Have you ever wondered what a stability constant is? Continue reading to find out!

• In this article, you will understand what a complex is.
• How the stability of the complex is defined.
• How the stability of a complex is quantified and calculated.
• What does a high stability constant signify.
• And the factors that affect the stability of a complex.

We talk about stability constant when there are complex ions involved. First of all, what is a complex?

A complex can either be an ion or electrically neutral. The central atom is usually a transition metal. This is because transition metals have partially filled d-orbital, and thus can form many dative bonds. The ligands donate their lone pair of electrons to the central atom and form dative or coordinate bonds with it.

Stability constant: definition

Now that you have an idea what a complex is, let's talk about its stability.

How do complex ions form in a solution? Let us understand this with an example.

When a solution of ammonia is added to a solution containing hexaaquacopper (II) ions, [Cu(H₂O)₆]²⁺, 4 of the water molecules in the ion gradually get replaced by 4 ammonia ions and form [Cu(NH₃)₄(H₂O)₂]²⁺. This exists in an equilibrium and can be written like this:

$$ [Cu(H_2O)_6]^{2+} + 4NH_3 \rightleftharpoons [Cu(NH_3)_4(H_2O)_2]^{2+} $$

The 4 water molecules do not get replaced all at once, but one at a time. So, an equilibrium reaction can be written for each water molecule that gets replaced:

$$ [Cu(H_2O)_6]^{2+} + NH_3 \rightleftharpoons [Cu(NH_3)(H_2O)_5]^{2+} + H_2O $$

$$ [Cu(NH_3)(H_2O)_5]^{2+} + NH_3 \rightleftharpoons [Cu(NH_3)_2(H_2O)_4]^{2+} + H_2O $$

$$ [Cu(NH_3)_2(H_2O)_4]^{2+} + NH_3 \rightleftharpoons [Cu(NH_3)_3(H_2O)_3]^{2+} + H_2O $$

$$ [Cu(NH_3)_3(H_2O)_3]^{2+} + NH_3 \rightleftharpoons [Cu(NH_3)_4(H_2O)_2]^{2+} + H_2O $$

Notice how in the complex produced at each step, there is one less H₂O molecule as it gets substituted by one NH₃ molecule.

Stability constant: formula

You saw how a complex can form. Now let's quantify its stability and write an expression for it. Continuing from the example, since the ions in each step exist in equilibrium, we can write the equilibrium constant for each step. Let us write the equilibrium constant for the first step:

$$ K_1 = \frac{[Cu(NH_3)(H_2O)_5^{2+}]}{[Cu(H_2O)_6^{2+}] \cdot [NH_3]}$$

$$ K_1 = 1.78 \times 10^4 mol^{-1} L^1 $$

For each step of the reaction (replacement of each consecutive H₂O molecule), there is equilibrium in the reaction, and a stability constant can be written for the ion produced.

The subsequent ions are more stable than the previous ones i.e. [Cu(NH₃)₂(H₂O)₄]²⁺ is more stable than [Cu(NH₃)(H₂O)₅]²⁺ and so on. But you'll notice that the stability constants are smaller for each subsequent ion. This is typical when studying individual equilibrium constants in a reaction.

The overall stability constant for the reaction is calculated by multiplying all four stability constants. Try it out on a piece of paper, and you'll end up with this:

$$ K_{stab} = \frac{[Cu(NH_3)_4(H_2O)_2^{2+}]}{[Cu(H_2O)_6^{2+}] \cdot [NH_3]^4}$$

$$ K_{stab} = 1.20 \times 10^{13} mol^{-4} L^4 $$

High Stability Constant

Stability constant tells us that at equilibrium, what the tendency is for the product complex to be formed. In terms of ligands, a high stability constant means that the interaction between the reagents that form the complex is strong and will form strong dative bonds with the central atom. Therefore, the bigger this constant is, stronger is the ligand interaction, and higher is the stability of the complex formed.

In the example of [Cu(H₂O)₆]²⁺, the ligands are H2O molecules, which are attached to the central copper atom via dative bonds. When ammonia solution is added to this, there is a stepwise ligand exchange that takes place, and the water ligands get replaced by the ammonia ligands. The most stable complex (one with the highest K_stab) is formed in this competitive equilibrium.

Factors Affecting Stability Constant

There are many factors that affect the stability of a complex formed in a solution.

Nature of ligands

Basicity of the ligand

According to Brønsted-Lowry theory, being more basic means it is easier for the ligand to donate its lone pair of electrons. The ease of donating an electron pair directly translated to the strength of the coordinate bond between the ligand and the central atom.

Order of stability of the complex with ligands NH₃, H₂O, and F (in 3D-series metal ions) is -

NH₃ > H₂O > F⁻

Metal-ligand bond nature

The stability of metal complexes will increase with increasing covalent character of the metal-ligand bond. For example, look at the stability of complex of silver with halides as the ligands -

AgI₂⁻ > AgBr₂⁻ > AgCl₂⁻ > AgF₂⁻

Some ligands like alkenes, CO, and CN^-, have vacant p- or d- orbital, which allows them to form 𝜋-bonds with the central metal atom. Formation of 𝜋-bond makes the complex even more stable.

Nature of the central atom

Naturally, like ligands, the nature of the central atom can also affect the stability of a complex.

Size of the central atom

Stability of the complex decreases with increasing size of the central metal cation. The order of stability of complex with M²⁺ ions is -

Ba²⁺ < Sr²⁺ < Ca²⁺ < Mg²⁺ < Mn²⁺ < Fe²⁺ < Co²⁺ < Ni²⁺ < Cu²⁺ > Zn²⁺

This is known as the Irving-Williams series. Notice the sign flip going from Cu²⁺ to Zn²⁺. This is because the cation radius actually increases going from Cu²⁺ to Zn²⁺.

Charge on the central atom

In general, higher oxidation states in metal cations produce more stable complexes than lower oxidation states. This trend can be seen in ligands like H₂O, NH₃ etc. However, like any trend in chemistry, there are exceptions to this. Ligands like CO, CN⁻, o-phenanthroline, PMe₃, bipyridyl form a more stable complex with metal cations with lower oxidation states.

Resonance

Resonance highly increases the stability of a complex. For example, complexes with acetylacetonate ligands are very stable. This is because there is resonance in the structure of this ligand. An example of a complex with acetylacetonate ligands is Chromium (III) acetylacetonate, or Cr(acac)₃.

Steric effects arise when atoms are situated rather closer together. The closeness of atoms increases the energy of the molecule, and hence decreases its stability. In complexes, steric hindrance can be caused due to bulky groups attached to the ligand.

Macrocyclic Effect

Macrocyclic effect comes into play when a macrocyclic ligand is present. A macrocyclic ligand is cyclic and large, with 9 or more atoms in a ring structure. But what is special about macrocyclic ligands is that they have a denticity of 3 or more. That means 3 or more donor atoms that can bind to a central atom. Macrocyclic ligands form extremely stable complex compounds.

Chelating Effect

Like macrocyclic ligands, chelating ligands are also multidentate ligands, but they are not cyclic. The multiple donor sites in such a ligand are open ended. Complexes formed with chelating ligands are thermodynamically more stable than complexes formed with non-chelating ligands. However, the stability of complexes formed with open-ended chelating ligands is less than those formed with comparatively sized macrocyclic ligands.

Calculating Stability Constant of a Complex