**3. Relationship or interaction between β<sup>n</sup> and K1, K2, K3, … Kn**

The parameters K and β are related together, and these are expressed in the following example:

$$
\beta\_3 = \frac{(\mathbf{M}L\_3)}{[\mathbf{M}][L]\mathbf{3}} \tag{8}
$$

Now the numerator and denominator are multiplied together with the use of [metalligand] [metal-ligand2], and after the rearranging we get the following equation:

$$\begin{split} \boldsymbol{\beta}\_{3} &= \frac{[\boldsymbol{M}\boldsymbol{L}\_{3}]}{[\boldsymbol{M}][\boldsymbol{L}]^{3}} \times \frac{[\boldsymbol{M}\boldsymbol{L}][\boldsymbol{M}\boldsymbol{L}\_{2}]}{[\boldsymbol{M}\boldsymbol{L}][\boldsymbol{M}\boldsymbol{L}\_{2}]} \\ &= \frac{[\boldsymbol{M}\boldsymbol{L}\_{1}]}{[\boldsymbol{M}][\boldsymbol{L}]} \times \frac{[\boldsymbol{M}\boldsymbol{L}\_{2}]}{[\boldsymbol{M}\boldsymbol{L}][\boldsymbol{L}]} \times \frac{[\boldsymbol{M}\boldsymbol{L}\_{3}]}{[\boldsymbol{M}\boldsymbol{L}\_{2}][\boldsymbol{L}]} = \mathbf{K}\_{1} \ge \mathbf{K}\_{2} \ge \mathbf{K}\_{3} \end{split} \tag{9}$$
 
$$\text{Thus } \boldsymbol{\beta}\_{n} = \frac{[\boldsymbol{M}\boldsymbol{L}\_{1}]}{[\boldsymbol{M}][\boldsymbol{L}]} \times \frac{[\boldsymbol{M}\boldsymbol{L}\_{2}]}{[\boldsymbol{M}\boldsymbol{L}][\boldsymbol{L}]} \cdots \frac{[\boldsymbol{M}\boldsymbol{L}\_{n}]}{[\boldsymbol{M}\boldsymbol{L}\_{n-1}][\boldsymbol{L}]} = \mathbf{K}\_{1} \ge \mathbf{K}\_{2} \dots \mathbf{K}\_{n} \tag{10}$$

*Stability Constants of Metal Complexes in Solution DOI: http://dx.doi.org/10.5772/intechopen.90183*

Now we expressed it as the following:

constant is applicable to measure the strength of interactions between the ligands and metal ions that are involved in complex formation in the solution [11]. A

Metal <sup>þ</sup> Ligand ⇆ Metal � Ligand K1 <sup>¼</sup> ð Þ *ML*

Metal <sup>þ</sup> Ligands ⇆ Metal <sup>þ</sup> Ligand2 K2 <sup>¼</sup> ð Þ *ML*<sup>2</sup>

Metal <sup>þ</sup> Ligand3 ⇆ Metal <sup>þ</sup> Ligand3 K3 <sup>¼</sup> ð Þ *ML*<sup>3</sup>

Metal <sup>þ</sup> Ligandn�<sup>1</sup> <sup>þ</sup> <sup>L</sup> ⇆ Metal <sup>þ</sup> Ligand�<sup>n</sup> Kn <sup>¼</sup> ð Þ *MLn*

stability constants. The formation of the metal-ligand-n complex may also be

expressed as equilibrium constants by the following steps:

Metal <sup>þ</sup> Ligand !*<sup>B</sup>*<sup>1</sup>

Metal <sup>þ</sup> 2Ligand !*<sup>B</sup>*<sup>2</sup>

Thus Metal <sup>þ</sup> nLigand !*Bn*

stepwise and cumulative stability constants.

*<sup>β</sup>*<sup>3</sup> <sup>¼</sup> ½ � *ML*<sup>3</sup>

<sup>¼</sup> ½ � *ML*<sup>1</sup> ½ � *M* ½ � *L*

½ � *M* ½ � *L*

Thus *<sup>β</sup><sup>n</sup>* <sup>¼</sup> ½ � *ML*<sup>1</sup>

following example:

**44**

K1, K2, K3, … Kn are the equilibrium constants and these are also called stepwise

*β*1, *β*2, *β*3, … *β*<sup>n</sup> are the equilibrium constants, and these equilibrium constants are known as overall stability constants or overall formation. *β*<sup>n</sup> is called as the nth cumulative or overall formation constant [12]. Any metal complexes will be of greater stability if its stability constant has the higher value. Sometimes the 1/k values are alternative values of stability constant, and now this is called as instability constant. Log10K1, log10K2 … log10Kn, and log10β<sup>n</sup> are the ways that expressed the

**3. Relationship or interaction between β<sup>n</sup> and K1, K2, K3, … Kn**

The parameters K and β are related together, and these are expressed in the

*<sup>β</sup>*<sup>3</sup> <sup>¼</sup> ð Þ *ML*<sup>3</sup>

ligand] [metal-ligand2], and after the rearranging we get the following equation:

½ � *ML* ½ � *ML*<sup>2</sup>

½ � *ML* ½ � *<sup>L</sup>* …*:* ½ � *MLn*

½ � *<sup>M</sup>* ½ � *<sup>L</sup>* <sup>3</sup> � ½ � *ML* ½ � *ML*<sup>2</sup>

� ½ � *ML*<sup>2</sup> ½ � *ML* ½ � *L*

� ½ � *ML*<sup>2</sup>

Now the numerator and denominator are multiplied together with the use of [metal-

� ½ � *ML*<sup>3</sup>

½ � *ML*<sup>2</sup> ½ � *<sup>L</sup>* <sup>¼</sup> K1 x K2 x K3

Metal � Ligand, *<sup>β</sup>* <sup>¼</sup> ð Þ *ML*

Metal � Ligand2, *<sup>β</sup>*<sup>2</sup> <sup>¼</sup> ð Þ *ML*<sup>2</sup>

Metal � ligandLn, *<sup>β</sup>*<sup>n</sup> <sup>¼</sup> ð Þ *MLn*

½ � *<sup>M</sup>* ½ � *<sup>L</sup>* <sup>3</sup> (8)

½ � *MLn*�<sup>1</sup> ½ � *<sup>L</sup>* <sup>¼</sup> K1 x K2 … Kn (10)

(9)

½ � *<sup>M</sup>* ½ � *<sup>L</sup>* (1)

½ � *ML* ½ � *<sup>L</sup>* (2)

½ � *ML*<sup>2</sup> ½ � *<sup>L</sup>* (3)

½ � *MLn*�<sup>1</sup> ½ � *<sup>L</sup>* (4)

½ � *<sup>M</sup>* ½ � *<sup>L</sup>* (5)

½ � *<sup>M</sup>* ½ � *<sup>L</sup>* <sup>2</sup> (6)

½ � *<sup>M</sup>* ½ � *<sup>L</sup> <sup>n</sup>* (7)

generally these 1-4 equations are expressed as the following ways:

*Stability and Applications of Coordination Compounds*

Thus

$$\beta\_n = \sum\_{n=1}^{n=n} K\_n \tag{11}$$

From the above relation, it is clear that the overall stability constant β<sup>n</sup> is equal to the product of the successive (i.e., stepwise) stability constants, K1, K2, K3, … Kn. This in other words means that the value of stability constants for a given complex is actually made up of a number of stepwise stability constants. The term stability is used without qualification to mean that the complex exists under a suitable condition and that it is possible to store the complex for an appreciable amount of time. The term stability is commonly used because coordination compounds are stable in one reagent but dissociate or dissolve in the presence of another regent. It is also possible that the term stability can be referred as an action of heat or light or compound. The stability of complex [13] is expressed qualitatively in terms of thermodynamic stability and kinetic stability.

