METAL LIGAND COMPLEXEs - Shodhganga

CHAPTER 4

METAL-LIGAND COMPLEXES

SECTION-1

DETERMINATION OF BINARY STABILITY CONSTANTS

Introduction

Stability constants are well known tools for solution chemists,
biochemists and chemists in general to help determine the properties
of metal-ligand reactions in water and biological systems. They have
important medicinal implication to measure the metal ligand
selectivity in terms of relative strength of metal-ligand bonds1. Metal
coordination complexes have been extensively used in clinical
applications as enzyme inhibitors2, anti-bacterial3,4, antiviral5-7 and as
anti-cancer8-10 drugs. Transition metal ion chelate complexes are also
exploited by industry in the large-scale purification of amino acids and
a wide range of drug and drug precursors containing an amino
carboxylic acid moiety11,12.

The formation of metal complexes can be represented by
Equilibrium 4.1.

pM + qL + rH MpLqHr -----4.1

The stability of complexes can be quantified by using

equilibrium constant as expressed in Eq. 4.2. The equilibrium

constant is also called as stability constant or formation constant.

βpqr = [MpLqHr]/[M]p[L]q[H]r -----4.2

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The concentration of metal ion depends on the stability constant
of the complex and free concentration of the ligand, which is
dependent upon corresponding pK and pH values. Very low stability
constant values mean that the metal-ligand complex is not only
soluble in water but readily dissociates into the metal ion and the
ligand at physiological pH. Consequently these metal ions are
available for absorption from the digestive tract and allow life to be
sustained in the case of metals that are nutrients, and harm life or
terminate life if the metal is toxin or promote tissue injury in the case
of biologically absorbable complexes. Even though metal-ligand
systems can be quite complex, the stability constant of equal molar
metal-ligand complexes decides the availability of the ionic metal in
aqueous solution, particularly in the acidic to neutral pH range
applicable to biological species.

Investigations of acido-basic equilibria of proline and valine and
their interaction with metal ions in media of varying ionic strength,
temperature and dielectric constant throw light on the mechanism of
enzyme catalyzed reactions. Although it is known that the polarity is
lower in some biochemical micro environments, such as active sites of
enzymes and side chains of proteins than that of the bulk, a direct
measurement of the dielectric constant is not possible. Comparison of
formation constants of metal complexes with those at biological
centers offers a way to estimate the effective dielectric constant or
equivalent solution dielectric constant for the active site cavity. This

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brought a renaissance in the study of complex equilibria in aqua-
organic mixtures.

Extinctometric and electrometric techniques have been
extensively employed13-15 for the evaluation of formation constants of
mononuclear metal ion complexes formed in solution by the
interaction of aqua-metal cation and the ligand. In extinctometric
(spectrophotometric) method, the absorbance of the colored complex is
monitored at a specified wavelength where the metal ion and ligands
have little extinction coefficients. But the interpretation of data is
rather difficult for systems containing two or more species with
overlapping spectral profiles. Since most of the ligands used are
conjugate bases of weak acids, liberation of protons is involved in the
complex reaction resulting in change in pH. Hence an appropriate
constant ionic strength and buffer are employed in the
spectrophotometric investigation and the constants thus obtained are
only the conditional (apparent) stability constants.

However, in electrometric methods this change in the proton
activity or one of the free reacting components is used as probe in
monitoring the complexation using an appropriate ion selective
electrode. Bjerrum showed that glass electrode is especially useful for
the measurement of hydrogen ion concentration. Though it is difficult
to apply pH metric technique with high accuracy for strong acids16,17
(pKa<2) or strong bases (pKb>12) the method gained wide popularity.
Bjerrum evaluated the stepwise equilibrium constants by measuring
the pH of a series of solutions containing a definite amount of metal

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salt and ligand but different concentrations of strong alkali. Calvin
and Wilson18 simplified the procedure by titrating a mixture of strong
mineral acid, metal salts and ligand with a standard alkali. Later
Calvin and Melchior19 investigated the systems in the absence of
initial strong acid.

L-Proline (2-pyrrolidine carboxylic acid) is an imino acid
containing pyrrole type nitrogen rather than the amino nitrogen of the
amino acids20. It is a bidentate ligand with a high affinity to metals
like Co(II), Ni(II) and Cu(II). Speciation in aqueous solutions containing
proline and transition metal ions has been the subject of intense
study because of their biological importance21-23.

Several literature reports24-39 have been devoted to the study of
stability constants of metal-proline complexes. Durrani24 carried out
pH metric studies on the complex formation of proline with Mn(II),
Fe(II) and Ni(II). Morzyk and Zelichowicz25 studied Co(II), Ni(II) and
Cu(II) complexes potentiometrically. Ni(II) complexes were studied
potentiometrically by Ammar et al.26. Stability constants of Ni(II) and
Cu(II) were studied by Tanaka and Tabata27. Aliyu and Naaliya28
during the course of the potentiometric studies reported the formation
of proline complexes of Cr(II), Mn(II), Fe(II), Co(II), Ni(II), Cu(II) and
Zn(II). El-Gaber et al.29 studied binary and ternary complexes of M(II)
potentiometrically. A thermodynamic study of Ce(III) and Y(III)
complexes was carried out potentiometrically by Sekhon and
Chopra30. Sanaie et al.31 studied Cu(II) complexes potentiometrically

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and evaluated stability constants using the computer program
CHEMEQ.

Paper electrophoretic technique was developed by Tewari32 for
the study of Be(II) and Co(II) complexes. pH metric study of Co(II),
Ni(II), Cu(II), Cd(II) and Zn(II) complexes was carried out and
thermodynamic parameters were established by Park et al.33. Batch
equilibrium method with cation exchange resin was employed to
determine the stability constants of Co(II) by Hirano and Koyanagi34.
Cu(II) and Pb(II) complexes were studied potentiometrically by
Shoukry et al.35 and evaluated with MINIQUAD75 by El-Sherif et al.36.
Hallman et al.37 used SCOGS computer program to calculate the
stability constants of Cu(II) and Zn(II) complexes. Sanaie et al.39
calculated stability constants of Cu(II) using CHEMEQ in aqueous and
methanol-water systems. They also studied the effect of temperature
and solvent on the stability of complexes.

The equilibrium studies involving various metals and proline
were not exhaustive and many of these studies were performed in
aqueous medium. Further, there are some differences in the nature of
the reported species. There are several instances where different
authors reported different species for the same system under
comparable conditions. Probably this may be attributed to the nature
of probes, the errors associated with the probing techniques or the
inadequacies associated with the modeling strategies. Most of the
authors reported ML+ species, some reported ML2 species and very few

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reported ML3-. But none of them reported protonated species for any
of the metal. These literature reports are recorded in Table 4.1.

L-Valine is a non-polar, essential and branched chain amino
acid. It acts as a bidentate ligand and has wide applications in the
field of pharmaceutical and food industry40. Even though proline has
the greatest avidity for metal ions, almost all the amino acids exert the
same order of preference for various metal ions. Hence speciation
studies of valine with transition metal ions have been an active field of
research41,42.

Valine complexes of Mn(II) were studied by Kumar et al.43
polarographically and they evaluated electrode kinetic parameters
also. Ammar et al.26 used MINIQUAD75 to calculate stability
constants of Ni(II) complexes. Aliyu and Naaliya28 used ORIGIN50 for
Fe(II), Ni(II), Co(II), Zn(II), Cu(II), Cr(II) and Mn(II) complexes. Ce(III)
and Y(III) complexes were studied by Sekhon and Chopra30
potentiometrically and they determined thermodynamic parameters
also. Sanaie et al.31 studied Cu(II) complexes potentiometrically and
evaluated stability constants using CHEMEQ. Co(II) complexes were
studied by Hirano and Koyanagi34 using batch equilibrium method.

