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November 20, 2024Stability of Coordination Compounds and reaction kinetics is an important aspect of coordination Chemistry and finds their application in all disciplines, from catalyst design to pharmaceutical studies of drug design and metabolism.
The study of stabilities and reaction mechanism of complexes is vital to determine the behaviour of metal complexes in different environments, including changes in temperature or changes in \({\rm{pH}}\) of the reaction medium. A higher equilibrium constant indicates the greater stability of a complex. Let’s understand the different types of stabilities present in metal complexes and their effect on reaction mechanisms. Read on to find out more.
According to the J. Bjerrum, the formation of a metal complex in solution proceeds by the stepwise addition of the ligands to the central metal ion. Thus, the formation of complex \({\rm{M}}{{\rm{L}}_{\rm{n}}}\) by the stepwise formation method can be given as:
Where \({{\rm{K}}_1},{\mkern 1mu} {{\rm{K}}_2},{\mkern 1mu} {{\rm{K}}_3}, \cdots .{{\rm{K}}_{\rm{n}}}\) are stepwise formation or stability constant for the complexes formed in the corresponding steps.
The formation of complex \({\rm{M}}{{\rm{L}}_{\rm{n}}}\) may also proceed in a single step which can be given as:
Where M represents the centre metal, n represents the number of ligands; L is the ligand type involved, and \({\rm{\beta }}\) represents the equilibrium constant for the whole process.
Study Isomerism in Coordination Compounds
From the expression of \({\beta _n}\), we can conclude that the magnitude of \({\beta _n}\) is:
Hence, the equilibrium constant \({\beta _n}\) is also called the formation constant or stability constant of the metal complex.
To define the stability of the complex compound formed in the solution, two types of the stability concept can be used, which are explained in the following section.
The thermodynamic stability of metal complexes is a function of the equilibrium constant and is defined by the thermodynamic parameters like bond energy, stability constant or formation constant of the metal complexes.
According to the thermodynamic stability concept, a complex compound can be categorised into two different types, which are given below:
1. Stable Complexes: Metal complexes that exhibit very high formation constant in the solution are known as stable complexes.
2. Unstable Complexes: Metal complexes that exhibit low formation constant in the solution are known as unstable complexes.
The stability of the complexes is a function of the rate constant of the metal complexes and is defined by the kinetic parameters. The reaction with a high rate constant is expected to proceed fast.
According to the kinetic stability concept, complex compounds in the solution can be divided into two types:
1. Inert Complex: Metal complexes that exhibit a very low or negligible replacement of ligands in the solution are known as inert complexes. This means the substitution of one or more ligands present in the coordination sphere of the complex takes place very slowly. The rate of substitution of inert complexes can be measured easily by conventional techniques.
2. Labile Complex: Metal complexes that exhibit a very high rate of replacement of one or more ligands in the solution are known as labile complexes. This means the substitution of one or more ligands present in the coordination sphere of the complex takes place quickly or rapidly.
\({\left[ {{\rm{Hg}}{{({\rm{CN}})}_4}} \right]^{2 – }}\) ion has a very high formation constant \(\left( {{{10}^{42}}} \right)\) but it can easily undergo a replacement reaction in the solution. Therefore, this complex is thermodynamically stable but kinetically labile.
Similarly, \({\left[ {{\rm{Co}}{{\left( {{\rm{N}}{{\rm{H}}_3}} \right)}_6}} \right]^{ + 3}}\) ion is kinetically inert but thermodynamically unstable.
Hence, a thermodynamically stable complex may be kinetically labile (fast-reacting complex) and a thermodynamically unstable complex may be kinetically inert (slow reacting complex).