#### **3.1 Thermodynamic stability**

In a chemical reaction, chemical equilibrium is a state in which the concentration of reactants and products does not change over time. Often this condition occurs when the speed of forward reaction becomes the same as the speed of reverse reaction. It is worth noting that the velocities of the forward and backward reaction are not zero at this stage but are equal.

If hydrogen and iodine are kept together in molecular proportions in a closed process vessel at high temperature (500°C), the following action begins:

$$\text{H}\_2 + \text{I}\_2 \rightarrow 2\text{HI} \tag{12}$$

In this activity, hydrogen iodide is formed by combining hydrogen and iodine, and the amount of hydrogen iodide increases with time. In contrast to this action, if the pure hydrogen iodide gas is heated to 500°C in the reaction, the compound is dissolved by reverse action, which causes hydrogen iodide to dissolve into hydrogen and iodine, and the ratio of these products increases over time. This is expressed in the following reaction:

$$\text{2HI} \rightarrow \text{H}\_2 + \text{I}\_2 \tag{13}$$

For the formation of metal chelates, the thermodynamic technique provides a very significant information. Thermodynamics is a very useful technique in distinguishing between enthalpic effects and entropic effects. The bond strengths are totally effected by enthalpic effect, and this does not make any difference in the whole solution in order/disorder. Based on thermodynamics the chelate effect below can be best explained. The change of standard Gibbs free energy for equilibrium constant is response:

$$
\Delta \mathbf{G} = -2.\mathbf{\hat{3}}0\mathbf{\hat{3}} \text{ RT } \log\_{10} \mathbf{\hat{\beta}}.\tag{14}
$$

Where: R = gas constant T = absolute temperature At 25°C,

<sup>Δ</sup>G=(� 5.708 kJ mol�<sup>1</sup> ) � log β. The enthalpy term creates free energy, i.e.,

$$
\Delta \mathbf{G} = \Delta \mathbf{H} \mathbf{\text{-T}} \Delta \mathbf{S} \tag{15}
$$

For similar complexes of various ions of the same charge of a particular transition series and particular ligand, ΔS0 values would not differ substantially, and hence a change in ΔH0 value would be related to change in β<sup>n</sup> values. So the order of

Kinetic stability is referred to the rate of reaction between the metal ions and ligand proceeds at equilibrium or used for the formation of metal complexes. To take a decision for kinetic stability of any complexes, time is a factor which plays an important role for this. It deals between the rate of reaction and what is the mech-

As we discuss above in thermodynamic stability, kinetic stability is referred for the complexes at which complex is inert or labile. The term "inert" was used by Tube for the thermally stable complex and for reactive complexes the term 'labile' used [16]. The naturally occurring chlorophyll is the example of polydentate ligand. This complex is extremely inert due to exchange of Mg2+ ion in the aqueous media.

The nature of central atom of metal complexes, dimension, its degree of oxida-

In the coordination chemistry, metal complexes are formed by the interaction between metal ions and ligands. For these type of compounds, metal ions are the coordination center, and the ligand or complexing agents are oriented surrounding it. These metal ions mostly are the transition elements. For the determination of stability constant, some important characteristics of these metal complexes may be

Ligands are oriented around the central metal ions in the metal complexes. The sizes of these metal ions determine the number of ligand species that will be attached or ordinated (dative covalent) in the bond formation. If the sizes of these metal ions are increased, the stability of coordination compound defiantly decreased. Zn(II) metal ions are the central atoms in their complexes, and due to their lower size (0.74A°) as compared to Cd(II) size (0.97A°), metal ions are formed more stable. Hence, Al3+ ion has the greatest nuclear charge, but its size is the smallest, and the ion N3 has the smallest nuclear charge, and its size is the largest [17]. Inert atoms like neon do not participate in the formation of the covalent or ionic compound, and these atoms are not included in isoelectronic series; hence, it is not easy

The properties of stability depend on the size of the metal ion used in the complexes and the total charge thereon. If the size of these metal ions is small and the total

tion, electronic structure of these complexes, and so many other properties of complexes are affected by the stability constant. Some of the following factors

values of ΔH0 is also the order of the β<sup>n</sup> value.

*Stability Constants of Metal Complexes in Solution DOI: http://dx.doi.org/10.5772/intechopen.90183*

anism of this metal complex reaction.

**4. Factors affecting the stability of complexes**

**3.2 Kinetic stability**

described are as follows.

as given below.

**4.2 Ionic size**

**4.3 Ionic charge**

**47**

**4.1 Nature of central metal ion**

to measure the radius of this type of atoms.

For metal complexes, thermodynamic stability and kinetic stability are two interpretations of the stability constant in the solution. If reaction moves from reactants to products, it refers to a change in its energy as shown in the above equation. But for the reactivity, kinetic stability is responsible for this system, and this refers to ligand species [14].

Stable and unstable are thermodynamic terms, while labile and inert are kinetic terms. As a rule of thumb, those complexes which react completely within about 1 minute at 25°C are considered labile, and those complexes which take longer time than this to react are considered inert. [Ni(CN)4] <sup>2</sup>� is thermodynamically stable but kinetically inert because it rapidly exchanges ligands.

The metal complexes [Co(NH3)6] 3+ and such types of other complexes are kinetically inert, but these are thermodynamically unstable. We may expect the complex to decompose in the presence of acid immediately because the complex is thermodynamically unstable. The rate is of the order of 10<sup>25</sup> for the decomposition in acidic solution. Hence, it is thermodynamically unstable. However, nothing happens to the complex when it is kept in acidic solution for several days. While considering the stability of a complex, always the condition must be specified. Under what condition, the complex which is stable or unstable must be specified such as acidic and also basic condition, temperature, reactant, etc.

A complex may be stable with respect to a particular condition but with respect to another. In brief, a stable complex need not be inert and similarly, and an unstable complex need not be labile. It is the measure of extent of formation or transformation of complex under a given set of conditions at equilibrium [15].