Cu(II) and Pb(II) complexes were studied potentiometrically by
Shoukry et al.35 and El-sherif et al.36 evaluated with MINIQUAD75.
Rengaraj et al.44 studied binary and ternary complexes of Co(II), Ni(II)
and Zn(II) complexes pH metrically. Co(II) and Ni(II) complexes were
studied potentiometrically and evaluated with SUPERQUAD by
Khatoon and Din45. The literature survey indicates that valine

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complexes were not extensively studied. Most of the studies were
performed in aqueous medium. ML+ and ML2 Species were common
for most of the systems. Some of these data are recorded in Table 4.2.

The earlier literature reports and the distribution patterns of
different forms of proline and valine in PG- and AN-water mixtures
reported in Chapter 3 indicate a high probability for the formation of
various protonated metal complexes of different stoichiometries.
Hence, the author has investigated the complex equilibria of proline
and valine with Co(II), Ni(II) and Cu(II) in PG- and AN-water mixtures.
This type of study throws light on 1) the effect of electrostatic and
non-electrostatic interactions (denaturation) on complex formation in
vitro, 2) the nature of active site cavities of enzymes, 3) detection of
specific solute-solvent interactions, and 4) understanding the
selectivity and sensitivity of various protonated complexes and relative
abundance of free components, 5) the type of complex formed by the
metal ion, and 6) the bonding behavior of the protein residues with
the metal ion.

The presence of PG or AN in aqueous solution considerably
decreases the dielectric constant of the medium and these solutions
are expected to mimic the physiological conditions where the concept
of the equivalent solution dielectric constant46 for protein cavities is
applicable. The species refined and their relative concentrations under
the present experimental conditions represent the possible forms of
metal ions in the biological fluids.

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Table 4.1: Stability constants of complexes of proline with metal ions
reported in literature.

Metal 110 log βmlh 130 Ionic Medium Instru Calculation T0 C Ref.
ion 3.81 120 strength mental method
4.92 mol dm-3 Aqueous technique 25 24
Mn(II) 3.66 10.86 1.0 ,, pH metry Irving Rossotti ,, 24
Fe(II) 5.05 8.47 NaClO4 ,, ,, technique ,, 24
Ni(II) 8.61 17.83 ,, 50% ,, ,, ,, 24
Mn(II) 7.22 ,, Ethanol ,, ,, ,, 24
Fe(II) 3.10 29.07 ,, ,, ,, ,, ,, 24
Ni(II) 2.98 28.78 ,, ,, ,, ,, ,, 24
Mn(II) 3.08 28.75 ,, 100% ,, ,, ,, 24
Fe(II) 4.80 29.03 ,, Ethanol ,, ,, ,, 24
Ni(II) 5.60 18.51 ,, ,, ,, ,, 15 25
Co(II) 7.60 19.56 ,, ,, Potentio ,, ,, 25
6.12 31.86 0.1 KNO3 Aqueous metry Bjerrum ,, 25
Ni(II) 4.53 ,, ,, ,, method 25 26
Cu(II) 9.40 10.21 ,, ,, ,, ,, ,, 27
Ni(II) 10.60 0.1 NaNO3 ,, ,, ,, ,, 27
Ni(II) 5.40 16.37 0.1 ,, --- MINIQUAD75 -- 28
6.25 16.08 ,, ,, --- Mechanistic -- 28
Cu(II) 9.00 15.80 -- ,, Potentio Consideration -- 28
Mn(II) 6.00 15.62 -- ,, metry ,, -- 28
Fe(II) 6.08 15.30 -- ,, ,, ORIGIN50 -- 28
Ni(II) 5.40 13.42 -- ,, ,, ,, -- 28
Co(II) 5.55 8.66 -- ,, ,, ,, -- 28
Zn(II) 8.87 -- ,, ,, ,, 25 29
Cu(II) 8.73 16.08 -- ,, ,, ,, ,, 29
Cr(II) 8.61 0.2 KCl ,, ,, ,, ,, 29
Co(II) 8.50 ,, ,, ,, ,, ,, 30
8.33 ,, ,, ,, Irving Rossotti 35 30
Ni(II) 7.61 0.1 KCl ,, ,, technique 25 30
Cu(II) 4.97 ,, ,, ,, ,, 35 30
Ce(III) 3.52 ,, ,, ,, ,, 15 31
Ce(III) 3.49 ,, ,, ,, ,, 25 31
Y(III) 3.62 0.1 KNO3 ,, ,, ,, 37 31
Y(III) 3.51 ,, ,, ,, ,, 45 31
Cu(II) 3.30 ,, ,, ,, ,, 60 31
Cu(II) 4.10 ,, ,, ,, CHEMEQ 35 32
Cu(II) 8.74 ,, ,, ,, ,, ,, 32
Cu(II) 0.1 ,, ,, ,, 25 33
Cu(II) 0.1 ,, PET ,, ,, 33
Be(II) 0.1 ,, ,, ,, ,, 33
NaClO4 ,, pH metry Graphical ,, 33
Co(II) ,, ,, ,, method ,, 33
Cd(II) ,, ,, ,, ,, 20 34
,, ,, ,, Least squares 25 35
Co(II) ,, ,, ,, analysis
Ni(II) 0.67 ,, BEM ,,
Cu(II) 0.1 NaNO3 Potentio ,,
Zn(II) metry ,,
Co(II) ,,
Cu(II) ---
MINIQUAD75

121

Pd(II) 11.16 ,, ,, ,, ,, ,, 36
Cu(II) 8.67 16.00 0.15 KNO3 ,, pH metry SCOGS 37 37
Zn(II) 5.13 9.69 11.16 ,, ,, ,, ,, ,, 37
Cd(II) 1.0 ,, Potentio n method 38
8.70 metry 20 38
Co(II) 38
Ni(II) 9.30 ,, ,, ,, ,, ,, 38
Cu(II) 11.30 ,, ,, ,, ,, ,, 38
Zn(II) 16.80 ,, ,, ,, ,, ,, 38
Fe(II) 10.20 ,, ,, ,, ,, ,, 38
Mn(II) 8.30 ,, ,, ,, ,, ,, 39
Cu(II) 5.50 ,, ,, ,, ,, ,, 39
Cu(II) 8.73 16.08 0.1 KNO3 ,, ,, CHEMEQ 25 39
Cu(II) 8.61 15.80 ,, ,, ,, ,, 37 39
Cu(II) 8.50 15.62 ,, ,, ,, ,, 45 39
Cu(II) 8.33 15.30 ,, ,, ,, ,, 60
20% ,, ,, 39
Cu(II) 8.91 16.42 ,, Methanol 25

9.11 16.74 ,, 40% ,, ,, ,,
Methanol
PET = Paper electrophoretic technique; BEM = Batch equilibrium
method

122

Table 4.2: Stability constants of complexes of valine with metal ions
in aqueous medium reported in literature.

