Stability Constants of Metal Complexes in Solution

*Jagvir Singh, Abhay Nanda Srivastav, Netrapal Singh and Anuradha Singh*

## **Abstract**

In the formation of metal complexes in an aqueous medium, equilibrium constant or stability constant is used to determine the strength of interaction between reagents that make the final product after the formation of bonds. In general stability means that a complex may be stored for a long time under suitable conditions or this compound may be existing under suitable conditions. Regarding how much is the concentration of complexes in solution, stability constant provides this information via calculations. These calculations are very much important in many areas of science like chemistry, biology, and medicine. During the complex formation in aqueous medium, two types of stabilities are considered: one is the thermodynamic stability, and the other is kinetic stability. Stability of metal complexes may be affected by various factors like nature of central metal ion and ligand, chelating effect, etc., and some parameters like distribution coefficients, conductance, refractive index, etc. are useful for the determination of stability constants. Various modern techniques are used to determine the stability constant of simple as well as mixed ligand compounds.

**Keywords:** thermodynamic stability, kinetic stability, chelate effect, distribution method, ion exchange method, Bjerrum's method

### **1. Introduction**

Stability constant of the formation of metal complexes is used to measure interaction strength of reagents. From this process, metal ion and ligand interaction formed the two types of metal complexes; one is supramolecular complexes known as host-guest complexes [1] and the other is anion-containing complexes. In the solution it provides and calculates the required information about the concentration of metal complexes.

Solubility, light, absorption conductance, partitioning behavior, conductance, and chemical reactivity are the complex characteristics which are different from their components. It is determined by various numerical and graphical methods which calculate the equilibrium constants. This is based on or related to a quantity, and this is called the complex formation function.

During the displacement process at the time of metal complex formation, some ions disappear and form a bonding between metal ions and ligands. It may be considered due to displacement of a proton from a ligand species or ions or molecules causing a drop in the pH values of the solution [2]. Irving and Rossotti

developed a technique for the calculation of stability constant, and it is called potentiometric technique.

formation of ternary metal complex formation was in a stepwise manner that provided an easy way to calculate stability constants for the formation of metal

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

surements have ascertained for the mode of ternary chelating complexes.

conjectures such metal complexes. It is only at alkaline pH values.

–7.0 <sup>10</sup><sup>3</sup> mol/dm3 for MG and 6.0 <sup>10</sup><sup>5</sup>

the applications and solutions of stability of metal complexes in solution.

**2. Stability constant of metal complexes**

The values of Δ log *K*, percentage of relative stabilization (% R. S.), and log *X* were evaluated and discussed. Now it provides the outline about the various complex species for the formation of different solvents, and using the concentration distribution, these complexes were evaluated and discussed. The conductivity mea-

A study by Kathrina and Pekar suggests that pH plays an important role in the formation of metal complexes. When epigallocatechin gallate and gallic acid combine with copper(II) to form metal complexes, the pH changes its speculation. We have been able to determine its pH in frozen and fluid state with the help of multifrequency EPR spectroscopy [8]. With the help of this spectroscopy, it is able to detect that each polyphenol exhibits the formation of three different mononuclear species. If the pH ranges 4–8 for di- or polymeric complex of Cu(II), then it

The line width in fluid solutions by molecular motion exhibits an incomplete average of the parameters of anisotropy spin Hamilton. If the complexes are different, then their rotational correlation times for this also vary. The analysis of the LyCEP anisotropy of the fluid solution spectra is performed using the parameters determined by the simulation of the rigid boundary spectra. Its result suggests that pH increases its value by affecting its molecular mass. It is a polyphenol ligand complex with copper, showing the coordination of an increasing number of its molecules or increasing participation of polyphenol dimers used as ligands in the

The study by Vishenkova and his co-worker [8] provides the investigation of electrochemical properties of triphenylmethane dyes using a voltammetric method with constant-current potential sweep. Malachite green (MG) and basic fuchsin (BF) have been chosen as representatives of the triphenylmethane dyes [9]. The electrochemical behavior of MG and BF on the surface of a mercury film electrode depending on pH, the nature of background electrolyte, and scan rate of potential

Using a voltammetric method with a constant-current potential sweep examines the electrical properties of triphenylmethane dye. In order to find out the solution of MG and BF, certain registration conditions have been prescribed for it, which have proved to be quite useful. The reduction peak for the currents of MG and BF has demonstrated that it increases linearly with respect to their concentration as

and correlation coefficients of these values are 0.9987 for MG and 0.9961 for BF [10]. 5.0 <sup>10</sup><sup>5</sup> and 2.0 <sup>10</sup><sup>5</sup> mol/dm3 are the values used as the detection limit of MG and BF, respectively. Stability constants are a very useful technique whose size is huge. Due to its usefulness, it has acquired an umbrella right in the fields of chemistry, biology, and medicine. No science subject is untouched by this. Stability constants of metal complexes are widely used in the various areas like pharmaceuticals as well as biological processes, separation techniques, analytical processes, etc. In the presented chapter, we have tried to explain this in detail by focusing our attention on

Stability or formation or binding constant is the type of equilibrium constant

used for the formation of metal complexes in the solution. Acutely, stability

–8.0 <sup>10</sup><sup>3</sup> mol/dm3 for BF

complexes.

copper coordination region.

sweep has been investigated.

