Complexomety in analytical study

1. Pabitra Kumar Mani , Assoc. Prof., Ph.D. ACSS, BCKV
Class - 14
Complexometric titrations

2. The classical rules of valency do not apply for complex ions.
To explain the particularities of chemical bonding in complex ions, various
theories have been developed.
As early as 1893, A. Werner suggested that, apart from normal valencies,
elements possess secondary valencies which are used when complex
ions are formed. He attributed directions to these secondary valencies, and
thereby could explain the existence of stereoisomers, which were prepared
in great numbers at that time.
Later G. N. Lewis (1916), when describing his theory of chemical bonds
based on the formation of electron pairs, explained the formation of
complexes by the donation of a whole electron pair by an atom of the
ligand to the central atom. This so-called dative bond is sometimes
denoted by an arrow, showing the direction of donation of electrons. In the
structural formula of the tetramminecuprate(ll) ion the arrows
indicate that an electron pair is donated by each
nitrogen to the copper ion.
Although the Lewis theory offers a comprehensive explanation of chemical
structures in relatively simple terms, a deeper understanding of the
nature of the chemical bond necessitated the formulation of new theories.

3. Among these the ligand field theory explains the
formation of complexes on the basis of an electrostatic field
created by the coordinated ligand around the inner sphere of
the central atom.
This ligand field causes the splitting of the energy
levels of the d-orbitals of the central atom, which in turn
produces the energy responsible for the stabilization of
the complex (ligand field stabilization energy).
A complex ion (or molecule) comprises a central atom (ion)
and a number of ligands closely attached to the former.
The relative amounts of these components in a stable complex seems to
follow a well-defined stoichiometry, although this cannot be interpreted
within the classical concept of valency.
The central atom can be characterized by the coordination number,
an integer figure, which shows the number of (monodentate) ligands which
may form a stable complex with one central atom.
In most cases the coordination number is 6 (as in the case of Fe2+ , Fe3+ ,
Zn2+ , Cr3+ , Co3+ , NF+ , Cd2+ ) sometimes 4 (Cu 2+ , Cu", Pt 2+), but the
numbers 2(Ag+) and 8 (some of the ions in the platinum group) do occur.

11. Formation of complex 
Many metal ions can accept unshared pairs of electrons from an anion or
molecule to form coordinate covalent bonds. The molecule or ion species
containing atom which donates the electrons is called a ligand or
complexing agent. The ion which accepts the donated electrons is called
the central ion or central atom. And the product resulting from a reaction
between a metal ion and a ligand is referred to as a coordination compound
or complex ion.
Central atom
Ligands(unidentate)
[CoCl(NH3)5]Cl2
Ionization sphere
Coordination sphere
Metal ions are Lewis acids, ligands are Lewis bases.
Ag+
+ 2 :C≡N: – = [N≡C—Ag—C≡N] –
Lewis acid
Lewis base
Complex ion
electron-pair acceptor electron-pair donor

12. When Co3+ ions react with ammonia, the Co3+ ion accepts pairs
of nonbonding electrons from six NH3 ligands to form covalent
cobalt-nitrogen bonds as shown in the figure below.
The metal ion is therefore a Lewis acid, and the ligands coordinated
to this metal ion are Lewis bases.
The Co3+ ion is an electron-pair acceptor, or Lewis acid, because
it has empty valence-shell orbitals that can be used to hold pairs of
electrons. To emphasize these empty valence orbitals we can write
the configuration of the Co3+ ion as follows.
Co3+: [Ar] 3d6 4s0 4p0
There is room in the valence shell of this ion for 12 more electrons.
(Four electrons can be added to the 3d subshell, two to the 4s orbital,
and six to the 4p subshell.) The NH3 molecule is an electron-pair
donor, or Lewis base, because it has a pair of nonbonding
electrons on the nitrogen atom.
According to this model, transition-metal ions form coordination
complexes because they have empty valence-shell orbitals that can
accept pairs of electrons from a Lewis base. Ligands must therefore
be Lewis bases: They must contain at least one pair of nonbonding
electrons that can be donated to a metal ion.