Metal log βmlh Ionic Instrumental Calculation T0 C Ref.
ion 110 120 130 strength technique method
mol dm-3
Ni(II) 5.32 9.93 0.1 NaNO3 Potentiometry MINIQUAD75 25 26
Fe(II) 27.48 -- ,, ORIGIN50 -- 28

Ni(II) 27.32 -- ,, ,, -- 28

Co(II) 27.09 -- ,, ,, -- 28

Zn(II) 17.66 -- ,, ,, -- 28

Cu(II) 18.53 -- ,, ,, -- 28

Cr(II) 29.18 -- ,, ,, -- 28

Mn(II) 27.04 -- ,, ,, -- 28

Ce(III) 5.02 0.1 KCl ,, Irving 25 30
Rossotti
technique
Ce(III) 5.22 ,, ,, ,, 35 30
Y(III) 4.79 9.06 ,, ,, ,,
25 30
Y(III) 4.59 9.07 ,, ,, ,,
35 30
Cu(II) 8.10 14.90 0.1 KNO3 ,, CHEMEQ
15 31
Cu(II) 8.05 14.79 ,, ,, ,, 25 31
Cu(II) 7.94 14.56 ,, ,, ,, 37 31
Cu(II) 7.89 14.47 ,, ,, ,, 45 31
Cu(II) 7.35 13.43 ,, ,, ,, 60 31
BEM ---
Co(II) 4.3 8.5 0.67 20 34
0.1 NaNO3 Potentiometry MINIQUAD75 25
Cu(II) 8.02 14.98 ,, ,, ,, 35

Pd(II) 10.33 0.15 KNO3 pH metry SCOGS ,, 36

Cu(II) 7.90 14.55 ,, ,, 37 37

Zn(II) 5.13 9.69 11.16 ,, Potentiometry n method ,, 37
Co(II)
8.6 1.0 20 38
Cu(II) 15.10 ,, ,, ,, 20 38
,, ,, ,,
Fe(II) 6.8 ,, 38
Polarography ---
Mn(II) 4.03 10.95 19.99 1.0 KCl 27 43
pH metry Bjerrum
Ni(II) 5.26 9.12 12.35 0.1 KNO3 method 30 44

Cu(II) 8.09 14.38 ,, ,, ,, ,, 44

Zn(II) 4.75 8.65 ,, ,, ,, ,, 44

Co(II) 4.24 7.56 0.15 KNO3 Potentiometry SUPERQUAD 37 45
,, ,,
Ni(II) 5.09 9.20 11.35 ,, ,, 45

BEM = Batch equilibrium method

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FORMATION OF SPECIES

It was observed from the data in Tables 4.1 and 4.2 that, there
were several instances where different species were reported for the
same chemical system by different researchers. The probes utilized
and the computational procedures adopted by them were sometimes
the same and sometimes different. In order to rationalize the
contradictory models reported by different authors, greater details are
required regarding the 1) ingredient concentration, 2) method of
pruning primary data for the refinement, 3) pH range and the number
of points in each sub range and 4) proportion of the points
corresponding to each species in the model. Further, different species
proposed for the same metal-ligand system are many a time judged on
the best fit criteria. It is very difficult to say a final word about it, as it
is unequivocally proved that different algorithms (or same algorithm
with different weighting schemes) produce different species.

In many chemical systems it was observed that, the predicted
species based on the pH range and the form of the ligand were in fact
not detected. This unexpected behavior could be attributed to the i)
hard and soft acid base theory of the metal ion and ligand, ii)
coordination number of the metal ion, and iii) stabilities of the
complexes formed.

If the ligand contains one or more donor atoms than those
participating in complexation, there is possibility for its participation
in acido-basic equilibria, thus resulting in the formation of protonated

124

species, MLlHh in addition to unprotonated MLl type of complexes.
With progressively increasing pH, the protonated species lose protons
to form unprotonated complexes and if the complex is not broken, it
may undergo hydrolysis resulting in MLl(OH)k. Finally, at high pH the
precipitation of the metal ion as hydroxide will takes place.

Typical alkalimetric titrations curves are given in Figs. 4.1 and
4.2 from which the stability constants of binary metal-ligand
complexes were determined. Since the ratio of TL0 to TM0 is greater
than unity in all the experiments, as clear from the data in Table 2.2
of Chapter 2, formation of polynuclear complexes is not considered.
The formation of polynuclear species is possible if TL0 : TM0 ≤ 2. Also
dimeric and trimeric species are ruled out since the experimental
conditions are not favorable for their formation. Hydroxylated species
are not considered in the present study because the titrations are
discontinued if precipitation occurs.

125

12 (A) ab c 12 (D) ab c

9 9

pH pH pH66
pH pH pH
3 3

0246 8 0246 8

Vol. of Alkali (cm3) Vol. of Alkali (cm3)

12 (B) a bc 12 (E) a bc

9 9

6 6

3 8 3 8
0246
0246
Vol. of Alakli (cm3)
Vol. of Alkali (cm3)
12 (C)
12 (F) ab c
9 a bc
9

66

3 3

02468 02468

Vol. of Alkali (cm3) Vol. of Alkali (cm3)

Fig. 4.1: Alkalimetric titration curves for proline complexes of (A)
Co(II), (B) Ni(II) and (C) Cu(II) in 20% v/v PG-water mixture
and valine complexes of (D) Co(II), (E) Ni(II) and (F) Cu(II) in
20% v/v PG-water mixture; (a) 0.25, (b) 0.38 and (c) 0.50
mmol.

126

12 (A) a bc 12 (D) a bc

9 9

pH pH pH66
pH pH pH
3 3

0246 8 0246 8

Vol. of Alkali (cm3) Vol. of Alkali (cm3)

12 (B) ab c 12 (E) a bc

9 9

66

3 6 3 246 8
0
024 Vol. of Alkali (cm3)
12 (F)
Vol. of Alkali (cm3) a bc
9
12 (C)

9 a bc

66

3 3

0246 02468

Vol. of Alkali (cm3) Vol. of Alkali (cm3)

Fig. 4.2: Alkalimetric titration curves for proline complexes of (A)
Co(II), (B) Ni(II) and (C) Cu(II) in 20% v/v AN-water mixture
and valine complexes of (D) Co(II), (E) Ni(II) and (F) Cu(II) in
20% v/v AN-water mixture; (a) 0.25, (b) 0.38 and (c) 0.50
mmol.

127

The formation function ( n –the number of moles of ligand bound
per mole of metal ion) is a good parameter for the detection of
protonated species. If there are no protonated species the plots of n
versus pL at all the ligand concentrations, with fixed metal ion
concentration should overlap and any deviation indicates the presence
of the protonated species. Some typical plots given in Figs. 4.3 and 4.4
show spread in some pH regions, indicating the presence of
protonated metal complexes.

Although the stability constants calculated from the formation
function data are vitiated in presence of protonated, hydroxylated or
polymeric species, still a wealth of information is hidden in n versus
pH or pL plots which can have many applications. For example,
PSEUDOPLOT47 technique has become very popular in detecting
species other than those invoked in the model and even in rejecting a
species refined by a computer program. Detection of systematic errors
in the concentrations of mineral acid and ligand and non-linear
response of glass electrode in extreme pH ranges etc. is another
interesting application of this auxiliary function.

Figs. 4.5 and 4.6 give the relation between the number of moles
of alkali consumed per mole of metal ion (a) and the pH. The number
of protons released in the equilibrium can be guessed depending on
the moles of alkali consumed.

128

(A) (D)

2 2

11
nnn
n nn 0 6 9 12 0 6 9 12
3 12 3
pL pL
(B) (E)

2.0 2

1.5 1

1.0 69 3 6 9 12

0.5 pL (F) pL
3
2
(C)

2

1
1

0 3 6 9 12
3 6 9 12

pL pL

Fig. 4.3: Formation curves of proline complexes of (A) Co(II), (B) Ni(II)
and (C) Cu(II) and valine complexes of (D) Co(II), (E) Ni(II)
and (F) Cu(II) in 30% v/v PG-water mixture; (□) 0.25, (○)
0.38 and (∆) 0.50 mmol.

129

(A) (D)

2 2

nn 11
nn
0 6 9 12 0 6 9 12
3
pL 3 pL
(B)
(E)
2
2

1

1

3 6 9 12 0 6 9 12
3
(C) pL pL
(F)
2
2

11
n n

0 6 9 12 0 6 9 12
3 3
pL pL

Fig. 4.4: Formation curves of proline complexes of (A) Co(II), (B) Ni(II)
and (C) Cu(II) and valine complexes of (D) Co(II) (E) Ni(II) (F)
Cu(II) in 20% v/v AN-water mixture; (□) 0.25, (○) 0.38, and
(∆) 0.50 mmol.