Thermodynamic stability has an important role in determining the bond strength between metal ligands. Some complexes are stable, but as soon as they are introduced into aqueous solution, it is seen that these complexes have an effect on stability and fall apart. For an example, we take the [Co (SCN)4] 2+ complex. The ion bond of this complex is very weak and breaks down quickly to form other compounds. But when [Fe(CN)6] <sup>3</sup>� is dissolved in water, it does not test Fe3+ by any sensitive reagent, which shows that this complex is more stable in aqueous solution. So it is indicated that thermodynamic stability deals with metal-ligand bond energy, stability constant, and other thermodynamic parameters.

This example also suggests that thermodynamic stability refers to the stability and instability of complexes. The measurement of the extent to which one type of species is converted to another species can be determined by thermodynamic stability until equilibrium is achieved. For example, tetracyanonickelate is a thermodynamically stable and kinetic labile complex. But the example of hexa-amine cobalt(III) cation is just the opposite:

$$\left[\text{Co(NH}\_3\text{)}\_6\right]^{\text{3+}} + \text{6H}\_3\text{O}^+ \rightarrow \left[\text{Co(H}\_2\text{O)}\_6\right]^{\text{3+}} + \text{6NH}\_4^+ \tag{16}$$

Thermodynamics is used to express the difference between stability and inertia. For the stable complex, large positive free energies have been obtained from ΔG0 reaction. The ΔH0, standard enthalpy change for this reaction, is related to the equilibrium constant, βn, by the well thermodynamic equation:

$$
\Delta \mathbf{G}\_0 = -\mathbf{R} \mathbf{T} \text{ \(\ln \beta\)}\tag{17}
$$

$$
\Delta \mathbf{G}\_0 = \Delta \mathbf{H}\_0 - \mathbf{T} \Delta \mathbf{S}\_0 \tag{18}
$$

For similar complexes of various ions of the same charge of a particular transition series and particular ligand, ΔS0 values would not differ substantially, and hence a change in ΔH0 value would be related to change in β<sup>n</sup> values. So the order of values of ΔH0 is also the order of the β<sup>n</sup> value.

## **3.2 Kinetic stability**

<sup>Δ</sup>G=(� 5.708 kJ mol�<sup>1</sup>

this refers to ligand species [14].

pounds. But when [Fe(CN)6]

cobalt(III) cation is just the opposite:

**46**

Co NH ð Þ<sup>3</sup> <sup>6</sup>

) � log β.

For metal complexes, thermodynamic stability and kinetic stability are two interpretations of the stability constant in the solution. If reaction moves from reactants to products, it refers to a change in its energy as shown in the above equation. But for the reactivity, kinetic stability is responsible for this system, and

Stable and unstable are thermodynamic terms, while labile and inert are kinetic terms. As a rule of thumb, those complexes which react completely within about 1 minute at 25°C are considered labile, and those complexes which take longer time

kinetically inert, but these are thermodynamically unstable. We may expect the complex to decompose in the presence of acid immediately because the complex is thermodynamically unstable. The rate is of the order of 10<sup>25</sup> for the decomposi-

nothing happens to the complex when it is kept in acidic solution for several days. While considering the stability of a complex, always the condition must be specified. Under what condition, the complex which is stable or unstable must be specified such as acidic and also basic condition, temperature, reactant, etc.

A complex may be stable with respect to a particular condition but with respect

tion in acidic solution. Hence, it is thermodynamically unstable. However,

to another. In brief, a stable complex need not be inert and similarly, and an unstable complex need not be labile. It is the measure of extent of formation or transformation of complex under a given set of conditions at equilibrium [15]. Thermodynamic stability has an important role in determining the bond strength between metal ligands. Some complexes are stable, but as soon as they are introduced into aqueous solution, it is seen that these complexes have an effect on

bond of this complex is very weak and breaks down quickly to form other com-

sensitive reagent, which shows that this complex is more stable in aqueous solution. So it is indicated that thermodynamic stability deals with metal-ligand bond energy,

This example also suggests that thermodynamic stability refers to the stability and instability of complexes. The measurement of the extent to which one type of species is converted to another species can be determined by thermodynamic stability until equilibrium is achieved. For example, tetracyanonickelate is a thermodynamically stable and kinetic labile complex. But the example of hexa-amine

Thermodynamics is used to express the difference between stability and inertia. For the stable complex, large positive free energies have been obtained from ΔG0 reaction. The ΔH0, standard enthalpy change for this reaction, is related to the

stability and fall apart. For an example, we take the [Co (SCN)4]

<sup>3</sup><sup>þ</sup> <sup>þ</sup> 6H3O<sup>þ</sup> ! Co Hð Þ 2O <sup>6</sup>

equilibrium constant, βn, by the well thermodynamic equation:

stability constant, and other thermodynamic parameters.

ΔG ¼ ΔH–TΔS (15)

3+ and such types of other complexes are

<sup>3</sup>� is dissolved in water, it does not test Fe3+ by any

<sup>3</sup><sup>þ</sup> <sup>þ</sup> 6NH4

ΔG0 ¼ �RT ln β (17) ΔG0 ¼ ΔH0 � TΔS0 (18)

<sup>2</sup>� is thermodynamically stable but

2+ complex. The ion

<sup>þ</sup> (16)

The enthalpy term creates free energy, i.e.,

*Stability and Applications of Coordination Compounds*

than this to react are considered inert. [Ni(CN)4]

The metal complexes [Co(NH3)6]

kinetically inert because it rapidly exchanges ligands.

Kinetic stability is referred to the rate of reaction between the metal ions and ligand proceeds at equilibrium or used for the formation of metal complexes. To take a decision for kinetic stability of any complexes, time is a factor which plays an important role for this. It deals between the rate of reaction and what is the mechanism of this metal complex reaction.

As we discuss above in thermodynamic stability, kinetic stability is referred for the complexes at which complex is inert or labile. The term "inert" was used by Tube for the thermally stable complex and for reactive complexes the term 'labile' used [16]. The naturally occurring chlorophyll is the example of polydentate ligand. This complex is extremely inert due to exchange of Mg2+ ion in the aqueous media.

#### **4. Factors affecting the stability of complexes**

The nature of central atom of metal complexes, dimension, its degree of oxidation, electronic structure of these complexes, and so many other properties of complexes are affected by the stability constant. Some of the following factors described are as follows.

#### **4.1 Nature of central metal ion**

In the coordination chemistry, metal complexes are formed by the interaction between metal ions and ligands. For these type of compounds, metal ions are the coordination center, and the ligand or complexing agents are oriented surrounding it. These metal ions mostly are the transition elements. For the determination of stability constant, some important characteristics of these metal complexes may be as given below.

#### **4.2 Ionic size**

Ligands are oriented around the central metal ions in the metal complexes. The sizes of these metal ions determine the number of ligand species that will be attached or ordinated (dative covalent) in the bond formation. If the sizes of these metal ions are increased, the stability of coordination compound defiantly decreased. Zn(II) metal ions are the central atoms in their complexes, and due to their lower size (0.74A°) as compared to Cd(II) size (0.97A°), metal ions are formed more stable.