13. Chelones: Chelate complex forming reagents which forms
exclusively 1:1 (mole ratio) complexes with any
metal ion. The reagents must be a polydentate
chelating agent containing more than 2 donor groups.
CH2 COOH
+
HN
CH2COOCH2COOH
NITRILO TRIACETIC ACID,
Zwitterion form
CH2 COOH
HN:
CH2COO
Cu-
CH2COOH
All the Co-Ordination no. of
Cu+2 are satisfied by 4 donor
group 1:1 complex

14. EDTA
Na2-EDTA
CH2COOH
CH2— N
CH2COOH
CH2COOH
CH2—N
CH2COOH
H
CH2— N:
+
+
CH2—N:
H
H
CH2— +
N
+
CH2—N
H
CH2COONa
CH2COOCH2COOCH COONa
highly soluble in 2
water, but free
EDTA is sparingly soluble
CH2COOCH2COOCH2COO-
CH2COOHexadentate Ligand
Ca
EDTA-2 (actual Chelone)
H2Y-2 + Ca+2 →Ca-Y-2 + 2H+

15. EDTA
HOOCCH2
HOOCCH2
+
NCH2CH2N +
CH2COOH
CH2COOH
H
H
Ethylenediaminetetraacetic acid (EDTA)
Hexatropic system :
H6Y2+
EDTA disodium salt Na2H2Y⋅2H2O
pK1 = 0.0
pK2 = 1.5
Carbonyl protons
pK3 = 2.0
pK4 = 2.66
pK5 = 6.16
pK = 10.24
Ammonium protons

16. Ethylenediamenetetraacetic acid (EDTA)
EDTA forms 1:1 complexes with metal ions by with 6 ligands: 4 O & 2N. EDTA is the
most used chelating agent in analytical chemistry, e.g. water hardness.

17. Structures of analytically useful chelating agents. NTA tends to form 2:1
(ligand:metal) complexes with metal ions, whereas the others form 1:1
complexes.

18. The Chelate Effect
A central metal ion bonds to a multidentate ligand in more
than one location to form a ring structure. Such compounds
are called chelates. Generally, ring formation results in
increased stability of the complex. This generalization is
called the chelate effect. The stability of the multidendate
complex is mainly an entropy effect.
a.The chelate effect is the ability of multidentate ligands to
form more stable metal complexes than those formed by
similar monodentate ligands.
② The chelate effect can be understood from
thermodynamics. The two tendencies that drive a chemical
reaction are decreasing enthalpy and increasing entropy

19. Cd(H2O)62+ with two molecules of ethylenediamine
2+
Ethylenediamine
ΔH = -55.6KJ/mol ΔS = -2J/(mol
K)
A reaction is favorable if ΔG < 0.
ΔG = ΔH -TΔS

20. Common monodentate ligands
Neutral
Anionic
H2O
F –,
Cl–,
NH3
SCN–,
Br –,
CN–
I–
RNH2(aliphatic amines)
OH–,
RCOO–,
S2–

23. EDTA Complexes
The equilibrium constant for the reaction of a metal with a ligand
is called the formation constant, Kf, or the stability constant
Formation constant :
Note that Kf for EDTA is defined in terms of the species
Y4- reacting with the metal ion.
The equilibrium constant could have been defined for
any of the other six forms of EDTA in the solution.

26. Y4-4-complexes with metal ions, and so the complexation equilibria are very pH dependent.
Y complexes with metal ions, and so the complexation equilibria are very pH dependent.
Only the strongest complexes form in acid solution, e.g., HgY 2-2-; CaY2-2-forms in alkaline solution.
Only the strongest complexes form in acid solution, e.g., HgY ; CaY forms in alkaline solution.
©Gary Christian,
Analytical Chemistry,
6th Ed. (Wiley)
Fig. 9.1. Fraction of EDTA species as a function of pH.

