Pabitra Kumar Mani , Assoc. Prof., Ph.D. ACSS, BCKV

Class - 14

Complexometric titrations

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.

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.

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).

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 CN – = [NC—Ag—CN] –

Lewis acid Lewis base Complex ion electron-pair acceptor electron-pair donor

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.

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 CH2COO-

CH2COOH

+

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

CH2COOHCH2— N

CH2COOH CH2COOHCH2—N CH2COOH

CH2COONaCH2— N

CH2COO-

CH2COO-

CH2—N CH2COONa

+

+

EDTA

H

H

Na2-EDTA

highly soluble in water, but free EDTA is sparingly soluble

CH2COO-

CH2— N: CH2COO-

CH2COO-

CH2—N: CH2COO-

Ca

H

H

+

+

EDTA-2 (actual Chelone)

H2Y-2 + Ca+2 →Ca-Y-2 + 2H+

Hexadentate Ligand

EDTA

HOOCCH2 NCH2CH2N CH2COOH HOOCCH2 CH2COOH

H HEthylenediaminetetraacetic acid (EDTA)

+ +

Hexatropic system : H6Y2+ EDTA disodium salt Na2H2Y2H2O pK1 = 0.0 pK2 = 1.5 Carbonyl protons pK3 = 2.0 pK4 = 2.66 pK5 = 6.16 Ammonium protons pK6 = 10.24

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.

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.

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.

①The 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

2+

Ethylenediamine

Cd(H2O)62+ with two molecules of ethylenediamine

ΔH = -55.6KJ/mol ΔS = -2J/(mol K)A reaction is favorable if ΔG < 0.ΔG = ΔH -TΔS

Common monodentate ligands Neutral Anionic H2O F–, Cl–, Br –, I–

NH3 SCN–, CN–

RNH2(aliphatic amines) OH–, RCOO–, S2–

EDTA ComplexesThe 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.

Fig. 9.1. Fraction of EDTA species as a function of pH.

Y4- complexes with metal ions, and so the complexation equilibria are very pH dependent.

Only the strongest complexes form in acid solution, e.g., HgY2-; CaY2- forms in alkaline solution.

Y4- complexes with metal ions, and so the complexation equilibria are very pH dependent.

Only the strongest complexes form in acid solution, e.g., HgY2-; CaY2- forms in alkaline solution.

©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.

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)

Influence of pH on the titration of 0.0100M Ca2+ with 0.0100M EDTA.

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

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

Minimum pH for effective titrations of various metal ions with EDTA.

The points represent the pH at which the conditional formation

constant, Kf', for each metal is 106, needed for a sharp end point.

The points represent the pH at which the conditional formation

constant, Kf', for each metal is 106, needed for a sharp end point.

©Gary Christian, Analytical Chemistry, 6th Ed. (Wiley)

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 methods.

Various types of application in Chelometric titration

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 introduced in the back-titration. Metals are : Fe+3, Al+3, Co+2

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

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.

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).

Discussion. When calcium ions are titrated with EDTA a relatively stablecalcium 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 calcium-indicator 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 colourand 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:

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 calcium-ion 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 individualelements, calcium may be evaluated by titration using a suitable indicator,e.g., Patton and Reeder's indicator or calcon

EDTA titration curve

Mn+ + EDTA = MYn –4

K = [MYn –4] / [Mn+][EDTA]

= Kf 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 Y 4– = (0.36)(6.2×108) = 2.2 ×108

Equivalence point :

0.0500M×50ml = 0.0500M×Ve

Ve = 50.0ml

In this region, there is excess Mn+ left in solution after the EDTA has been consumed.

There is exactly as much EDTA as

metal in the solution. [Mn+ ] = [EDTA]

There is excess EDTA, and vitually all the metal ion is in the form Myn-4

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.

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) (Blue)

2) Mercury electrode

3) Glass(pH) electrode

4) Ion selective electrode

Theory of the visual use of metal ion indicatorsThe use of a metal ion indicator in an EDTA titration may be written as:

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:

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

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

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 ,and OH-

H4In- ⇋ H3In

-2 → H2In-3

(reddish violet) pH 9-11 (violet) pH 9-11 (blue violet)

Ca+2 + H3In-2 ⇋ (Ca-Hin)-2 + 2H+

(violet) Red at pH 11 (Chelated or M-In)

[N(CH2.CH2.OH)3]

Murexide

Solochrome Black (Eriochrome Black T ): Sodium 1-(1- hydroxy-2-naphthylazo)-6-nitro-2-naphthol-4-sulphonate(II). In strongly acidic solutions the dye tends topolymerise 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)

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.

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.

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 EDTA Mg-EDTA (V1) Ca+2 NH4 –buffer Ca-EDTA

Mg-In + EDTA → Mg-EDTA + In Red 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

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 Titrated value of Zn (V3)

[Zn (CN)4]-2 + 4CCl3CHO + 4H+ Zn+2 + 4CCl3—CH

OH

CNcyanohydrinEDTACu = V1 –(V2+V3)

The conjugate base of DTPA has a high affinity for metal cations. Thus, the penta-anion 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.

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?

EDTA mmol 1.32M) 3mL)(0.0528 (25.00 EDTA mol 22 Znmmol 4049.0M) 9mL)(0.0229 (17.61 Znmol

mmol 916.0 Znmmol 0.4049-EDTA mmol 321.1 Ni mol 22

M 0.0366mL) 00mmol)/(25. 916.0( Ni M 2

-2-42 ZnYY Zn

-2-42 NiY Y Ni

(This, for the above indicator, is equal to [H2In-] + [HIn2-] + [In3-].)

The equation may be expressed as:

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 :