Hence, Al3+ ion has the greatest nuclear charge, but its size is the smallest, and the ion N3 has the smallest nuclear charge, and its size is the largest [17]. Inert atoms like neon do not participate in the formation of the covalent or ionic compound, and these atoms are not included in isoelectronic series; hence, it is not easy to measure the radius of this type of atoms.

#### **4.3 Ionic charge**

The properties of stability depend on the size of the metal ion used in the complexes and the total charge thereon. If the size of these metal ions is small and the total charge is high, then their complexes will be more stable. That is, their ratio will depend on the charge/radius. This can be demonstrated through the following reaction:

$$\mathrm{Fe^{3+} + 6CN^{-} \Leftrightarrow \left[ \mathrm{Fe(CN)\_{6}} \right]^{3-} \log \mathfrak{b} = \mathfrak{X} \text{ (More Table)} \tag{19}$$

$$\mathrm{Fe^{2+} + 6CN^{-} \Leftrightarrow \left[ \mathrm{Fe(CN)\_{6}} \right]^{4-} \log \mathfrak{h} = 8.3 \text{ (Less Stable)} \tag{20}$$

An ionic charge is the electric charge of an ion which is formed by the gain (negative charge) or loss (positive charge) of one or more electrons from an atom or group of atoms. If we talk about the stability of the coordination compounds, we find that the total charge of their central metal ions affects their stability, so when we change their charge, their stability in a range of constant can be determined by propagating of error [18]. If the charge of the central metal ion is high and the size is small, the stability of the compound is high:

$$\text{Li}^+ > \text{Na}^+ > \text{K}^+ > \text{Rb}^+ > \text{Cs}^+ \tag{21}$$

complexes with a single metal ion; the series has been developed by overlapping different sequences obtained from spectroscopic studies [19]. The order of common

The above spectrochemical series help us to for determination of strength of ligands. The left last ligand is as weaker ligand. These weaker ligand cannot forcible binding the 3d electron and resultant outer octahedral complexes formed. It is as-Mn2<sup>þ</sup> < Ni2<sup>þ</sup> <Co2<sup>þ</sup> < Fe2<sup>þ</sup> < V2<sup>þ</sup> <Fe3<sup>þ</sup> < Cr3<sup>þ</sup> < V3<sup>þ</sup> <Co3þ. For the given ligand, it is not possible to say about the exerted strong or weaker field on the central metal

However, when we consider the metal ion, the following two useful trends are

2.Δ increases down a group. For the determination of stability constant, the

The size and charge are two factors that affect the production of metal complexes. The less charges and small sizes of ligands are more favorable for less stable bond formation with metal and ligand. But if this condition just opposite the product of metal and ligand will be a more stable compound. So, less nuclear charge and more size= less stable complex whereas if more nuclear charge and small in size= less stable complex. We take fluoride as an example because due to their smaller size than other halide and their highest electro negativity than the other halides formed more stable complexes. So, fluoride ion complexes are more stable than the

<sup>þ</sup> log β ¼ 6*:*0 (26)

<sup>þ</sup> log β ¼ 1*:*3 (27)

<sup>2</sup>� ions formed more stable complexes.

FeF2

FeCl2

donating power of ligands to central metal ions is high [20].

It is suggested by Calvin and Wilson that the metal complexes will be more stable if the basic character or strength of ligands is higher. It means that the

� <PPh3 < CN� <CO < CH2

� < F� < NCO� < OH� < C2O4

2

(25)

ligands according to their increasing ligand field strength is

� <sup>&</sup>lt; H2O <sup>&</sup>lt; NCS� ð Þ <sup>N</sup>–bonded <sup>&</sup>lt; CH3CN <sup>&</sup>lt;gly glycine <sup>&</sup>lt;py pyridine

1. Increasing the oxidation number the value of Δ increased.

� <sup>&</sup>lt;Br� <sup>&</sup>lt; <sup>S</sup><sup>2</sup>� <sup>&</sup>lt;SCN� ð Þ <sup>S</sup>–bonded <sup>&</sup>lt;Cl� <sup>&</sup>lt; N3

<sup>&</sup>lt; NH3 <sup>&</sup>lt;en ethylenediamine <sup>&</sup>lt;bipy 2, 2' � bipyridine

1.Δ increases with increasing oxidation number.

nature of the ligand plays an important role.

The following factors described the nature of ligands.

<phen 1, 10 ð Þ � phenanthroline < NO2

*Stability Constants of Metal Complexes in Solution DOI: http://dx.doi.org/10.5772/intechopen.90183*

ion. The values of Δ are observed as:

2.Δ increases from top to bottom.

O2 <sup>2</sup>� < I

observed:

**4.7 Size and charge**

other halides:

**4.8 Basic character**

**49**

As compared to S2� ion, O2

$$\text{"Th}^{4+} > \text{Y}^{3+} > \text{Ca}^{2+} > \text{Na}^{+} \text{ and } \text{La}^{3+} > \text{Sr}^{2+} > \text{K}^{+} \tag{22}$$

In general, the most stable coordination bonds can cause smaller and highly charged rations to form more stable coordination compounds.

#### **4.4 Electronegativity**

When an electron pair attracts a central ion toward itself, a strong stability complex is formed, and this is due to electron donation from ligand! metal ion. This donation process is increasing the bond stability of metal complexes exerted the polarizing effect on certain metal ions. Li+ , Na+ , Mg2+, Ca2+, Al3+, etc. are such type of metal cation which is not able to attract so strongly from a highly electronegative containing stable complexes, and these atoms are O, N, F, Au, Hg, Ag, Pd, Pt, and Pb. Such type of ligands that contains P, S, As, Br and I atom are formed stable complex because these accepts electron from M ! <sup>π</sup>-bonding. Hg2+, Pb2+, Cd2+, and Bi3+ metal ions are also electronegative ions which form insoluble salts of metal sulfide which are insoluble in aqueous medium.