To give the relationship between stepwise formation constants and overall formation constant, let us consider the formation of \({\rm{M}}{{\rm{L}}_3}\) complex by the stepwise formation method and overall formation method. According to the stepwise formation method:
According to the overall formation method-
Dividing and multiplying Eqn \((4)\) with \(\left[ {{\rm{M}}{{\rm{L}}_2}} \right][{\rm{ML}}]\), we get-
\({\beta _3} = \frac{{\left[ {{\rm{M}}{{\rm{L}}_3}} \right]}}{{[{\rm{M}}]{{[{\rm{L}}]}^3}}} \times \frac{{\left[ {{\rm{M}}{{\rm{L}}_2}} \right]}}{{\left[ {{\rm{M}}{{\rm{L}}_2}} \right]}} \times \frac{{[{\rm{ML}}]}}{{[{\rm{ML}}]}}\)
\({\beta _3} = \frac{{\left[ {{\rm{M}}{{\rm{L}}_3}} \right]}}{{\left[ {{\rm{M}}{{\rm{L}}_2}} \right][{\rm{L}}]}} \times \frac{{\left[ {{\rm{M}}{{\rm{L}}_2}} \right]}}{{[{\rm{ML}}][{\rm{L}}]}} \times \frac{{[{\rm{ML}}]}}{{[{\rm{M}}][{\rm{L}}]}}\)
From Eqn \(\left( 1 \right),\,\left( 2 \right),\,\left( 3 \right)\) and \((4)\), we get-
\({\beta _3} = {{\rm{K}}_3} \times {{\rm{K}}_2} \times {{\rm{K}}_1}\)
\({\beta _{\rm{n}}} = {{\rm{K}}_{\rm{n}}} \ldots \ldots \ldots \ldots .{{\rm{K}}_3} \times {{\rm{K}}_2} \times {{\rm{K}}_1}\)
Thus, from the above equation, it is observed that the product of the stepwise formation constant is always equal to the overall formation constant for any particular complex.
The overall stability constant is generally reported in the logarithmic scale as \(\log \beta \) shown below.
\(\log {\beta {\rm{n}}} = \log \left( {{{\rm{K}}{\rm{n}}} \ldots \ldots \ldots \ldots .{{\rm{K}}_3} \times {{\rm{K}}_2} \times {{\rm{K}}_1}} \right)\)
\(\log {\beta _{\rm{n}}} = \log {{\rm{K}}_{\rm{n}}} + \ldots \ldots \ldots \ldots .. + \log {{\rm{K}}_3} + \log {{\rm{K}}_2} + \log {{\rm{K}}_1}\))
Or, \(\log {\beta _{\rm{n}}} = \sum\limits_{{\rm{i}} = 1}^{{\rm{i}} = {\rm{n}}} {\log {{\rm{K}}_{\rm{i}}}} \)
If the value of the \(\log \beta \) is more than \(8\) the complex is considered thermodynamically stable.
In an aqueous solution, a complex ion dissociates, and an equilibrium exists between the undissociated complex ion and the species obtained by the dissociation of the complex ion.
For example, The dissociation of \({\left[ {{\rm{Cu}}{{\left( {{\rm{N}}{{\rm{H}}_3}} \right)}_4}} \right]^{2 + }}\) ion in solution is represented by the equilibrium:
The dissociation (or instability) constant \({{\rm{K}}_{\rm{i}}}\) of the above equilibrium is given by:
\({{\rm{K}}_{\rm{i}}} = \frac{{\left[ {{\rm{C}}{{\rm{u}}^{2 + }}} \right]{{\left[ {{\rm{N}}{{\rm{H}}_3}} \right]}^4}}}{{{{\left[ {{\rm{Cu}}{{\left( {{\rm{N}}{{\rm{H}}_3}} \right)}_4}} \right]}^{2 + }}}} \ldots \ldots \ldots \ldots \ldots \ldots ..{\rm{eqn}}({\rm{i}})\)
The formation of \({\left[ {{\rm{Cu}}{{\left( {{\rm{N}}{{\rm{H}}_3}} \right)}_4}} \right]^{2 + }}\) ion in a solution can be represented by the equilibrium given below:
The formation (or stability) constant for the above reaction, which is represented by \(\beta \) is given by:
\(\beta = \frac{{{{\left[ {{\rm{Cu}}{{\left( {{\rm{N}}{{\rm{H}}_3}} \right)}_4}} \right]}^{2 + }}}}{{\left[ {{\rm{C}}{{\rm{u}}^{2 + }}} \right]{{\left[ {{\rm{N}}{{\rm{H}}_3}} \right]}^4}}} \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots {\rm{eqn}}({\rm{ii}})\)
On comparing eqn \(\left( {\rm{i}} \right)\) and \(\left( {\rm{ii}} \right)\), we get-
Thus, the formation constant (or stability constant), \(\beta \) is reciprocal of dissociation constant (or instability constant), \({{\rm{K}}_{\rm{i}}}\).