130

aa 12 (A) 6 9 12 a aa (D) 6 9 12
12 12
8 pH 12 8 pH 12
4 4
0 6 9 0 6 9
-4 -4
-8 pH -8 pH

a 3 3

(B) 6 9 (E) 6 9

8 pH 8 pH
4 4
0 0
-4 -4
-8 -8

3 3

(C) (F)

8 8
4 4
0 0
-4 -4
-8 -8

3 3

Fig. 4.5: Number of moles of alkali versus pH curves of proline
complexes of (A) Co(II), (B) Ni(II) and (C) Cu(II) and valine
complexes of (D) Co(II), (E) Ni(II) and (F) Cu(II) in 40% v/v
PG-water mixture; (□) 0.25, (○) 0.38, and (∆) 0.50 mmol.

131

aa (A) 6 9 12 aa (D) 6 9 12

8 pH 8 pH
4 4
0 6 9 12 0 6 9 12
-4 -4
-8 pH -8 pH

a 3 a 3

(B) 6 9 12 (E) 6 9 12

8 pH 8 pH
4 4
0 0
-4 -4
-8 -8

3 3

(C) (F)

8 8
4 4
0 0
-4 -4
-8 -8

3 3

Fig. 4.6: Number of moles of alkali versus pH curves of proline
complexes of (A) Co(II), (B) Ni(II) and (C) Cu(II) and valine
complexes of (D) Co(II), (E) Ni(II) and (F) Cu(II) in 20% v/v
AN-water mixture; (□) 0.25, (○) 0.38, and (∆) 0.50 mmol.

132

Now-a-days knowledge based or expert systems are gaining
importance in chemical research, as they mimic the human expert in
typical tasks. Some of the thumb rules embedded in computer
assisted modeling studies are documented in the form of IF-THEN-
ELSE rules in Table 4.3.
Selection of species

Based on the earlier reports the maximum number of ligands
bound to metal ion is restricted to three. In all the cases the
maximum n values observed were less than three, with no ascending
slope48. The n values greater than three or ascending slope indicates
the presence of a complex species with higher ligand number. All the
possible expected species are represented in Table 4.4 for
consideration in developing different models that are to be tested.

133

Table 4.3: Heuristics in the detection of metal complexes by pH metry
Protonated/hydroxylated species

IF A single experiment with any ratio of TL0 and TM0 is
performed,

THEN and n exp− n cal > TL0 for more than 5 consecutive
IF points,

Species other than MLn may be present.

Experiments with more than one TL0 to TM0 ratio are
performed

THEN and TL0/TM0>1, and n versus pH (or pL) curves do
IF not coincide at least in some regions and formation
THEN curves are not equidistant(parallel)

IF Protonated or hydroxylated species may be present.

THEN TL0/TM0=1, and n exp− n cal deviate near n =0,
IF
Hydroxylated species may be formed.
THEN
Polynuclear species

TL0/TM0=1 in more than one concentrations and
formation curves are equidistant

Dimers and trimers may be formed.

TL0/TM0≤2, and formation curves are not overlapping
for different concentrations,

Polynuclear complexes may be present.

134

Table 4.4: Some of the possible binary metal complex species in M(II)-
proline (L) and M(II)-valine(X) systems.

Constraints: 1) Maximum number of metal ions =1
2) Maximum ligand number = 3

Ligand form Ligand number
LH2+ 1(a) 2(b) 3(c)
LH MLH2+ ML2H22+, ML2H+ ML3H32+, ML3H2+, ML3H
XH2+ ML+ ML2 ML3-
XH MXH2+
MX+ MX2H22+, MX2H+ MX3H32+, MX3H2+, MX3H
Ligand MX2 MX3-
No. of
proline Ligands Number of Exhaustive No. of
species rm∑n=o2dneClsr
valine 2 (n) 26
3 5(a+b ) 502
2 9(a+b+c )
3
5(a+b ) 26
9(a+b+c ) 502

In view of the large number, it is not pragmatic to consider all
models for refinement process. Hence, several thumb rules based on
chemical principles and well established practices in multiple linear
regression analysis are resorted to, for this purpose. Hence the species
considered to develop different models are MLH2+, ML+, ML2H22+,
ML2H+, ML2, ML3H and ML3-. The preliminary screening of a number of
species based on several thumb rules49 resulted in a short list of
MLH2+, ML+, ML2H22+, ML2H+ and ML2.

135

SELECTION OF BEST FIT MODEL

The models containing different number of species were tried
from the primary alkalimetric titration data. Only a few species were
refined while other species were rejected by MINIQUAD7550. The
models with combinations of different species at a time were also
tested. After arriving at a valid model, the species rejected in the
primary scrutiny were again tried. Some species were removed from
the model if their percentage is less than 10.

Existence of species was determined by performing exhaustive
modeling51 and the result of one such typical system was given in
Table 4.5. The models were evaluated assuming the simultaneous
existence of different combinations of species. Models containing
various number and combinations of species were generated using an
expert system package CEES52 and these models were refined using
MINIQUAD75. As the number of species was increased, the models
gave better statistics denoting better fit. This indicates that the final
model appropriately fits the experimental data. Such exhaustive
modeling was performed for all the systems and the final models are
given in Tables 4.6-4.9 for Co(II), Ni(II) and Cu(II) complexes of proline
and valine in PG- and AN-water mixtures. The tables contain the
stoichiometric coefficients and stability constants of the complex
species, standard deviations in the stability constants and residual
statistics of the best fit models.

136

Table 4.5: Results of some exhaustive modeling studies for Cu(II)-
proline complexes in 30% v/v AN-water mixture (pH range
= 2.1-7.5; Number of points = 61).

Model log βmlh(SD) Ucorr χ2 Skew Kurt- R-
num *108 -ness osis factor
ber ML+ ML2 MLH2+
9.47(8)
1 ----- ----- 4.93 33.17 -0.05 4.98 0.0146

2 ----- 17.41(14) ----- 9.84 81.09 -0.70 2.49 0.0206

3 ----- ----- 13.41(37) 44.14 284.89 -0.01 10.96 0.0435

4 9.43(7) 16.84(18) ----- 2.95 62.29 -1.05 4.02 0.0113

5 ------ 17.91(13) 13.36(13) 5.21 110.46 -1.15 5.92 0.0149

6 9.59(7) ------ 13.18(10) 2.59 91.58 1.07 13.56 0.0105

7 9.54(3) 17.05(7) 13.20(4) 0.44 22.60 -0.45 5.11 0.0044

Ucorr= U/(NP-m); NP = Number of points; m = Number of formation
constants; SD = Standard deviation.

137

Table 4.6: Parameters of best fit chemical models of Co(II),

PG ML+ log βmlh(SD) MLH2+ pH-
% ML2 Range
v/v
0.0 5.03(8) 9.12(7) 11.88(14) Co(
10.0 5.14(9) 9.51(8) 12.18(11) 1.8-9.6
20.0 5.18(8) 9.60(7) 12.27(7) 1.8-9.6
30.0 5.23(19) 9.42(19) 12.73(12) 1.8-9.6
40.0 5.57(9) 9.86(9) 12.57(6) 1.6-9.6
50.0 6.01(12) 10.49(12) 13.15(6) 1.8-9.6
60.0 6.26(9) 10.89(10) 13.40(4) 1.8-9.6
0.0 6.51(12) 11.51(13) 12.73(8) 1.8-9.6
10.0 6.50(8) 11.43(9) 13.11(6)
20.0 6.69(6) 11.72(6) 13.30(3) Ni(
30.0 6.85(5) 11.89(6) 13.50(3) 1.8-9.0
40.0 6.96(7) 12.22(8) 13.19(4) 1.8-9.0
50.0 7.26(8) 12.71(8) 13.52(4) 1.8-9.0
60.0 7.37(8) 12.74(9) 13.84(4) 1.8-9.0
0.0 8.92(8) 16.23(9) 11.90(55) 1.8-9.0
10.0 8.91(9) 16.33(9) 12.27(33) 1.8-9.0
20.0 9.05(4) 16.40(8) 12.48(5) 1.8-9.0
30.0 9.21(11) 16.54(16) 12.81(20)
40.0 9.53(3) 17.14(5) 12.85(5) Cu(
50.0 9.64(3) 17.37(6) 12.75(7) 2.6-7.5
60.0 9.89(5) 17.17(11) 13.18(9) 3.4-7.5
1.8-7.5
2.4-7.5
2.2-7.5
2.3-7.5
2.4-7.5

13

Ni(II) and Cu(II)-proline complexes in PG-water mixtures.