27. As the pH increases, the equilibrium shifts to the right.
As the pH increases, the equilibrium shifts to the right.
©Gary Christian,
Analytical Chemistry,
6th Ed. (Wiley)
Fig. 9.3. Titration curves for 100 mL 0.1 M Ca2+
versus 0.1 M Na2EDTA at pH 7 and 10.

28. Note that the effect of increasing pH on the relative change of pCa before and
after the equivalence point. The endpoint becomes sharper as pH increases
Influence of pH on the titration of 0.0100M Ca2+ with 0.0100M EDTA.

29. Titration curves for 50.0 ml of 0.01M solutions of various cations at pH
6.0.
As KMY becomes larger, there is a greater relative change between analyte
(or reagent) concentrations at the equivalence point

30. The points represent the pH at which the conditional formation
The points represent the pH at which the conditional formation
constant, Kf', for each metal is 1066,needed for a sharp end point.
constant, Kf', for each metal is 10 , needed for a sharp end point.
©Gary Christian,
Analytical Chemistry,
6th Ed. (Wiley)
Minimum pH for effective titrations of various metal ions with EDTA.

31. Various types of application in Chelometric titration
A. Direct titration.
A metal ion having appreciable value of stability
constant can be directly titrated by the std. EDTA soln.
The solution containing the metal ion to be determined is
buffered to the desired pH (e.g. to pH = 10 with NH4+-aq.
NH3) and titrated directly with the standard EDTA solution.
It may be necessary to prevent precipitation of the
hydroxide of the metal (or a basic salt) by the addition of
some auxiliary complexing agent, such as tartrate or citrate
or triethanolamine.
At the equivalence point the magnitude of the concentration of
the metal ion being determined decreases abruptly. This is
generally determined by the change in colour of a metal
indicator and the end point may be determined by
amperometric, spectrophotometric,or potentiometric

32. B. Back-titration.
Many metals cannot, for various reasons, be titrated directly;
(i) thus they may precipitate from the solution in the pH range
necessary for the titration,
(ii) or they may form inert complexes,
or (iii) a suitable metal indicator is not available.
In such cases an excess of standard EDTA solution is
added, the resulting solution is buffered to the desired pH,
and the excess of the EDTA is back-titrated with a standard
metal ion (Mg or Zn) solution; a solution of zinc chloride or
sulphate or of magnesium chloride or sulphate is often
used for this purpose.
The end point is detected with the aid of the metal indicator
(EBT) which responds to the zinc or magnesium ions
+3
+3
+2
introduced in the back-titration.
Metals are : Fe , Al , Co

33. C. Replacement or substitution titration.
Substitution titrations may be used for metal ions that do
not react (or react unsatisfactorily) with a metal indicator, or
for metal ions which form EDTA complexes that are more
stable than those of other metals such as Mg and Ca.
The metal cation Mn+ to be determined may be treated
with the magnesium complex of EDTA, when the following
reaction occurs :
The amount of Mg+2 ion set free is equivalent to the cation
present and can be titrated with a standard solution of EDTA
and a suitable metal indicator (EBT).
An interesting application is the titration of Ca. In the
direct titration of Ca+2 ions, solochrome black gives a poor
end point; if Mg is present, it is displaced from its EDTA
complex by calcium and an improved end point results

34. D. Alkalimetric titration.
In an unbuffered solution, When a solution of disodium salt of
EDTA ( ethylenediaminetetraacetate, Na2H2Y), is added to a soln
containing metallic ions, complexes are formed with the
liberation of two equivalents of H ion:
The H+ thus set free can be titrated with a standard solution of
NaOH using an acid-base indicator or a potentiometric end
point.
Only metals forming EDTA complexes of very high stability
constatnts can be determined by this method.
The solution of the metal to be determined must be
accurately neutralised before titration; this is often a difficult
matter on account of the hydrolysis of many salts, and
constitutes a weak feature of alkalimetric titration.

