is called macrocyclic effect.**

(v) Macrocyclic effect:

(v) Macrocyclic effect:

(2) The nature of the ligand

(2) The nature of the ligand

**The more basic a ligand, the greater is the ease with which it can donate its lone pairs of electrons and, therefore, the greater is the stability of the complexes formed by it. Thus, CN¯ and F¯ ions and NH**

(i) Basic strength:

(i) Basic strength:

_{3}molecules, which are strong bases, are also good ligands and form many stable complexes.

**For anionic ligands, the higher the charge and the smaller the size, the more stable is the complex formed. Thus, F¯ ion gives more stable complexes than does Cl¯ ion.**

(ii) Size and charge of ligands:

(ii) Size and charge of ligands:

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