#### **4.5 Temperature and pressure**

Volatile ligands may be lost at higher temperature. This is exemplified by the loss of water by hydrates and ammonia:

$$\left[\text{Co}(\text{NH}\_3)\_6\right] \text{Cl}\_3 \left(\Delta \text{175} - \text{180°C}\right) \rightarrow \left[\text{Co}(\text{NH}\_3)\_5\text{Cl}\right] \text{Cl}\_2 + \text{NH}\_3 \tag{23}$$

The transformation of certain coordination compounds from one to another is shown as follows:

$$\mathbf{AgHg} \text{[AgI}\_4\text{]} \text{ (red)} \left(4 \text{5°C}\right) \Leftrightarrow \mathbf{Ag}\_2 \left[\text{HgI}\_4\right] \text{ (yellow)}\tag{24}$$

#### **4.6 Ligand nature**

A ligand is an ion or small molecule that binds to a metal atom (in chemistry) or to a biomolecule (in biochemistry) to form a complex, such as the iron-cyanide coordination complex Prussian blue or the iron-containing blood-protein hemoglobin. The ligands are arranged in spectrochemical series which are based on the order of their field strength. It is not possible to form the entire series by studying

charge is high, then their complexes will be more stable. That is, their ratio will depend on the charge/radius. This can be demonstrated through the following reaction:

An ionic charge is the electric charge of an ion which is formed by the gain (negative charge) or loss (positive charge) of one or more electrons from an atom or group of atoms. If we talk about the stability of the coordination compounds, we find that the total charge of their central metal ions affects their stability, so when we change their charge, their stability in a range of constant can be determined by propagating of error [18]. If the charge of the central metal ion is high and the size is

In general, the most stable coordination bonds can cause smaller and highly

When an electron pair attracts a central ion toward itself, a strong stability complex is

formed, and this is due to electron donation from ligand! metal ion. This donation process is increasing the bond stability of metal complexes exerted the polarizing effect

is not able to attract so strongly from a highly electronegative containing stable complexes, and these atoms are O, N, F, Au, Hg, Ag, Pd, Pt, and Pb. Such type of ligands that contains P, S, As, Br and I atom are formed stable complex because these accepts electron from M ! <sup>π</sup>-bonding. Hg2+, Pb2+, Cd2+, and Bi3+ metal ions are also electronegative ions which form insoluble salts of metal sulfide which are insoluble in aqueous medium.

Volatile ligands may be lost at higher temperature. This is exemplified by the

The transformation of certain coordination compounds from one to another is

A ligand is an ion or small molecule that binds to a metal atom (in chemistry) or to a biomolecule (in biochemistry) to form a complex, such as the iron-cyanide coordination complex Prussian blue or the iron-containing blood-protein hemoglobin. The ligands are arranged in spectrochemical series which are based on the order of their field strength. It is not possible to form the entire series by studying

ð Þ red ð Þ 45°C ⇆ Ag2 HgI4

Cl3 <sup>ð</sup>*Δ*<sup>175</sup> � 180°CÞ ! Co NH ð Þ<sup>3</sup> <sup>5</sup>Cl Cl2 <sup>þ</sup> NH3 (23)

charged rations to form more stable coordination compounds.

, Na+

<sup>3</sup>� log<sup>β</sup> <sup>¼</sup> 31 More Stable ð Þ (19)

<sup>4</sup>� log<sup>β</sup> <sup>¼</sup> <sup>8</sup>*:*3 Less Stable ð Þ (20)

Liþ>Naþ>Kþ>Rb<sup>þ</sup>>Cs<sup>þ</sup> (21)

, Mg2+, Ca2+, Al3+, etc. are such type of metal cation which

yellow

(24)

Th4þ>Y3þ>Ca2þ>Na<sup>þ</sup> and La<sup>3</sup>þ>Sr2þ>K<sup>þ</sup> (22)

Fe3<sup>þ</sup> <sup>þ</sup> 6CN� ⇆ Fe CN ð Þ<sup>6</sup>

*Stability and Applications of Coordination Compounds*

Fe2<sup>þ</sup> <sup>þ</sup> 6CN� ⇆ Fe CN ð Þ<sup>6</sup>

small, the stability of the compound is high:

**4.4 Electronegativity**

on certain metal ions. Li+

**4.5 Temperature and pressure**

Co NH ð Þ<sup>3</sup> <sup>6</sup>

shown as follows:

**4.6 Ligand nature**

**48**

loss of water by hydrates and ammonia:

AgHg AgI4

complexes with a single metal ion; the series has been developed by overlapping different sequences obtained from spectroscopic studies [19]. The order of common ligands according to their increasing ligand field strength is

O2 <sup>2</sup>� < I � <sup>&</sup>lt;Br� <sup>&</sup>lt; <sup>S</sup><sup>2</sup>� <sup>&</sup>lt;SCN� ð Þ <sup>S</sup>–bonded <sup>&</sup>lt;Cl� <sup>&</sup>lt; N3 � < F� < NCO� < OH� < C2O4 2 � <sup>&</sup>lt; H2O <sup>&</sup>lt; NCS� ð Þ <sup>N</sup>–bonded <sup>&</sup>lt; CH3CN <sup>&</sup>lt;gly glycine <sup>&</sup>lt;py pyridine <sup>&</sup>lt; NH3 <sup>&</sup>lt;en ethylenediamine <sup>&</sup>lt;bipy 2, 2' � bipyridine <phen 1, 10 ð Þ � phenanthroline < NO2 � <PPh3 < CN� <CO < CH2 (25)

The above spectrochemical series help us to for determination of strength of ligands. The left last ligand is as weaker ligand. These weaker ligand cannot forcible binding the 3d electron and resultant outer octahedral complexes formed. It is as-Mn2<sup>þ</sup> < Ni2<sup>þ</sup> <Co2<sup>þ</sup> < Fe2<sup>þ</sup> < V2<sup>þ</sup> <Fe3<sup>þ</sup> < Cr3<sup>þ</sup> < V3<sup>þ</sup> <Co3þ. For the given ligand, it is not possible to say about the exerted strong or weaker field on the central metal ion. The values of Δ are observed as:

1. Increasing the oxidation number the value of Δ increased.

2.Δ increases from top to bottom.

However, when we consider the metal ion, the following two useful trends are observed:


The following factors described the nature of ligands.

### **4.7 Size and charge**

The size and charge are two factors that affect the production of metal complexes. The less charges and small sizes of ligands are more favorable for less stable bond formation with metal and ligand. But if this condition just opposite the product of metal and ligand will be a more stable compound. So, less nuclear charge and more size= less stable complex whereas if more nuclear charge and small in size= less stable complex. We take fluoride as an example because due to their smaller size than other halide and their highest electro negativity than the other halides formed more stable complexes. So, fluoride ion complexes are more stable than the other halides:

$$\text{FeF}\_2^{+} \text{ log } \mathfrak{h} = \mathfrak{G}.\text{0}\tag{26}$$

$$\text{FeCl}\_2^+ \text{ log } \mathfrak{h} = \text{1.3} \tag{27}$$

As compared to S2� ion, O2 <sup>2</sup>� ions formed more stable complexes.

#### **4.8 Basic character**

It is suggested by Calvin and Wilson that the metal complexes will be more stable if the basic character or strength of ligands is higher. It means that the donating power of ligands to central metal ions is high [20].

It means that the donating power of ligands to central metal ions is high. In the case of complex formation of aliphatic diamines and aromatic diamines, the stable complex is formed by aliphatic diamines, while an unstable coordination complex is formed with aromatic diamines. So, from the above discussion, we find that the stability will be grater if the e-donation power is greater.

Thus it is clear that greater basic power of electron-donating species will form always a stable complex. NH3, CN�, and F� behaved as ligands and formed stable complexes; on the other hand, these are more basic in nature.