NP Ucorr χ2 Skew- Kurt- R-
*108 ness osis factor

(II) 1.02 30.23 -0.10 3.34 0.0053
94 1.42 72.67 -0.26 3.87 0.0064
94 1.14 101.09 1.01 8.17 0.0055
113 7.80 218.54 0.16 8.47 0.0118
128 1.42 69.71 -0.17 4.30 0.0062
100 2.69 48.14 -0.32 4.05 0.0083
102 1.15 31.45 0.12 4.98 0.0053
68 2.44 5.41 0.0082
1.40 74.20 -0.07 3.55 0.0065
(II) 0.62 108.64 0.00 4.64 0.0041
94 0.51 31.37 -0.28 3.62 0.0037
101 1.10 22.41 -0.06 4.31 0.0055
107 0.99 35.89 -0.27 4.41 0.0051
98 1.15 24.58 -0.16 4.60 0.0054
100 0.44 51.58 -0.19 2.97 0.0060
101 0.12 4.32 0.0033
99 0.98 12.04 -0.19 4.91 0.0051
2.16 9.70 0.62 2.14 0.0105
(II) 0.42 66.03 0.44 4.08 0.0046
30 0.49 5.63 -0.01 3.20 0.0052
18 1.00 8.51 0.05 2.97 0.0075
109 9.81 -0.07
30 3.62 -0.18
57
53
47

38

Table 4.7: Parameters of best fit chemical models of Co(II), N

AN log βmlh(SD) MLH2+ pH-
% v/v ML+ ML2 Range

0.0 5.03(8) 9.12(7) 11.88(14) Co(
10.0 5.09(22) 9.15(21) 13.07(15) 1.8-9.6
20.0 5.47(17) 9.65(17) 13.40(10) 1.8-9.6
30.0 5.95(15) 10.35(16) 13.71(10) 1.8-9.6
40.0 6.19(19) 10.65(21) 13.86(15) 2.0-9.6
50.0 6.43(15) 11.03(17) 14.14(11) 2.1-9.6
60.0 6.44(22) 11.04(27) 14.19(13) 2.1-9.6
2.0-9.6
0.0 6.51(12) 11.51(13) 12.73(8)
10.0 6.47(13) 11.06(16) 13.70(9) Ni(
20.0 6.68(13) 11.75(14) 13.65(8) 1.8-9.0
30.0 6.99(12) 11.88(15) 13.99(7) 1.8-9.0
40.0 7.09(19) 12.31(23) 14.20(12) 1.8-9.0
50.0 7.36(22) 12.38(30) 14.49(13) 1.8-9.0
60.0 7.56(22) 13.23(23) 14.20(10) 1.8-9.0
1.8-9.0
0.0 8.92(8) 16.23(9) 11.90(55) 1.8-9.0
10.0 8.72(10) 15.92(17) 12.72(16)
20.0 8.97(6) 16.31(10) 12.63(10) Cu(
30.0 9.54(3) 17.05(7) 13.20(4) 2.6-7.5
40.0 9.67(7) 17.36(17) 13.20(7) 2.1-7.5
50.0 10.13(6) 17.59(20) 13.52(8) 2.1-7.5
60.0 10.50(6) 18.36(17) 13.88(8) 2.1-7.5
1.8-7.5
2.0-7.5
2.1-7.5

13

Ni(II) and Cu(II)-proline complexes in AN-water mixtures.

NP Ucorr χ2 Skew- Kurt- R-
e *108 ness osis factor
(II) 1.02 30.23
6 94 8.69 87.13 -0.10 3.34 0.0053
6 89 5.61 93.62 0.05 3.61 0.0160
6 91 3.94 43.26 0.02 3.86 0.0126
6 71 5.47 45.46 0.19 4.41 0.0122
6 63 3.72 31.58 0.11 3.39 0.0157
6 65 9.92 34.72 0.05 4.37 0.0126
6 74 2.44 74.20 -0.05 3.43 0.0193
(II) 2.43 14.42
0 94 3.01 32.61 -0.07 5.41 0.0082
0 88 2.55 67.75 0.54 4.31 0.0082
0 91 4.84 14.68 0.09 3.39 0.0091
0 93 9.97 18.71 0.22 5.14 0.0082
0 59 8.65 27.31 0.12 2.89 0.0129
0 94 0.44 12.04 0.21 3.40 0.0165
0 98 2.50 37.14 -0.56 5.37 0.0153
(II) 1.08 29.33
5 30 0.44 22.60 -0.19 2.97 0.0060
5 56 2.57 45.33 -0.04 3.81 0.0110
5 60 2.55 11.20 -0.06 3.71 0.0070
5 61 2.42 20.99 -0.45 5.11 0.0044
5 96 -0.65 4.24 0.0082
5 75 -0.30 4.04 0.0095
5 66 0.62 4.48 0.0099

39

Table 4.8: Parameters of best fit chemical models of Co(II), N

PG log βmlh(SD) MLH2+ pH-
% v/v ML+ ML2 Range

0.0 4.44(10) 8.07(9) 10.97(17) Co(
10.0 4.51(4) 7.98(4) 11.25(4) 2.0-9.0
20.0 4.41(7) 8.30(5) 10.96(16) 2.0-9.0
30.0 4.50(21) 8.13(19) ----- 2.5-9.0
40.0 4.69(8) 8.35(8) 11.16(12) 3.5-8.6
50.0 4.89(11) 8.91(10) 11.09(20) 2.0-9.0
60.0 4.98(8) 8.98(7) 11.51(8) 2.0-9.0
2.0-9.0
0.0 5.31(9) 9.52(9) 11.36(9)
10.0 5.55(6) 9.78(6) 11.84(4) Ni(
20.0 5.80(7) 10.46(7) 11.97(4) 2.0-9.0
30.0 6.44(62) 11.62(60) 12.10(92) 1.9-9.0
40.0 6.72(13) 11.50(13) 12.69(8) 2.0-9.0
50.0 7.05(18) 12.27(18) 12.89(11) 3.2-8.0
60.0 7.68(20) 12.52(21) 13.61(15) 2.0-9.0
2.0-9.0
0.0 8.35(5) 14.80(8) 12.04(4) 1.9-9.0
10.0 8.46(3) 15.15(6) 11.73(4)
20.0 8.75(4) 15.41(9) 11.94(5) Cu(
30.0 8.63(74) 15.59(74) 12.48(91) 1.8-6.5
40.0 8.88(5) 15.97(9) 12.29(5) 2.0-6.5
50.0 9.28(6) 16.44(13) 12.59(7) 2.0-6.5
60.0 9.41(8) 16.76(15) 12.66(8) 3.5-6.5
1.8-6.5
2.0-6.5
1.8-6.5

14

Ni(II) and Cu(II)-valine complexes in PG-water mixtures.