\({\rm{\beta }}\,{\rm{ = \;}}\,\frac{{\rm{1}}}{{{{\rm{K}}_{\rm{i}}}}}{\rm{\;}}\)
Higher is the value of the stability constant, \(\beta \) (formation constant) for a complex ion, greater is the stability of the complex ion. Now since \(\beta \alpha \frac{1}{{{{\rm{K}}_{\rm{i}}}}}\), we can say that smaller is the value of instability constant, \({{\rm{K}}_{\rm{i}}}\) (dissociation constant) of a complex ion, greater is the stability of the complex ion.
The different factors that affect the stability of complexes formed in the solution are given as below:
i) Size of the Central Metal Atom: As the size of metal ions decreases, the stability of the complex increases; thus, the stability of isovalent complexes decreases down the group and increases along the period as the size varies in the reverse order.
If we consider the divalent metal ions \({\rm{M}}{{\rm{n}}^{2 + }},\,{\rm{F}}{{\rm{e}}^{2 + }},\,{\rm{C}}{{\rm{o}}^{2 + }},\,{\rm{N}}{{\rm{i}}^{2 + }},\,{\rm{C}}{{\rm{u}}^{2 + }},\,{\rm{Z}}{{\rm{n}}^{2 + }}\) then the stability of their complexes increases with a decrease in the ionic radius of the central metal as given below:
Ion | \({\rm{M}}{{\rm{n}}^{2 + }}\) | \({\rm{F}}{{\rm{e}}^{2 + }}\) | \({\rm{C}}{{\rm{o}}^{2 + }}\) | \({\rm{N}}{{\rm{i}}^{2 + }}\) | \({\rm{C}}{{\rm{u}}^{2 + }}\) | \({\rm{Z}}{{\rm{n}}^{2 + }}\) |
lonic radius \({\rm{pm}}\) | \(91\) | \(83\) | \(82\) | \(78\) | \(73\) | \(74\) |
Therefore, the order of the stability is: \({\rm{M}}{{\rm{n}}^{2 + }} < {\rm{F}}{{\rm{e}}^{2 + }} < {\rm{C}}{{\rm{o}}^{2 + }} < {\rm{N}}{{\rm{i}}^{2 + }} < {\rm{C}}{{\rm{u}}^{2 + }} > {\rm{Z}}{{\rm{n}}^{2 + }}\)
This order is called the natural order of stability or Irving William’s order, which is due to the regular decrease in size from \({\rm{M}}{{\rm{n}}^{2 + }}\) to \({\rm{C}}{{\rm{u}}^{2 + }}\) and increase in size from \({\rm{C}}{{\rm{u}}^{2 + }}\) to \({\rm{Z}}{{\rm{n}}^{2 + }}\) ion.
ii) Charge on the Central Metal Atom: A smaller, more highly charged ion allows a closer and faster approach of the ligands and greater force of attraction. This results in the formation of a stable complex. In general, the greater the charge on the central metal ion, the greater the complex’s stability.
Stability \(\alpha + ve\) oxidation state of Central Metal ion
iii) Charge to size ratio: Metal ions having high charge density forms stable complexes. Charge density means the ratio of the charge to the radius of the ion. Thus, the smaller the size and higher the charge of the metal ion, i.e. larger is the charge/radius ratio of a metal ion, the greater is the stability of its complex.