9.0 <sup>10</sup><sup>5</sup>

**43**

To determine the stability constant, Bjerrum has used a very simple method, and that is metal salt solubility method. For the studies of a larger different variety of polycarboxylic acid-, oxime-, phenol-containing metal complexes, Martel and Calvin used the potentiometric technique for calculating the stability constant. Those ligands [3, 4] which are uncharged are also examined, and their stability constant calculations are determined by the limitations inherent in the ligand solubility method. The limitations of the metal salt solubility method and the result of solubility methods are compared with this. M-L, MLM, and (M3) L are some types of examples of metal-ligand bonding. One thing is common, and that is these entire types metal complexes all have one ligand.

The solubility method can only usefully be applied to studies of such complexes, and it is best applied for ML; in such types of system, only ML is formed. Jacqueline Gonzalez and his co-worker propose to explore the coordination chemistry of calcium complexes. Jacqueline and et al. followed this technique for evaluate the as partial model of the manganese-calcium cluster and spectrophotometric studies of metal complexes, i.e., they were carried calcium(II)-1,4-butanediamine in acetonitrile and calcium(II)-1,2-ethylendiamine, calcium(II)-1,3-propanediamine by them.

Spectrophotometric programming of HypSpec and received data allows the determination of the formation of solubility constants. The logarithmic values, log β<sup>110</sup> = 5.25 for calcium(II)-1,3-propanediamine, log β<sup>110</sup> = 4.072 for calcium(II)- 1,4-butanediamine, and log β<sup>110</sup> = 4.69 for calcium(II)-1,2-ethylendiamine, are obtained for the formation constants [5]. The structure of Cimetidine and histamine H2-receptor is a chelating agent. Syed Ahmad Tirmizi has examined Ni(II) cimetidine complex spectrophotometrically and found an absorption peak maximum of 622 nm with respect to different temperatures.

Syed Ahmad Tirmizi have been used to taken 1:2 ratio of metal and cimetidine compound for the formation of metal complex and this satisfied by molar ratio data. The data, 1.40–2.4 108 , was calculated using the continuous variation method and stability constant at room temperature, and by using the mole ratio method, this value at 40°C was 1.24–2.4 <sup>10</sup><sup>8</sup> . In the formation of lead(II) metal complexes with 1-(aminomethyl) cyclohexene, Thanavelan et al. found the formation of their binary and ternary complexes. Glycine, L-proline, L-alanine, L-isoleucine, L-valine, and L-leucine are α-amino acids, and these are important biologically [6]. These α-amino acids are also investigated by potentiometric technique at 32°C. The mixed ligands were also studied using these methods. 50% (v/v) DMSO-water medium used for the determination of acidity constants and their stability constants these type ligands. In a stepwise manner, the ternary complexes were synthesized.

Using the stability constant method, these ternary complexes were found out, and using the parameters such as Δ log *K* and log *X*, these ternary complex data were compared with binary complex. The potentiometric technique at room temperature (25°C) was used in the investigation of some binary complex formations by Abdelatty Mohamed Radalla. These binary complexes are formed with 3D transition metal ions like Cu2+, Ni2+, Co2+, and Zn2+ and gallic acid's importance as a ligand and 0.10 mol dm<sup>3</sup> of NaNO3. Such types of aliphatic dicarboxylic acids are very important biologically. Many acid-base characters and the nature of using metal complexes have been investigated and discussed time to time by researchers [7].

The above acids (gallic and aliphatic dicarboxylic acid) were taken to determine the acidity constants. For the purpose of determining the stability constant, binary and ternary complexes were carried in the aqueous medium using the experimental conditions as stated above. The potentiometric pH-metric titration curves are inferred for the binary complexes and ternary complexes at different ratios, and

developed a technique for the calculation of stability constant, and it is called

To determine the stability constant, Bjerrum has used a very simple method, and that is metal salt solubility method. For the studies of a larger different variety of polycarboxylic acid-, oxime-, phenol-containing metal complexes, Martel and Calvin used the potentiometric technique for calculating the stability constant. Those ligands [3, 4] which are uncharged are also examined, and their stability constant calculations are determined by the limitations inherent in the ligand solubility method. The limitations of the metal salt solubility method and the result of solubility methods are compared with this. M-L, MLM, and (M3) L are some types of examples of metal-ligand bonding. One thing is common, and that is these entire

The solubility method can only usefully be applied to studies of such complexes, and it is best applied for ML; in such types of system, only ML is formed. Jacqueline Gonzalez and his co-worker propose to explore the coordination chemistry of calcium complexes. Jacqueline and et al. followed this technique for evaluate the as partial model of the manganese-calcium cluster and spectrophotometric studies of metal complexes, i.e., they were carried calcium(II)-1,4-butanediamine in acetonitrile and

calcium(II)-1,2-ethylendiamine, calcium(II)-1,3-propanediamine by them.

Spectrophotometric programming of HypSpec and received data allows the determination of the formation of solubility constants. The logarithmic values, log β<sup>110</sup> = 5.25 for calcium(II)-1,3-propanediamine, log β<sup>110</sup> = 4.072 for calcium(II)- 1,4-butanediamine, and log β<sup>110</sup> = 4.69 for calcium(II)-1,2-ethylendiamine, are obtained for the formation constants [5]. The structure of Cimetidine and histamine H2-receptor is a chelating agent. Syed Ahmad Tirmizi has examined Ni(II) cimetidine complex spectrophotometrically and found an absorption peak maximum of

Syed Ahmad Tirmizi have been used to taken 1:2 ratio of metal and cimetidine compound for the formation of metal complex and this satisfied by molar ratio data.

stability constant at room temperature, and by using the mole ratio method, this

Using the stability constant method, these ternary complexes were found out, and using the parameters such as Δ log *K* and log *X*, these ternary complex data were compared with binary complex. The potentiometric technique at room temperature

Abdelatty Mohamed Radalla. These binary complexes are formed with 3D transition metal ions like Cu2+, Ni2+, Co2+, and Zn2+ and gallic acid's importance as a ligand and 0.10 mol dm<sup>3</sup> of NaNO3. Such types of aliphatic dicarboxylic acids are very important biologically. Many acid-base characters and the nature of using metal complexes have been investigated and discussed time to time by researchers [7]. The above acids (gallic and aliphatic dicarboxylic acid) were taken to determine the acidity constants. For the purpose of determining the stability constant, binary and ternary complexes were carried in the aqueous medium using the experimental conditions as stated above. The potentiometric pH-metric titration curves are inferred for the binary complexes and ternary complexes at different ratios, and

(25°C) was used in the investigation of some binary complex formations by

1-(aminomethyl) cyclohexene, Thanavelan et al. found the formation of their binary and ternary complexes. Glycine, L-proline, L-alanine, L-isoleucine, L-valine, and L-leucine are α-amino acids, and these are important biologically [6]. These α-amino acids are also investigated by potentiometric technique at 32°C. The mixed ligands were also studied using these methods. 50% (v/v) DMSO-water medium used for the determination of acidity constants and their stability constants these type ligands. In a stepwise manner, the ternary complexes were synthesized.

, was calculated using the continuous variation method and

. In the formation of lead(II) metal complexes with

potentiometric technique.

types metal complexes all have one ligand.

*Stability and Applications of Coordination Compounds*

622 nm with respect to different temperatures.

The data, 1.40–2.4 108

**42**

value at 40°C was 1.24–2.4 <sup>10</sup><sup>8</sup>

formation of ternary metal complex formation was in a stepwise manner that provided an easy way to calculate stability constants for the formation of metal complexes.

The values of Δ log *K*, percentage of relative stabilization (% R. S.), and log *X* were evaluated and discussed. Now it provides the outline about the various complex species for the formation of different solvents, and using the concentration distribution, these complexes were evaluated and discussed. The conductivity measurements have ascertained for the mode of ternary chelating complexes.

A study by Kathrina and Pekar suggests that pH plays an important role in the formation of metal complexes. When epigallocatechin gallate and gallic acid combine with copper(II) to form metal complexes, the pH changes its speculation. We have been able to determine its pH in frozen and fluid state with the help of multifrequency EPR spectroscopy [8]. With the help of this spectroscopy, it is able to detect that each polyphenol exhibits the formation of three different mononuclear species. If the pH ranges 4–8 for di- or polymeric complex of Cu(II), then it conjectures such metal complexes. It is only at alkaline pH values.

The line width in fluid solutions by molecular motion exhibits an incomplete average of the parameters of anisotropy spin Hamilton. If the complexes are different, then their rotational correlation times for this also vary. The analysis of the LyCEP anisotropy of the fluid solution spectra is performed using the parameters determined by the simulation of the rigid boundary spectra. Its result suggests that pH increases its value by affecting its molecular mass. It is a polyphenol ligand complex with copper, showing the coordination of an increasing number of its molecules or increasing participation of polyphenol dimers used as ligands in the copper coordination region.