NP Ucorr χ2 Skew- Kurt- R-factor
*108 ness osis
(II)
75 1.67 31.11 0.09 3.71 0.0082
78 0.30 49.49 1.02 9.04 0.0034
55 0.63 39.95 1.41 7.49 0.0064
21 8.01 110.3 0.04 7.55 0.0267
82 1.22 59.95 -0.70 5.17 0.0066
82 1.88 60.86 -0.79 5.50 0.0082
82 0.99 56.96 -0.48 5.24 0.0058

(II) 1.39 32.49 0.02 3.62 0.0075
76 0.72 40.05 -0.28 3.75 0.0050
99 3.01 56.82 1.32 7.97 0.0065
91 0.67 44.56 0.19 8.93 0.0123
21 8.37 18.23 0.14 3.47 0.0098
81 6.28 30.05 0.73 5.43 0.0111
55 4.46 14.46 0.58 3.56 0.0118
87
0.95 14.17 -0.20 3.39 0.0050
(II) 0.63 5.79 0.03 2.59 0.0048
94 1.23 18.59 -0.19 4.29 0.0066
75 1.19 3.75 -0.11 4.08 0.0103
86 1.80 17.92 -0.59 4.67 0.0069
17 2.73 17.07 -0.69 7.32 0.0098
100 2.08 20.62 -0.53 4.01 0.0116
77
97

40

Table 4.9: Parameters of best fit chemical models of Co(II), N

AN MLH2+ log βmlh(SD) ML2 N
% v/v ML+
Co(II) (pH ra
0.0 10.97(17) 4.44(10) 8.07(9) 75
10.0 11.73(17) 4.24(20) 7.79(16) 72
20.0 11.60(16) 4.39(16) 7.99(14) 86
30.0 11.68(13) 4.63(11) 8.28(11) 77
40.0 11.67(19) 4.83(15) 8.62(15) 79
50.0 11.68(22) 4.84(14) 8.70(15) 91
60.0 12.03(26) 5.04(21) 9.05(22) 88
Ni(II) (pH ra
0.0 11.36(9) 5.31(9) 9.52(9) 77
10.0 11.69(6) 5.45(6) 9.77(6) 78
20.0 11.75(11) 5.47(13) 10.22(11) 78
30.0 11.93(5) 5.73(6) 10.17(6) 81
40.0 12.02(15) 5.88(20) 10.64(21) 10
50.0 12.23(14) 6.10(17) 10.66(22) 80
60.0 12.38(13) 6.35(15) 11.16(19) 81
Cu(II) (pH ra
0.0 12.04(4) 8.35(5) 14.80(8) 94
10.0 11.86(5) 8.31(4) 14.86(8) 72
20.0 12.03(6) 8.63(5) 15.52(11) 94
30.0 12.33(6) 9.19(4) 16.02(12) 75
40.0 12.28(6) 9.29(3) 16.54(9) 78
50.0 12.92(9) 9.67(8) 17.06(19) 11
60.0 13.02(12) 10.02(8) 17.97(16) 99

14

Ni(II) and Cu(II)-valine complexes in AN-water mixtures.

NP Ucorr χ2 Skew- Kurt- R-factor
*108 ness osis
31.11
ange 2.0-9.0) 66.81 0.09 3.71 0.0082
5 1.67 58.71 -0.01 4.51 0.0150
2 6.04 63.55 -0.48 4.15 0.0117
6 4.47 31.73 -0.10 4.44 0.0094
7 2.53 112.4 -0.59 4.01 0.0126
9 4.51 144.9 -1.41 7.49 0.0105
1 3.84 32.49 -1.60 7.82 0.0156
8 8.04 27.33
ange 2.0-9.0) 49.42 0.02 3.62 0.0075
7 1.39 62.68 0.28 4.94 0.0051
8 0.76 95.59 0.01 5.03 0.0106
8 1.08 73.13 0.05 6.17 0.0048
1 1.68 96.98 -1.03 5.68 0.0147
04 2.43 14.17 -0.95 5.67 0.0149
0 3.27 38.59 -1.32 6.77 0.0126
1 0.41 59.05
ange 1.8-6.5) 3.59 -0.20 3.39 0.0050
4 0.95 40.80 -0.12 4.36 0.0052
2 0.74 38.32 -0.82 6.16 0.0069
4 1.85 55.24 -0.25 2.92 0.0072
5 1.52 -0.97 7.60 0.0064
8 1.22 -1.71 12.1 0.0113
15 6.23 -1.48 7.88 0.0126
9 6.33

41

Residuals analysis

The residuals-differences between what is actually measured or
observed (EMF, pH, volume, concentration of ingredients etc.) and
that predicted by a model-measure the unexplained variation in the
dependent variable by the regression equation. The goal of rigorous
residual analysis is to conclude that the assumptions in regression
analysis and of chemical laws (mass-balance equations, electrode
response, equilibrium expression etc.) are valid for a data set on hand.
The residuals should follow normal distribution for the best fit model.
The use of plots of residuals versus calculated volumes of dependent
variables (EMF or volume) and independent variables (TM, TL) is
popular.

Gans et al.53 applied sample standard deviation (SD) in weighted
least squares analysis for the calculation of β’s and suggested that
any value less than three is satisfactory. Of course, the ideal value of
1 was observed only in a single titration curve (unlike pooled data)
inferring that the data have been correctly weighted. The SD and
confidence intervals in β are meaningful only when unweighted
residuals follow χ2 distribution, which measures the possibility of
residuals forming a part of standard normal distribution with zero
mean and unit standard deviation.

Higher χ2 values than expected are due to 1) the inadequacy of
the model although the experimental data are of high quality, 2) use of

142

poor data even though the model is appropriate and 3) invoking
optimistic estimates of errors in primary data.

A perusal of Tables 4.6-4.9 indicates that the χ2 values range
between 3.62 – 218.54 for PG-water and 3.59 – 144.90 for AN-water
mixtures. The values of kurtosis and skewness range from 2.14 – 9.04
and -0.79 – 1.41 for PG-water mixtures and 2.89 – 12.10 and -1.71 –
0.62 for AN-water mixtures, respectively. Deviation of the values of
kurtosis and skewness from three and zero, respectively, show the
tendency of these residuals to concentrate more to the left or right of
the mean and broadening of the peak. However, the values of Ucorr in
all the three mass-balance equations, are very low confirming the
adequacy of the chemical model to represent the experimental data.

Retrieval of protonation constants

Protonation constants were retrieved from the metal-ligand
titrations and compared with those obtained from proton-ligand
titration data. The proximity of the two values confirms the existence
of only reported metal-ligand species and accuracy of the titration
data. Such comparisons for some typical systems are given in Table
4.10. Then simultaneous refinement of all the constants revealed that
when the approximate constants are very close to the true values,
either fixing some of the species or ingredient concentrations do not
have any ill- effects on modeling studies.

143

Table 4.10: Comparison of protonation constants determined from
proton-ligand and metal-ligand titration data.

From proton-ligand From metal-ligand
System titration data titration data
log β1 log β2 log β1 log β2
Ni(II)-proline in 10% v/v PG
Co(II)-proline in 20% v/v PG 10.48 12.48 10.48 12.48
Ni(II)-proline in 30% v/v PG
Cu(II)-proline in 30% v/v PG 10.45 12.69 10.44 12.68
Cu(II)-proline in 40% v/v PG
Cu(II)-proline in 50% v/v PG 10.60 12.88 10.62 12.90
Cu(II)-proline in 10% v/v AN
Ni(II)-proline in 30% v/v AN 10.60 12.88 10.62 12.87
Co(II)-valine in 10% v/v PG
Cu(II)-valine in 10% v/v PG 10.49 12.86 10.52 12.85
Ni(II)-valine in 30% v/v PG
Co(II)-valine in 40% v/v PG 10.48 12.97 10.53 12.98
Co(II)-valine in 50% v/v PG
Cu(II)-valine in 60% v/v PG 10.72 12.75 10.75 12.73
Ni(II)-valine in 10% v/v AN
Cu(II)-valine in 10% v/v AN 10.88 13.33 10.93 13.37
Co(II)-valine in 20% v/v AN
Co(II)-valine in 30% v/v AN 9.36 11.84 9.35 11.83
Ni(II)-valine in 30% v/v AN
Co(II)-valine in 40% v/v AN 9.36 11.84 9.40 11.87
Co(II)-valine in 50% v/v AN
Cu(II)-valine in 50% v/v AN 9.56 12.25 9.55 12.00
Co(II)-valine in 60% v/v AN
9.46 12.22 9.44 12.21

9.54 12.44 9.51 12.42

9.50 12.66 9.51 12.66

9.71 12.19 9.70 12.19

9.71 12.19 9.69 12.19

9.72 12.32 9.70 12.32

9.74 12.63 9.72 12.63

9.74 12.63 9.72 12.62

9.78 12.79 9.75 12.80

9.91 13.20 9.91 13.20

9.91 13.20 9.99 13.26

10.02 13.58 10.01 13.59

Perturbation in Stability Constants due to Systematic Errors

The computer program refines the stability constants by
minimizing the random errors in the data. But in the presence of

144

considerable systemic errors, not only the β’s are in errors; even some
species may be rejected. MINIQUAD75 has no provision to vary the
influential parameters. Hence, some representative systems were
studied in order to have a cognizance of the effect of errors in
concentrations of ingredients on the stability constants of binary
metal complexes. These results are given in Tables 4.11 and 4.12. The
data shows that the magnitudes of stability constants are more
affected by acid and alkali than ligand and metal. The increased
standard deviation in stability constants and even rejection of some
species on the introduction of errors confirms the correctness of the
proposed models. This type of investigation is significant as the data
acquisition was done under varied experimental conditions with
different accuracies.

145

Table 4.11: Effect of errors in influential parameters on the stability
constants of Co(II)-proline binary complexes in 40% v/v
PG-water mixture.

Ingredient % log βmlh(SD)
Error
ML+ ML2 MLH2+
0 5.57(9)
9.86(9) 12.57(6)

-5 4.07(36) 7.03(62) Rejected
-2 4.82(15) 8.61(17) Rejected
Alkali +2 6.56(8) 11.30(8) 13.21(4)
+5 10.56(8) 15.99(17) 13.61(10)

Acid -5 Rejected Rejected Rejected
-2 6.92(8) 11.61(9) 13.65(4)
+2 4.83(17) 8.70(18) Rejected
+5 4.14(47) 7.34(62) Rejected

Ligand -5 5.34(8) 9.70(8) 11.13(75)
-2 5.48(8) 9.79(8) 12.31(8)
+2 5.67(9) 9.93(10) 12.78(5)
+5 5.82(9) 10.05(10) 13.03(5)

-5 5.60(10) 10.01(9) 12.61(6)
-2 5.58(9) 9.92(9) 12.59(6)
Metal +2 5.56(8) 9.80(8) 12.56(6)
+5 5.54(8) 9.71(9) 12.54(6)

-5 5.76(10) 10.05(10) 12.92(5)
-2 5.65(9) 9.94(10) 12.73(6)
Log F +2 5.50(8) 9.79(8) 12.41(7)

+5 5.41(8) 9.70(8) 12.08(11)

146

Table 4.12: Effect of errors in influential parameters on the stability
constants of Ni(II)-valine binary complexes in 30% v/v AN-
water mixture.

Ingredient % MLH2+ log βmlh(SD) ML2
Error ML+
11.93(5) 5.73(6) 10.17(6)
0

Alkali -5 Rejected 4.34(26) 6.45(127)
-2 Rejected 5.06(10) 8.77(70)
+2 12.54(5) 6.55(10) 11.48(10)
+5 12.89(11) 9.62(9) 15.13(19)

Acid -5 Rejected Rejected Rejected
-2 12.81(5) 6.77(10) 11.65(10)
+2 Rejected 5.06(12) 8.90(16)
+5 Rejected 4.43(33) 7.05(79)

Ligand -5 11.96(5) 5.75(6) 10.34(6)
-2 11.94(5) 5.74(6) 10.24(6)
+2 11.92(5) 5.73(6) 11.11(6)
+5 11.90(5) 5.72(5) 10.01(7)

Metal -5 11.03(22) 5.51(7) 10.03(7)
-2 11.68(6) 5.64(6) 10.11(6)
+2 12.13(4) 5.83(6) 10.25(7)
+5 12.38(3) 5.99(6) 10.37(7)

Log F -5 12.11(4) 5.83(6) 10.28(7)
-2 12.01(4) 5.78(6) 10.22(7)
+2 11.85(5) 5.69(6) 10.13(6)
+5 11.73(6) 5.64(6) 10.08(6)

147

SECTION-2

EFFECT OF SOLVENT ON METAL-LIGAND EQUILIBRIA

Cosolvent influences the equilibria in solution due to change in
the dielectric constant (D) of the medium that varies the relative
contribution of electrostatic and non-electrostatic interactions which
in turn vary the magnitude of stability constants.

The variation of overall stability constant values or change in
free energy with cosolvent content depends upon electrostatic and
non–electrostatic factors. Born’s classical treatment54 holds good in
accounting for the electrostatic contribution to the free energy change.
According to this treatment, the energy of electrostatic interaction is
related to dielectric constant. Hence, the log β value should vary
linearly as a function of reciprocal of the dielectric constant (1/D) of
the medium.

PG-water mixtures

PG is an amphiprotic and coordinating solvent. It is a structure
former and enhances the water structure in PG-water mixtures. Hence
it removes water from the coordination sphere of metal ions, making
them more reactive towards the ligands. As a result, the stability of the
complex is expected to increase. It is also a coordinating solvent and
competes with the ligands for coordinating the metals. This decreases
the stability of the complexes. Hence, the stability of the complex is
expected to either increase or decrease linearly.

148

The linear trend observed in the present study (Fig. 4.7)
indicates that electrostatic forces are dominating the equilibrium
process under the present experimental conditions. The linear increase
in the stabilities of the complexes with 1/D confirms the dominance of
structure forming nature of PG over its coordinating nature.

AN-water mixtures

AN is a protophobic, dipolar aprotic and coordinating solvent. It
is a structure breaker of water and disrupts the water structure to
form AN-water complex55 of the formula AN.H2O. When small amount
of AN is added to water, the water structure breaks down resulting in
more basic monomeric water molecules. Hence water molecules
compete with the ligands for coordination with metal ions, decreasing
the stability of the complexes. But the formation of solvent-water
complex decreases the coordinating power of water thereby increases
the stability of the complex. The linear increase in the stabilities of the
complexes (Fig. 4.8) with 1/D confirms the dominance of complexing
ability of AN with water over its coordinating nature.

Since complex formation can be viewed as a competition
between the pure and solvated forms of ligand and the metal ion, the
solute-solvent interactions, relative thermodynamic stabilities and
kinetic labilities are also expected to play an important role. Different
types of electrostatic forces dominate in different ranges of the
composition of PG- and AN-water mixtures. With the increase in the
percentage of PG and AN from 0.0-60.0% v/v, the dielectric constant

149

of the medium decreases from 78.5 to 51.2 and 50.8, respectively.
Thus the variation of stability constants was studied over a range of
the dielectric constant from 78.5 to 50.8. It is concluded from these
studies that there is considerable increase in the stabilities of proline
metal complexes in AN than in PG. But the increase in the case of
valine metal complexes is negligible. This is attributed to the
dominance of complex forming ability of AN with water than the
structure forming nature of PG.

150

15 (A) 12 (D)

12 10

log β 9 log β 8

6 6
0.014 0.016 0.018 0.020
4
1/D
15 (B) 0.014 0.016 0.018 0.020

12 1/D

log β 9 log β (E)

6 14
0.014 0.016 0.018 0.020 12
10
1/D 8
18 (C) 6

0.014 0.016 0.018 0.020

1/D
18 (F)

log β 15 log β 15

12 12

9 9
0.014 0.016 0.018 0.020 0.014 0.016 0.018 0.020

1/D 1/D

Fig. 4.7: Variation of stability constants of proline complexes (A)
Co(II), (B) Ni(II) and (C) Cu(II) and valine complexes of (D)
Co(II), (E) Ni(II) and (F) Cu(II) with reciprocal of dielectric
constant (1/D) of PG-water mixtures: (□) log βML, (○) log βML2
and (∆) log βMLH.