For example, the stability of hydroxide complexes of \({\rm{L}}{{\rm{i}}^ + },\,{\rm{C}}{{\rm{a}}^{2 + }},\,{\rm{N}}{{\rm{i}}^{2 + }},\, \ldots .{\rm{B}}{{\rm{e}}^{2 + }}\) ions whose charge density increases from \({\rm{L}}{{\rm{i}}^ + }\) to \({\rm{B}}{{\rm{e}}^{2 + }}\) ions also increase in the same direction as shown below.
iv) Electronegativity: Electronegativity of the central ion also influences the stability of its complexes. This is because the bonding between a central ion and ligand is due to the donation of electron pairs by the ligands. Hence, a strongly electron-attracting central ion will give stable complexes. Hence, the greater the positive charge density (i.e., charge/size ratio) and greater the central ion’s electronegativity, the higher the stability of the complex formed by it.
v) Class of the Metal Ion: Chatt and Ahrland have classified metals into three categories: \({\rm{a}},\,{\rm{b}}\) and borderline, based on their electron-acceptor properties. This classification is shown below:
Class ‘\({\rm{a}}\)’ metals form more stable complexes with ligands having the coordinating atoms from the second-period elements (e.g., \({\rm{N}},\,{\rm{O}},\,{\rm{F}}\)) than those of an analogous ligand in which the donor atom is from the third or later period (e.g., \({\rm{P}},\,{\rm{S}},\,{\rm{Cl}}\)). Class \({\rm{b}}\) metals have the relative stabilities reversed.
For class ‘\({\rm{a}}\)’ metals, the stability of metal complexes with different ligands follows the order:
For class ‘\({\rm{b}}\)’ metals, the stability of metal complexes with different ligands follow the order:
Class \(‘{\rm{b’}}\) metals form more stable complexes due to the presence of a number of d-electrons beyond an inert gas core. The transfer of these \({\rm{d}}\)-electrons is used to form \(\pi \)-bond with ligand atoms. The most stable complexes of class \(‘{\rm{b’}}\) metals are formed with ligands like \({\rm{PM}}{{\rm{e}}_3},\,{{\rm{S}}^{2 – }},\,{{\rm{I}}^ – }\) which have vacant \({\rm{d}}\)-orbitals or like \({\rm{CO}},\,{\rm{C}}{{\rm{N}}^ – }\) which have vacant molecular orbitals of low energy.
For borderline metals, the stability constants do not display either class \(‘{\rm{a’}}\) or class \(‘{\rm{b’}}\) behaviour uniquely.
vi) Polarising Power: With the increase in the polarising power of Central Metal Atom, the stability of complexes also increases. Stability \(\alpha \) Polarising power of Central Metal atom
i) Size and Charge of the Ligands: Cationic ligands with higher positive charges have small sizes and form more stable compounds. Though the size of the anion increases with an increase in the \( – {\rm{ve}}\) charge, the stability of complexes decreases with the increase in the \( – {\rm{ve}}\) charge value of the anionic ligands.
For example: \({{\rm{F}}^ – }\) forms more stable complexes with \({\rm{F}}{{\rm{e}}^{ + 3}}\) than \({\rm{C}}{{\rm{l}}^ – },\,{\rm{B}}{{\rm{r}}^ – }\) or \({{\rm{I}}^ – }\) . Thus, a small fluoride \({{\rm{F}}^ – }\) ion forms more stable \({\rm{F}}{{\rm{e}}^{ + 3}}\) complex as compared to the large \({\rm{C}}{{\rm{l}}^ – }\) ion. This is due to the easy approach of the ligand towards metal ions. Similarly, a small dinegative anion \({{\rm{O}}^{2 – }}\) forms more stable complexes than does the large \({{\rm{S}}^{2 – }}\) ion.
For class \(‘{\rm{a}}’\) metals: The stability of the complexes of a given metal ion with halide ion used as ligands is in the order:
\({{\rm{F}}^ – } > {\rm{C}}{{\rm{l}}^ – } > {\rm{B}}{{\rm{r}}^ – } > {{\rm{I}}^ – }\)
For class \(‘{\rm{a}}’\) metals (e.g. \({\rm{Pd}},\,{\rm{Ag}},\,{\rm{Pt}},\,{\rm{Hg}}\) etc.): The stability of the complexes of a given metal ion with halide ion used as ligands is reversed:
\({{\rm{F}}^ – } < {\rm{C}}{{\rm{l}}^ – } < {\rm{B}}{{\rm{r}}^ – } < {{\rm{I}}^ – }\)
ii) Basic Character: Higher the basic character or strength of the ligand, the higher will be the stability of coordination compounds. This is because the electron-donating tendency of ligands to the central metal ion is higher. The more basic is the ligand, the more easily it can donate electron pairs to the central ion, and hence more easily it can form complexes of greater stability. The ligand that binds \({{\rm{H}}^ + }\) firmly form stable complexes with metal ions.