The study by Vishenkova and his co-worker [8] provides the investigation of electrochemical properties of triphenylmethane dyes using a voltammetric method with constant-current potential sweep. Malachite green (MG) and basic fuchsin (BF) have been chosen as representatives of the triphenylmethane dyes [9]. The electrochemical behavior of MG and BF on the surface of a mercury film electrode depending on pH, the nature of background electrolyte, and scan rate of potential sweep has been investigated.

Using a voltammetric method with a constant-current potential sweep examines the electrical properties of triphenylmethane dye. In order to find out the solution of MG and BF, certain registration conditions have been prescribed for it, which have proved to be quite useful. The reduction peak for the currents of MG and BF has demonstrated that it increases linearly with respect to their concentration as 9.0 <sup>10</sup><sup>5</sup> –7.0 <sup>10</sup><sup>3</sup> mol/dm3 for MG and 6.0 <sup>10</sup><sup>5</sup> –8.0 <sup>10</sup><sup>3</sup> mol/dm3 for BF and correlation coefficients of these values are 0.9987 for MG and 0.9961 for BF [10].

5.0 <sup>10</sup><sup>5</sup> and 2.0 <sup>10</sup><sup>5</sup> mol/dm3 are the values used as the detection limit of MG and BF, respectively. Stability constants are a very useful technique whose size is huge. Due to its usefulness, it has acquired an umbrella right in the fields of chemistry, biology, and medicine. No science subject is untouched by this. Stability constants of metal complexes are widely used in the various areas like pharmaceuticals as well as biological processes, separation techniques, analytical processes, etc. In the presented chapter, we have tried to explain this in detail by focusing our attention on the applications and solutions of stability of metal complexes in solution.

### **2. Stability constant of metal complexes**

Stability or formation or binding constant is the type of equilibrium constant used for the formation of metal complexes in the solution. Acutely, stability

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

$$\text{Metal} + \text{Ligand} \leftrightharpoons \text{Metal} - \text{Ligand} \,\mathrm{K}\_1 = \frac{(ML)}{[M][L]} \tag{1}$$

Now we expressed it as the following:

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

thermodynamic stability and kinetic stability.

**3.1 Thermodynamic stability**

the following reaction:

rium constant is response:

R = gas constant

T = absolute temperature

Where:

At 25°C,

**45**

are not zero at this stage but are equal.

*<sup>β</sup><sup>n</sup>* <sup>¼</sup> <sup>X</sup>*n*¼*<sup>n</sup> n*¼1

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

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

If hydrogen and iodine are kept together in molecular proportions in a closed

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

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 equilib-

H2 þ I2 ! 2HI (12)

2HI ! H2 þ I2 (13)

ΔG ¼ �2*:*303 RT log <sup>10</sup> β*:* (14)

process vessel at high temperature (500°C), the following action begins:

*Kn* (11)

$$\text{Metal} + \text{Ligands} \leftrightharpoons \text{Metal} + \text{Ligand}\_2\text{ K}\_2 = \frac{(ML\_2)}{[ML][L]} \tag{2}$$

$$\text{Metal} + \text{Ligmoid}\_{\text{\textsuperscript{\text{\tiny}}}} \text{\textsuperscript{\text{\tiny}} \text{Metal} + \text{Ligmoid}\_{\text{\tiny}} \text{K}\_{\text{\tiny}} = \frac{(ML\_3)}{[ML\_2][L]} \tag{3}$$

Thus

$$\text{Metal} + \text{Ligand}\_{n-1} + \text{L} \leftrightharpoons \text{Metal} + \text{Ligand}\_{-n}\text{K}\_{n} = \frac{(ML\_{n})}{[ML\_{n-1}][L]} \tag{4}$$

K1, K2, K3, … Kn are the equilibrium constants and these are also called stepwise stability constants. The formation of the metal-ligand-n complex may also be expressed as equilibrium constants by the following steps:

$$\text{Metal} + \text{Ligand} \xrightarrow{R\_1} \text{Metal} - \text{Ligand}, \beta = \frac{(\text{ML})}{[\text{M}][\text{L}]} \tag{5}$$

$$\text{Metal} + 2\text{Ligand} \xrightarrow{B\_1} \text{Metal} - \text{Ligand}\_2,\\ \beta\_2 = \frac{(ML\_2)}{[M][L]^2} \tag{6}$$

$$\text{Thus } \text{Metal} + \text{nLigand} \xrightarrow{B\_s} \text{Metal} - \text{ligand} \\ \text{Ln}, \beta\_n = \frac{(MLn)}{[M][L]^n} \tag{7}$$

*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 stepwise and cumulative stability constants.