151

log β 15 (A) log β (D)

log β 12 log β 12

log β 9 log β 9

6 6
0.014 0.016 0.018 0.020
0.014 0.016 0.018 0.020
1/D
15 (B) 1/D

12 (E)

9 12
10
6 8
0.014 0.016 0.018 0.020 6

1/D 0.014 0.016 0.018 0.020

20 (C) 1/D

16 18 (F)

12 15

8 12
0.014 0.016 0.018 0.020
9
1/D 0.014 0.016 0.018 0.020

1/D

Fig. 4.8: Variation of stability constants of proline complexes (A)
Co(II), (B) Ni(II) and (C) Cu(II) and valine complexes (D) Co(II),
(E) Ni(II) and (F) Cu(II) with reciprocal of dielectric constant
(1/D) of AN-water mixtures: (□) log βML, (○) log βML2 and (∆)
log βMLH.

152

SECTION- 3

DISTRIBUTION DIAGRAMS

The percentage of metal ion in the form of various complex
species is given by Eq. 4.3.

PS = m(j)∗βm(j)l(j)h(j ) ∗FLli(j) ∗FHhi (j) ∗100
N ∗FLli(j) ∗FHih(j)
j=∑0 βm(j)l(j)h(j ) (4.3)

Using the formation constant in the best fit model, distribution

diagrams were obtained with the computer programs DISPLOT56 and

SCPHD57. These programs can be used to output distribution

contours in any required pH range and to study the effect of errors in

stability constants or variation in the concentration of ingredients.

This information is highly useful in choosing ingredient

concentrations to increase or decrease the concentrations of selected

species in PG- and AN-water mixtures. The variation of species

concentration with pH is shown in Figs. 4.9-4.21 for metal-proline and

metal-valine complexes in PG- and AN-water mixtures. The patterns of

the distribution of species with pH show that the concentrations of

species are affected by solvent.

Proline exists as LH2+, LH and L- in the pH ranges 1.5-3.5, 3.0-

10.0 and 9.0-11.0, and valine in the pH ranges 1.5-4.0, 4.0-9.0 and

9.0-11.0, respectively58. Therefore, the stability constants of metal-

ligand complexes of proline and valine will depend on the pH range of

study. Under the present experimental conditions, the predominant

153

forms of the ligands are LH2+ and LH which limits the probable metal-
ligand species to be ML+, ML2, MLH2+, ML2H22+ and ML2H+. The
species that are refined are ML+, ML2 and MLH2+ for Co(II), Ni(II) and
Cu(II) with proline and valine in PG- and AN-water mixtures. The
stability constants of these species are found to follow the trend Co(II)
< Ni(II) << Cu(II). This is in conformity with the Irving-Williams order59.
The additional high stability of Cu(II) complex may be due to Jahn-
Teller distortion.

ML+ and ML2 species were reported in the literature24-45 for
Co(II), Ni(II) and Cu(II) with proline and valine. But the present study
reports MLH2+ species also for both the ligands. The formation of
various binary complex species is represented in the following general
Equilibria (4.4-4.10) for both the ligands.

M(II) + LH2+ MLH2+ + H+ (4.4)

MLH2+ ML+ + H+ (4.5)

M(II) + LH2+ ML+ + 2H+ (minor process) (4.6)

M(II) + LH ML+ + H+ (4.7)

M(II) + 2LH ML2 + 2H+ (4.8)

MLH2+ + LH ML2 + 2H+ (4.9)

ML+ + LH ML2 + H+ (4.10)

154

MLH2+, ML+ and ML2 species are formed in the pH range 3.0-9.5
(Figs. 4.9-4.21). For all metal-ligand systems in PG- and AN-water
mixtures, MLH2+ species is formed by the interaction of metal ion with
LH2+ (Equilibrium 4.4), because the percentages of metal ion and LH2+
are decreasing with increasing percentage of MLH2+. ML+ species can
be formed by the deprotonation of MLH2+ (Equilibrium 4.5), the
interaction of metal ion with LH2+ (Equilibrium 4.6) and the interaction
of metal ion with LH (Equilibrium 4.7). Equilibria 4.5 and 4.7 are
more predominant than Equilibrium 4.6 because the concentrations
of metal ion, MLH2+ and LH are decreasing with increasing
concentration of ML+. Equilibrium 4.6 is responsible for the initial
formation of ML+. The simultaneous formation of ML+ and ML2
suggests the existence of Equilibria 4.7 and 4.8. ML2 is formed by the
interaction of metal ion with LH (Equilibrium 4.8), MLH2+ with LH
(Equilibrium 4.9) and ML+ with LH (Equilibrium 4.10). The Equilibria
4.8 and 4.9 are more appropriate because the concentrations of metal
ion, MLH2+ and LH are decreasing where ML2 species is increasing.

An observation made from the distribution diagrams (Figs. 4.9-
4.21) is that the free metal ion concentration is more in the case of
valine than proline for Co(II) and Ni(II) in PG- and AN-water mixtures.
This infers the stronger complexing ability of proline than valine, even
though the distinctive cyclic structure of proline's side chain gives
proline an exceptional conformational rigidity compared to other
amino acids.

155

100 (A) LH ML2 100 (D) LH
FM ML FM
75 75
9
% Species 50 % Species 50 ML ML2
LH2 MLH 9
LH2
25 MLH 25 pH 6

0 6 0
3 3
pH

100 (B) 100 (E)

LH ML 75 LH
2 FM
75 ML2
ML
% Species MLH % Species ML
50 FM
50
25 LH2
LH2
0 MLH
3
25

pH 6 9 0 6 9
3
pH

100 (C) LH ML2 80 (F) LH ML ML2
FM MLH
75 ML 60 FM

% Species 50 % Species 40
LH2
LH2
25 20

MLH

00

2 4 pH 6 8 246

pH

Fig. 4.9: Distribution diagrams of M(II)-proline/valine in aqueous
media (A) Co(II)-proline, (B) Ni(II)-proline, (C) Cu(II)-proline,

(D) Co(II)-valine, (E) Ni(II)-valine and (F) Cu(II)-valine.

156

100 (A) LH 100 (B) LH ML2
ML
FM ML2 75
75 ML FM

% Species 50 % Species 50 MLH
LH2 LH2
MLH
25 25

0 6 9 0
3 369
pH
pH

100 (C) LH ML2 100 (D) LH ML2
FM ML FM ML
75 75
MLH
% Species 50 % Species 50
LH2
LH2 MLH
25 25

0 0
369 369

pH pH

80 (E) LH ML 90 (F) LH ML2
2
% Species 60 60 MLH
MLH ML ML

FM % Species
40

20 LH2 FM
30

LH2

0 9 0
36 369

pH pH

Fig. 4.10: Distribution diagrams of Co-proline in PG-water mixtures.
% v/v: (A) 10.0, (B) 20.0, (C) 30.0, (D) 40.0, (E) 50.0 and (F)
60.0.

157

90 (A) LH ML2 80 (B) ML2
MLH ML 9
60 LH
% Species
FM % Species 60
30 MLH
ML
LH2
40
0 FM
3
20
LH2

6 9 0 6
3
pH pH

90 (C) MLH LH ML2 90 (D) LH ML
ML MLH 2
60 60
ML

% Species LH2 % Species 30 FM
30
LH2
FM
0
0 6 9 3 6 9
3
pH pH

90 (E) 90 (F) MLH

MLH ML2 LH ML2
ML ML
LH
% Species 60 % Species 60
LH2

30 FM 30
LH FM

2

0 6 9 0 6 9
3 3
pH pH

Fig. 4.11: Distribution diagrams of Ni-proline in PG-water mixtures.
% v/v: (A) 10.0, (B) 20.0, (C) 30.0, (D) 40.0, (E) 50.0 and (F)
60.0.

158