Thus, \({{\rm{F}}^ – }\) should form more stable complexes than \({\rm{C}}{{\rm{l}}^ – },\,{\rm{B}}{{\rm{r}}^ – }\), and \({{\rm{I}}^ – }\) and \({\rm{N}}{{\rm{H}}_{\rm{3}}},\) should be better ligand than \({{\rm{H}}_2}{\rm{O}}\) which in turn should be better than \({\rm{HF}}\). \(\left( {{\rm{N}}{{\rm{H}}_3} > {{\rm{H}}_2}{\rm{O}} > {\rm{HF}}} \right)\). This behaviour is observed for alkali, alkaline earth and other electropositive metals like first row transition elements, lanthanides and actinides.
Stability \(\alpha \) Basic character of the ligand
iii) The Dipole Moment of Ligands: For neutral ligands, the larger the magnitude of permanent dipole moment, the greater the complexes’ stability. For example, the order of stability of complexes formed by some neutral ligands is ammonia \( > \) ethylamine \( > \) diethylamine \( > \) triethylamine.
iv) π- Bonding Capacity of Ligands: The ligands like \({\rm{C}}{{\rm{N}}^ – },{\rm{CO}},\,{\rm{P}}{{\rm{R}}_3},\,{\rm{As}}{{\rm{R}}_3}\), alkenes, alkynes, which are capable of forming \(\pi \)-bonds with transition metal ions, give more stable complexes.
v) Steric Hindrance due to Bulky Ligands: When a bulky group is linked to or present near a ligand’s donor atom, repulsion occurs between the ligand’s donor atom and the bulky group, weakening the metal-ligand interaction. As a result, the complex becomes less stable.
For example, The complex of \({\rm{N}}{{\rm{i}}^{2 + }}\) ion with \(2\)-methyl-\(8\)-hydroxy quinoline \(\left( {{{\log }_{10}}\beta = 17.8} \right)\) is less stable than that with \(8\)-hydroxy quinoline \(\left( {{{\log }_{10}}\beta = 17.8} \right)\). The effect of the presence of a bulky group on the stability of a complex is commonly called a steric hindrance.
\(2,\,2’\)-bipyridine (also called \(2,\,2’\)-dipyridyl) forms complexes with metal ions which are stable, but the substitution of an alkyl group in \(4,\,4’\) or \(5,\,5’\) positions gives less stable complexes. This is because the substituents crowd the metal ion, mutual repulsion occurs, and consequently, the complexes formed are of lower stability.
vi) Chelate Effect: The ligands which can form five or six-membered ring structures with the metal centre usually form more stable complexes than the others. This effect is called chelation, and the ligands are called chelating ligands.
For example:
The complex formation of \({\rm{N}}{{\rm{i}}^{2 + }}\) with ammonia and \(1,\,2\)-diaminoethane can be expressed by the following equations:
\({\left[ {{\rm{Ni}}{{\left( {{{\rm{H}}_2}{\rm{O}}} \right)}_6}} \right]^{2 + }} + 6{\rm{N}}{{\rm{H}}_3} \to {\left[ {{\rm{Ni}}{{\left( {{\rm{N}}{{\rm{H}}_3}} \right)}_6}} \right]^{2 + }} + 6{{\rm{H}}_2}{\rm{O}}\,{\beta _6} = {10^{8.76}}\)
\({\left[ {{\rm{Ni}}{{\left( {{{\rm{H}}_2}{\rm{O}}} \right)}_6}} \right]^{2 + }} + 3{\rm{en}} \to {\left[ {{\rm{Ni}}{{({\rm{en}})}_3}} \right]^{2 + }} + 6{{\rm{H}}_2}{\rm{O}}\,{\beta _6} = {10^{18.28}}\)
The overall stability constant value for the \({\rm{N}}{{\rm{i}}^{2 + }}\) complex with three chelate rings \(\left( {{\rm{en}}} \right)\) is about \({10^{10}}\) greater than that formed with six monodentate ligands \(\left( {{\rm{N}}{{\rm{H}}_3}} \right)\).