35. E. Miscellaneous methods.
Exchange reactions between the tetracyanonickelate(II) ion
[Ni(CN)4] 2- (the potassium salt is readily prepared) and the
element to be determined, whereby Ni ions are set free, have a
limited application. Thus Ag and gold, which themselves cannot
be titrated complexometrically, can be determined in this way.
These reactions take place with sparingly soluble silver salts,
and hence provide a method for the determination of the ions
like Cl-, Br-, I-, and the SCN-. The anion is first precipitated as
the silver salt, the latter dissolved in a solution of [Ni(CN)4] 2-,
and the equivalent amount of nickel thereby set free is
determined by rapid titration with EDTA using an appropriate
indicator (murexide, bromopyrogallol red).

36. Discussion.
When calcium ions are titrated with EDTA a relatively stable
calcium complex is formed:
With Ca ions alone, no sharp end point can be obtained with solochrome
black indicator and the transition from red to pure blue is not observed.
With Mg ions, a somewhat less stable complex is formed:
and the magnesium indicator complex is more stable than the calciumindicator complex'but less stable than the magnesium-EDTA complex.
Consequently, during.the titration of a solution containing Mg and
Ca ions with EDTA in the presence of solochrome black the EDTA reacts
first with the free calcium ions, then with the free magnesium ions, and
finally with the magnesium indicator complex.
Snce the magnesium-indicator complex is wine red in colour
and the free indicator is blue between pH 7 and 11, the colour of the
solution changes from wine red to blue at the end point:

37. If Mg ions are not present in the solution containing Ca ions they must be
added, since they are required for the colour change of the indicator.
A common procedure is to add a small amount of magnesium
chloride to the EDTA solution before it is standardised. Another procedure,
which permits the EDTA solution to be used for other titrations, is to
incorporate a little magnesium-EDTA (MgY2-) (1-10 per cent) in the buffer
solution or to add a little 0.1 M magnesium-EDTA (Na2MgY) to the calciumion solution:
Traces of many metals interfere in the determination of Ca and Mg
using solochrome black indicator, e.g. Co, Ni, Cu, Zn, Hg, and Mn.
Their interference can be overcome by the addition of a little
hydroxylammonium chloride (which reduces some of the metals to their
lower oxidation states), or also of NaCN or KCN which form very stable
cyanide complexes ('masking'). Iron may be rendered harmless by the
addition of a little sodium sulphide.
The titration with EDTA, using solochrome black as indicator, will yield
the Ca content of the sample (if no Mg is present) or the total Ca and Mg
content if both metals are present. To determine the individual
elements, calcium may be evaluated by titration using a suitable indicator,
e.g., Patton and Reeder's indicator or calcon

38. EDTA titration curve
Mn+ + EDTA = MYn –4
K = [MYn –4] / [Mn+][EDTA]
= Kf α
Y 4–
Ex. 0.0500M Mg2+ 50.0ml (pH=10.00) vs 0.0500M EDTA
Titration reaction :
Mg2+ + EDTA = MgY2 –
K = [MgY2–] / [Mg2+][EDTA]
= Kf α
Y 4–
= (0.36)(6.2×108) = 2.2 ×108
Equivalence point :
0.0500M×50ml = 0.0500M×Ve
Ve = 50.0ml

39. There is excess EDTA, and vitually
all the metal ion is in the form Myn-4
There is exactly as much EDTA as
metal in the solution. [Mn+ ] = [EDTA]
In this region, there is excess Mn+
left in solution after the EDTA has
been consumed.
Three regions in an EDTA titration illustrated for reaction of 50.0mL
of 0.05 M Mn+ with 0.05M EDTA, assuming Kf’ = 1.15 × 1016.