#### **4.9 Ligand concentration**

We know that if the concentration of coordination group is higher, these coordination compounds will exist in the water as solution. It is noted that greater coordinating tendency show the water molecules than the coordinating group which is originally present. SCN� (thiocynate) ions are present in higher concentration; with the Co2+ metal ion, it formed a blue-colored complex which is stable in state, but on dilution of water medium, a pink color is generated in place of blue, or blue color complex is destroyed by [Co(H2O)6] 2+, and now if we added further SCN�, the pink color will not appear:

$$\begin{aligned} \left[\text{Co(SCN)}\_{4}\right]^{2} &- + \text{H}\_{2}\text{O} \Leftrightarrow \left[\text{Co(H}\_{2}\text{O)}\_{6}\right]^{2+} + 4\text{SCN}^{-}\\ \text{Blue} & \text{Pink} \end{aligned} \tag{28}$$

Metal <sup>þ</sup> 2 Ligand \$ MetalLigand2 <sup>K</sup> <sup>¼</sup> ð Þ *ML*<sup>2</sup>

or (33)

The sizes of the chelating ring are increased as well as the stability of metal complex decreased. According to Schwarzenbach, connecting bridges form the chelating rings. The elongated ring predominates when long bridges connect to the ligand to form a long ring. It is usually observed that an increased a chelate ring size

He interpreted this statement. The entropy of complex will be change if the size of chelating ring is increased, i.e., second donor atom is allowed by the chelating ring. As the size of chelating ring increased, the stability should be increased with entropy effect. Four-membered ring compounds are unstable, whereas five-membered are more stable. So the chelating ring increased its size and the

The number of chelating rings also decides the stability of complexes. Nonchelating metal compounds are less stable than chelating compounds. These numbers increase the thermodynamic volume, and this is also known as an entropy term. In recent years ligands capable of occupying as many as six coordination positions on a single metal ion have been described. The studies on the formation constants of coordination compounds with these ligands have been reported.

Some factors are of much importance for chelation as follows.

**4.11 Ring size**

**Figure 2.**

**Figure 3.**

leads to a decrease in complex stability.

*Structure of chelating configuration of ethylenediamine ligand.*

*Stability Constants of Metal Complexes in Solution DOI: http://dx.doi.org/10.5772/intechopen.90183*

*Structure of chelate with three ethylenediamine ligands.*

stability of the formed metal complexes.

**4.12 Number of rings**

**51**

Metal þ Ligand–Ligand \$ MetalLigand � Ligand (32)

½ � *<sup>M</sup>* ½ � *<sup>L</sup>* <sup>2</sup> (31)

Now it is clear that H2O and SCN� are in competition for the formation of Co(II) metal-containing complex compound. In the case of tetra-amine cupric sulfate metal complex, ammonia acts as a donor atom or ligand. If the concentration of NH3 is lower in the reaction, copper hydroxide is formed but at higher concentration formed tetra-amine cupric sulfate as in the following reaction:

$$\text{CuSO}\_4 + \text{NH}\_4\text{OH} \rightarrow \text{Cu(OH)}\_2 \text{ (Small quantity of ligand)}\tag{29}$$

CuSO4 þ NH4OH ! Cu OH ð Þ2½ � Cu NH ð Þ<sup>4</sup> 2SO4*:*H2O ð Þ High concentration of ligand (30)

#### **4.10 Chelating effect**

For a metal ion, chelating ligand is enhanced and affinity it and this is known as chelate effect and compared it with non-chelating and monodentate ligand or the multidentate ligand is acts as chelating agent. Ethylenediamine is a simple chelating agent (**Figure 1**).

Due to the bidentate nature of ethylenediamine, it forms two bonds with metal ion or central atom. Water forms a complex with Ni(II) metal ion, but due to its monodentate nature, it is not a chelating ligand (**Figures 2** and **3**).

The dentate cheater of ligand provides bonding strength to the metal ion or central atom, and as the number of dentate increased, the tightness also increased. This phenomenon is known as chelating effect, whereas the formation of metal complexes with these chelating ligands is called chelation:

$$
\sim \sim^{\text{NH}\_2}
$$

**Figure 1.** *Structure of ethylenediamine.* *Stability Constants of Metal Complexes in Solution DOI: http://dx.doi.org/10.5772/intechopen.90183*

**Figure 2.** *Structure of chelating configuration of ethylenediamine ligand.*

**Figure 3.** *Structure of chelate with three ethylenediamine ligands.*

$$\text{Metal} + 2\text{ Ligand} \leftrightarrow \text{MetalLigand}\_2\text{ K} = \frac{(\text{ML2})}{[\text{M}][\text{L}]2} \tag{31}$$

$$\text{Metal} + \text{Ligand-Ligand} \leftrightarrow \text{MetalLigand} - \text{Ligand} \tag{32}$$

It means that the donating power of ligands to central metal ions is high. In the case of complex formation of aliphatic diamines and aromatic diamines, the stable complex is formed by aliphatic diamines, while an unstable coordination complex is formed with aromatic diamines. So, from the above discussion, we find that the

Thus it is clear that greater basic power of electron-donating species will form always a stable complex. NH3, CN�, and F� behaved as ligands and formed stable

We know that if the concentration of coordination group is higher, these coor-

Now it is clear that H2O and SCN� are in competition for the formation of Co(II)

metal-containing complex compound. In the case of tetra-amine cupric sulfate metal complex, ammonia acts as a donor atom or ligand. If the concentration of NH3 is lower in the reaction, copper hydroxide is formed but at higher concentration

CuSO4 þ NH4OH ! Cu OH ð Þ<sup>2</sup> Small quantity of ligand

CuSO4 þ NH4OH ! Cu OH ð Þ2½ � Cu NH ð Þ<sup>4</sup> 2SO4*:*H2O ð Þ High concentration of ligand

For a metal ion, chelating ligand is enhanced and affinity it and this is known as chelate effect and compared it with non-chelating and monodentate ligand or the multidentate ligand is acts as chelating agent. Ethylenediamine is a simple chelating

Due to the bidentate nature of ethylenediamine, it forms two bonds with metal ion or central atom. Water forms a complex with Ni(II) metal ion, but due to its

The dentate cheater of ligand provides bonding strength to the metal ion or central atom, and as the number of dentate increased, the tightness also increased. This phenomenon is known as chelating effect, whereas the formation of metal

2+, and now if we added further

(29)

(28)

(30)

<sup>2</sup><sup>þ</sup> <sup>þ</sup> 4SCN�

dination compounds will exist in the water as solution. It is noted that greater coordinating tendency show the water molecules than the coordinating group which is originally present. SCN� (thiocynate) ions are present in higher concentration; with the Co2+ metal ion, it formed a blue-colored complex which is stable in state, but on dilution of water medium, a pink color is generated in place of blue, or

<sup>2</sup> � þH2O ⇆ Co Hð Þ 2O <sup>6</sup>

Blue Pink

formed tetra-amine cupric sulfate as in the following reaction:

monodentate nature, it is not a chelating ligand (**Figures 2** and **3**).

complexes with these chelating ligands is called chelation:

stability will be grater if the e-donation power is greater.