vii) Macrocyclic Ligands and Macrocyclic Effect: A macrocyclic ligand is a nine or more membered cyclic molecule having \(3\) or more potential donor atoms that can bind to a metal atom inside the cavity of the macrocycle. Some macrocyclic ligands have conjugated π system. The stability of a complex of a particular metal ion with a macrocyclic ligand is several times greater than that of an open-ended multidentate ligand (chelating ligand) containing an equal number of equivalent donor atoms.
The increase in stability due to the presence of multidentate cyclic ligands is called the macrocyclic effect. Thus, if ligands are multidentate and cyclic without any steric effects, the stability of the complexes is increased.
The cyclic crown polyether complexes are far more stable than those of their corresponding open-chain analogues.
In some complexes, the stability of the complex is influenced by the amount of metal-ligand covalent character present in the complex. This is more pronounced in complexes of the metals like those of copper and zinc family, \({\rm{Sb}},\,{\rm{Pb}}\). For example, the stability of \(\left[ {{\rm{Ag}}{{\rm{X}}_2}} \right]\) and \(\left[ {{\rm{Ag}}{{\rm{X}}_3}} \right]\) are found to be in the following order:
\({\rm{Ag}}{{\rm{I}}_2} > {\rm{AgB}}{{\rm{r}}_2} > {\rm{AgC}}{{\rm{l}}_2} > {\rm{Ag}}{{\rm{F}}_2} > {\rm{Ag}}{{\rm{I}}_3} > {\rm{AgB}}{{\rm{r}}_3} > {\rm{AgC}}{{\rm{l}}_3} \ge {\rm{Ag}}{{\rm{F}}_3}\)
This is due to the increase in the covalent character of the \({\rm{Ag}} – {\rm{X}}\) bond as we move from \({\rm{Ag}} – {\rm{F}}\) to \({\rm{Ag}} – {\rm{I}}\).
A coordination compound is formed by the reaction between a metal ion and ligands and is said to be stable if strong forces of attraction are present between metal ions and ligands. Mostly complex ions are stable, but they undergo dissociation in an aqueous solution though to a very little extent. In this article, we learnt the different types of stabilities of coordination compounds and chemical equilibrium established between the undissociated complex and the dissociated ions in solution. We also learnt the various factors affecting the stabilities of these compounds.
Below are the most frequently asked questions on Stability of Coordination Compounds:
Q.1: What is the stability of a coordination compound in solution?
Ans: The degree of interaction between the metal ion and the ligands involved in the state of equilibrium determines the stability of coordination compounds in solution. The equilibrium constant for the interaction of metal ions and ligands is used to quantify stability.
Q.2: What are the factors that affect the stability of coordination compounds?
Ans: Several factors affect the stability of the metal complexes. These are:
1. Nature of the central metal ion (size and charge).
2. Nature of the ligand (size and charge).
3. Class of metals
4. Electronegativity and Polarising power
5. Basic character and dipole moment
6. Chelating effect.
7. Macrocyclic effect.
8. Steric effect or steric hindrance.
Q.3: Why are chelate complexes more stable?
Ans: Chelating ligands can form a ring with central metal. Therefore, these ligands have ability to delocalise electrons within a ring which results in an increased force of attraction between the central metal ion and chelating agent. Hence, chelating complexes are more stable.
Q.4: What is the chelate effect?
Ans: The chelate effect is the increased stability of the metal complexes in which there is an enhanced affinity of a chelating ligand for a metal ion compared to monodentate ligands. This term comes from the Greek word ‘chelos’, meaning “crab”. Tridentate ligands are chelating ligands that can bind through three donor atoms compared to bidentate ligands that bind through two donor atoms.
Q.5: Do ligands act like Lewis acids or Lewis bases? Why?
Ans: Ligands act like Lewis bases because they donate their electron pairs (electron donors) to the central metal atom.
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