40. End point detection methods
1) Metal ion indicator
Compound whose color changes when it binds to a metal
ion.
Ex. Eriochrome black T
Mg2+ + In → MgIn
MgIn + EDTA → MgEDTA + In
(Red) (Colorless) (Colorless)
2) Mercury electrode
3) Glass(pH) electrode
4) Ion selective electrode
(Blue)

42. Theory of the visual use of metal ion indicators
The use of a metal ion indicator in an EDTA titration may be written as:
M-EDTA must be more more stable complex than M-In
complex
M+ + In
M-In
large amount 1 or 2 drops
colour difft from that of indicator
This reaction will proceed if the metal-indicator complex M-In is less
stable than the metal-EDTA complex M-EDTA. The former
dissociates to a limited extent, and during the titration the free metal
ions are progressively complexed by the EDTA until ultimately the
metal is displaced from the complex M-In to leave the free indicator
(In). The stability of the metal-indicator complex may be expressed in
terms of the formation constant (or indicator constant) KIn:

43. Eriochrome Black T,
(polybasic organic acids of high molecular wt containing
conjugated systems )
H2In-, exhibits the following acid-base behaviour
At pH 9.0-10.0 (NH4 + NH4OH buffer , free indicator(HIn-2) is
blue in colour
Mn+ + HIn-2
M-In +(n-3) + H+
Blue
Red
Coloue change Red to Blue when Mn+ is titrated by EDTA in
presence of EBT indicator

44. Below pH 6.5, the indicator can’t be used as it tends to
polymerize. This colour change can be observed with the ions of
Mg, Mn, Zn, Cd, Hg, Pb,Cu, Al, Fe, Ti, Co, Ni, and the Pt metals.
To maintain the pH constant (ca 10) a buffer mixture is added, and most of
the above metals must be kept in solution with the aid of a weak complexing
reagent such as ammonia or tartrate.
Ca+2 does not form red colour with EBT indicator.
In case of titration of a mixture of sevral metal ions suitable masking agents
can be used so that one metal ion can be specifically titrated.
The usual musking agents are : tartrate4-, Cit3-, CN-, O-pn,
triethanolamine [N(CH2.CH2.OH)3] ,and OH Murexide
H4In(reddish violet)
⇋
pH 9-11
Ca+2 + H3In-2
(violet)
at pH 11
H3In-2
(violet)
⇋
→
H2In-3
pH 9-11 (blue violet)
(Ca-Hin)-2
+ 2H +
Red
(Chelated or M-In)

45. Solochrome Black (Eriochrome Black T ): Sodium 1-(1- hydroxy-2naphthylazo)-6-nitro-2-naphthol-4-sulphonate(II).
In strongly acidic solutions the dye tends to
polymerise to a red-brown product, and consequently the indicator is rarely applied in
titrations of solutions more acidic than pH = 6.5. The sulphonic acid group gives up its
proton long before the pH range of 7-12, which is of immediate interest for metal-ion
indicator use. Only the dissociation of the two hydrogen atoms of the phenolic groups
need therefore be considered, and so the dyestuff may be represented by the formula
H2D-.
The two pK values for these hydrogen atoms are 6.3 and 11.5 respectively. Below pH
= 5.5, the solution of solochrome black is red (due to H2D -), between pH 7 and 11 it
is blue (due to HD2-), and above pH = 11.5 it is yellowish-orange (due to D3-). In the
pH range 7-11 the addition of metallic salts produces a brilliant change in colour from
blue to red:
+ M2+
+ 2H+
Blue (pH 10)

46. Solochrome Dark Blue or Calcon : referred to as
Eriochrome Blue Black; it is in fact
Sodium 1-(2-hydroxy-1-naphthylazo)-2-naphthol-4-sulphonate.
The dyestuff has two ionisable phenolic hydrogen atoms; the protons
ionise stepwise with pK values of 7.4 and 13.5 respectively.
An important application of the indicator is in the complexometric
titration of Ca in the presence of Mg; this must be carried out at
a pH of about 12.3 (obtained, for example, with a diethylamine buffer: 5
mL for every 100 mL of solution) in order to avoid the interference of Mg.
Under these conditions Mg is precipitated quantitatively as the
hydroxide. The colour change is from pink to pure blue.