*Stability and Applications of Coordination Compounds*

blue color complex is destroyed by [Co(H2O)6]

Co SCN ð Þ<sup>4</sup>

SCN�, the pink color will not appear:

**4.9 Ligand concentration**

**4.10 Chelating effect**

agent (**Figure 1**).

**Figure 1.**

**50**

*Structure of ethylenediamine.*

complexes; on the other hand, these are more basic in nature.

$$\text{or} \tag{33}$$

$$\text{For} \tag{34}$$

$$\text{If } \underbrace{\text{(2-10)}}\_{\text{(2-10)}} = \text{N} \tag{35}$$

Some factors are of much importance for chelation as follows.

#### **4.11 Ring size**

The sizes of the chelating ring are increased as well as the stability of metal complex decreased. According to Schwarzenbach, connecting bridges form the chelating rings. The elongated ring predominates when long bridges connect to the ligand to form a long ring. It is usually observed that an increased a chelate ring size leads to a decrease in complex stability.

He interpreted this statement. The entropy of complex will be change if the size of chelating ring is increased, i.e., second donor atom is allowed by the chelating ring. As the size of chelating ring increased, the stability should be increased with entropy effect. Four-membered ring compounds are unstable, whereas five-membered are more stable. So the chelating ring increased its size and the stability of the formed metal complexes.

#### **4.12 Number of rings**

The number of chelating rings also decides the stability of complexes. Nonchelating metal compounds are less stable than chelating compounds. These numbers increase the thermodynamic volume, and this is also known as an entropy term. In recent years ligands capable of occupying as many as six coordination positions on a single metal ion have been described. The studies on the formation constants of coordination compounds with these ligands have been reported.

The numbers of ligand or chelating agents are affecting the stability of metal complexes so as these numbers go up and down, the stability will also vary with it.

For the Ni(II) complexes with ethylenediamine as chelating agent, its log K1 value is 7.9 and if chelating agents are trine and penten, then the log K1 values are 7.9 and 19.3, respectively. If the metal ion change Zn is used in place of Ni (II), then the values of log K1 for ethylenediamine, trine, and penten are 6.0, 12.1, and 16.2, respectively. The log βMY values of metal ions are given in **Table 1**.

Ni(NH3)6 2+ is an octahedral metal complex, and at 25 °C its log β<sup>6</sup> value is 8.3, but Ni(ethylenediamine)3 2+ complex is also octahedral in geometry, with 18.4 as the value of log β6. The calculated stability value of Ni(ethylenediamine)3 2+ 1010 times is more stable because three rings are formed as chelating rings by ethylenediamine as compared to no such ring is formed. Ethylenediaminetetraacetate (EDTA) is a hexadentate ligand that usually formed stable metal complexes due to its chelating power.

#### **4.13 Steric effect**

A special effect in molecules is when the atoms occupy space. This is called steric effect. Energy is needed to bring these atoms closer to each other. These electrons run away from near atoms. There can be many ways of generating it. We know the repulsion between valence electrons as the steric effect which increases the energy of the current system [21]. Favorable or unfavorable any response is created.

For example, if the static effect is greater than that of a product in a metal complex formation process, then the static increase would favor this reaction. But if the case is opposite, the skepticism will be toward retardation.

This effect will mainly depend on the conformational states, and the minimum steric interaction theory can also be considered. The effect of secondary steric is seen on receptor binding produced by an alternative such as:

tetradentate cyclic ligand, we can use heme-B which forms a metal complex using

*Structure of hemoglobin is the biological complex compound which contains Fe(II) metal ion.*

stable metal complexes as compared to n-unidentate ligands. But the n-dentate macrocyclic ligand gives more stable environment in the metal complexes as compared to open-chain ligands. This change is very favorable for entropy (ΔS) and

**5. Determination of stability constants of complexes in solution**

**5.1 Methods based on study of heterogeneous equilibrium**

The n-dentate chelating agents play an important role for the formation of more

There are so many parameters to determination of formation constants or stability constant in solution for all types of chelating agents. These numerous parameters or techniques are refractive index, conductance, temperature, distribution coefficients, refractive index, nuclear magnetic resonance volume changes, and

Solubility products are helpful and used for the insoluble salt that metal ions formed and complexes which are also formed by metal ions and are more soluble. The formation constant is observed in presence of donor atoms by measuring

Fe+2 ions in biological systems (**Figure 4**).

*Stability Constants of Metal Complexes in Solution DOI: http://dx.doi.org/10.5772/intechopen.90183*

enthalpy (ΔH) change.

**Figure 4.**

optical activity.

*5.1.1 Solubility methods*

increased solubility.

**53**


#### **4.14 Macrocyclic effect**

The macrocyclic effect is exactly like the image of the chelate effect. It means the principle of both is the same. But the macrocyclic effect suggests cyclic deformation of the ligand. Macrocyclic ligands are more tainted than chelating agents. Rather, their compounds are more stable due to their cyclically constrained constriction. It requires some entropy in the body to react with the metal ion. For example, for a


**Table 1.** *Metal ion vs. log βMY values.* *Stability Constants of Metal Complexes in Solution DOI: http://dx.doi.org/10.5772/intechopen.90183*

The numbers of ligand or chelating agents are affecting the stability of metal complexes so as these numbers go up and down, the stability will also vary with it. For the Ni(II) complexes with ethylenediamine as chelating agent, its log K1 value is 7.9 and if chelating agents are trine and penten, then the log K1 values are 7.9 and 19.3, respectively. If the metal ion change Zn is used in place of Ni (II), then the values of log K1 for ethylenediamine, trine, and penten are 6.0, 12.1, and 16.2,

stable because three rings are formed as chelating rings by ethylenediamine as compared to no such ring is formed. Ethylenediaminetetraacetate (EDTA) is a hexadentate

A special effect in molecules is when the atoms occupy space. This is called steric effect. Energy is needed to bring these atoms closer to each other. These electrons run away from near atoms. There can be many ways of generating it. We know the repulsion between valence electrons as the steric effect which increases the energy of the current system [21]. Favorable or unfavorable any response is created. For example, if the static effect is greater than that of a product in a metal complex formation process, then the static increase would favor this reaction. But if

This effect will mainly depend on the conformational states, and the minimum steric interaction theory can also be considered. The effect of secondary steric is

The macrocyclic effect is exactly like the image of the chelate effect. It means the principle of both is the same. But the macrocyclic effect suggests cyclic deformation of the ligand. Macrocyclic ligands are more tainted than chelating agents. Rather, their compounds are more stable due to their cyclically constrained constriction. It requires some entropy in the body to react with the metal ion. For example, for a

**Metal ion log βMY (25°C, I = 0.1 M)**

Ca2+ 11.2 Cu2+ 19.8 Fe3+ 24.9

ligand that usually formed stable metal complexes due to its chelating power.

2+ is an octahedral metal complex, and at 25 °C its log β<sup>6</sup> value is 8.3, but

2+ complex is also octahedral in geometry, with 18.4 as the value

2+ 1010 times is more

respectively. The log βMY values of metal ions are given in **Table 1**.

of log β6. The calculated stability value of Ni(ethylenediamine)3

*Stability and Applications of Coordination Compounds*

the case is opposite, the skepticism will be toward retardation.

seen on receptor binding produced by an alternative such as:

3.Electronic resonance substitution bond by repulsion.

4.Population of a conformer changes due to active shielding effect.

1.Reduced access to a critical group.

Ni(NH3)6

**4.13 Steric effect**

2. Stick barrier.

**4.14 Macrocyclic effect**

**Table 1.**

**52**

*Metal ion vs. log βMY values.*

Ni(ethylenediamine)3

**Figure 4.** *Structure of hemoglobin is the biological complex compound which contains Fe(II) metal ion.*

tetradentate cyclic ligand, we can use heme-B which forms a metal complex using Fe+2 ions in biological systems (**Figure 4**).

The n-dentate chelating agents play an important role for the formation of more stable metal complexes as compared to n-unidentate ligands. But the n-dentate macrocyclic ligand gives more stable environment in the metal complexes as compared to open-chain ligands. This change is very favorable for entropy (ΔS) and enthalpy (ΔH) change.

## **5. Determination of stability constants of complexes in solution**

There are so many parameters to determination of formation constants or stability constant in solution for all types of chelating agents. These numerous parameters or techniques are refractive index, conductance, temperature, distribution coefficients, refractive index, nuclear magnetic resonance volume changes, and optical activity.

#### **5.1 Methods based on study of heterogeneous equilibrium**

#### *5.1.1 Solubility methods*

Solubility products are helpful and used for the insoluble salt that metal ions formed and complexes which are also formed by metal ions and are more soluble. The formation constant is observed in presence of donor atoms by measuring increased solubility.

#### *5.1.2 Distribution method*

To determine the solubility constant, it involves the distribution of the ligands or any complex species; metal ions are present in two immiscible solvents like water and carbon tetrachloride, benzene, etc.

equilibrium concentration of the ion studied may be determined by the action of

The solution of 25 ml is adopted by preparing at the 1.0 � <sup>10</sup>�<sup>5</sup> M ligand or

The solutions containing the metal ions were considered both at a pH sufficiently high to give almost complete complexation and at a pH value selected in

In order to avoid modification of the spectral behavior of the ligand due to pH variations, it has been verified that the range of pH considered in all cases does not affect absorbance values. Use the collected pH values adopted for the determinations as well as selected wavelengths. The ionic strengths calculated from the composition of solutions allowed activity coefficient corrections. Absorbance values

For a successive metal complex formation, use this method. If ligand is protonate and the produced complex has maximum number of donate atoms of ligands, a selective light is absorbed by this complex, while for determination of stability

Bjerrum (1941) used the method stepwise addition of the ligands to coordination

sphere for the formation of complex. So, complex metal–ligand-n forms as the following steps [22]. The equilibrium constants, K1, K2, K3, … Kn are called stepwise stability constants. The formation of the complex metal-ligandn may also be

N = maximum coordination number for the metal ion M for the ligand

Metal <sup>þ</sup> Ligand ⇆ Metal � Ligand K1 <sup>¼</sup> ð Þ *ML*

Metal � Ligand ⇆ Metal � Ligand2 K2 <sup>¼</sup> ð Þ *ML*<sup>2</sup>

Metal � Ligand2 ⇆ Metal � Ligand3 K3 <sup>¼</sup> ð Þ *ML*<sup>3</sup>

If a complex ion is slow to reach equilibrium, it is often possible to apply the method of isotopic dilution to determine the equilibrium concentration of one or

Thus Metal � Ligandn�<sup>1</sup> <sup>þ</sup> Ligand ⇆ Metal � Ligandn Kn <sup>¼</sup> ð Þ *MLn*

more of the species. Most often radioactive isotopes are used.

½ � *<sup>M</sup>* ½ � *<sup>L</sup>* (34)

½ � *ML* ½ � *<sup>L</sup>* (35)

½ � *ML*<sup>2</sup> ½ � *<sup>L</sup>* (36)

½ � *MLn*�<sup>1</sup> ½ � *<sup>L</sup>* (37)

1.0 � <sup>10</sup>�<sup>5</sup> M concentration and 1.0 � <sup>10</sup>�<sup>5</sup> M for the metal ion:

order to obtain an equilibrium system of ligand and complexes.

were determined at wavelengths in the range 430–700 nm, every 2 nm.

constant, it is just known about the composition of formed species.

expressed by the following steps and equilibrium constants.

this organ in systems with complex formation.

*Stability Constants of Metal Complexes in Solution DOI: http://dx.doi.org/10.5772/intechopen.90183*

*5.2.4 Spectrophotometric method*

*5.2.5 Bjerrum's method*

Where:

M = central metal cation L = monodentate ligand

*5.2.6 Isotopic dilution method*

**55**

#### *5.1.3 Ion exchange method*

In this method metal ions or ligands are present in solution and on exchanger. A solid polymers containing with positive and negative ions are ion exchange resins. These are insoluble in nature. This technique is helpful to determine the metal ions in resin phase, liquid phase, or even in radioactive metal. This method is also helpful to determine the polarizing effect of metal ions on the stability of ligands like Cu(II) and Zn(II) with amino acid complex formation.

#### *5.1.4 Electrometric techniques*

At the equilibrium free metal and ions are present in the solution, and using the different electrometric techniques as described determines its stability constant.

#### *5.1.5 Potentiometric methods*

This method is based upon the titration method or follows its principle. A stranded acid-base solution used as titrate and which is titrated, it may be strong base or strong acid follows as potentiometrically. The concentration of solution using 10<sup>3</sup> M does not decomposed during the reaction process, and this method is useful for protonated and nonprotonated ligands.

#### *5.1.6 Polarographic method*

This is the graphic method used to determine the stability constant in producing metal complex formation by plotting a polarograph between the absences of substances and the presence of substances. During the complex formation, the presence of metal ions produced a shift in the half-wave potential in the solution.

#### **5.2 Other methods**

#### *5.2.1 Rate method*

If a complex is relatively slow to form and also decomposes at measurable rate, it is possible, in favorable situations, to determine the equilibrium constant.

#### *5.2.2 Freezing technique*

This involves the study of the equilibrium constant of slow complex formation reactions. The use of tracer technique is extremely useful for determining the concentrations of dissociation products of the coordination compound.

#### *5.2.3 Biological method*

This method is based on the study of the effect of an equilibrium concentration of some ions on the function at a definite organ of a living organism. The

equilibrium concentration of the ion studied may be determined by the action of this organ in systems with complex formation.