48. EDTA titration curves for 50.0 ml 0f 0.00500 M Ca2+ (K’CaY = 1.75 ×1010) and
Mg2+ (K’MgY= 1.72 × 108) at pH 10.00.

49. Differential titration using EDTA
I. Mix. of Ca+2 and Mg+2
(a) Total Ca and Mg is directly titrated by EDTA using
Eriochrome Black T indicator (in NH4-buffer soln.)
Mg+2
Ca+2
EDTA
NH4 –buffer
Mg-EDTA
Ca-EDTA
Mg-In + EDTA → Mg-EDTA
Red
(V 1)
+ In
Blue
(b)
2nd Aliquot + NH4–buffer + KOH soln. (Mg is masked as
Mg(OH)2
titration with EDTA
only Ca+2 is titrated
using Murexide or Calcon
(V2)
V1-V2 = titration value for Mg

50. II. Mix. of Zn+2, Cu+ and Mg+2
(a) Aliquot + Excess EDTA soln.
Total metals (V1
ml)
back titrated with
Mg+2 soln in NH4–buffer
using EBT indicator
(b) 2nd Aliquot + NH4–buffer + KCN soln.
Only Mg
(titration directly with EDTA
using EBT
(V2)
(Cu and Zn form cyano complex)
(c) After the e.p. in (b), add Chloral hydrate (CCl3.CH2O) to
‘demusk’ the Zn-complex [Zn (CN) 4 ] -2 which is less stable
(titration by EDTA
[Zn (CN)4]-2 + 4CCl3CHO + 4H+
Cu = V1 –(V2+V3)
Titrated value of Zn
(V3)
OH
Zn+2 + 4CCl3—CH
EDTA
cyanohydrin
CN

52. The conjugate base of DTPA has a high affinity for metal cations. Thus, the pentaanion DTPA5- is potentially an octadentate ligand. In contrast, EDTA possesses 6
centres to form coordination bonds with metals.[1] The formation constants for its
complexes are about 100 greater than those for EDTA.[2]
As a chelating agent, DTPA wraps around a metal ion by forming up to eight bonds.
Transition metals, however, usually have a limited coordination capacity and can
form less than eight coordination bonds with ligands. So, after forming a complex
with a metal, DTPA still has the ability to bind to other reagents, as is shown by its
derivative pendetide. For example, in its complex with copper(II), DTPA binds in a
hexadentate manner utilizing the three amine centres and three of the five
carboxylates.[3] Like many other chelating agents, DTPA has been considered for
treatment of internal contamination from radioactive materials such as plutonium,
americium and other actinides. In theory, these complexes are more apt to be
eliminated in urine. It is normally administered as the calcium or zinc salt.

53. Example Titration
• 25.0 mL of an unknown Ni2+ solution was treated with
25.00 mL of 0.05283 M Na2EDTA. The pH of the
solution was buffered to 5.5 and than back-titrated
with 17.61 mL of 0.02299 M Zn2+. What was the
unknown Ni2+ M?
Zn 2+ + Y 4- ↔ ZnY 2-
mol EDTA = (25.00 mL)(0.05283 M) = 1.32 mmol EDTA
mol Zn 2+ = (17.61 mL)(0.02299 M) = 0.4049 mmol Zn 2+
Ni 2+ + Y 4- ↔ NiY 2mol Ni 2+ = 1.321 mmol EDTA - 0.4049 mmol Zn 2+ = 0.916 mmol
M Ni 2+ = (0.916 mmol)/(25.00 mL) = 0.0366 M

54. In the pH range 7- 11, in which the dye itself exhibits a blue colour,
many metal ions form red complexes; these colours are extremely
sensitive, as is shown, for example, by the fact that - molar solutions
of magnesium ion give a distinct red colour with the indicator. From
the practical viewpoint, it is more convenient to define the apparent
indicator constant K/In, which varies with pH, as :
(This, for the above indicator, is equal to [H2In-] + [HIn2-] + [In3-].)
The equation may be expressed as: