POTENTIOMETRIC TITRATIONS

The titrations which involve the measurement of electrode potentials with the addition of the titrant, are called potentiometric titrations.

Generally, potentiometric titrations fall into the following three categories---

(1). Acid-Base Titrations

(2). Redox Titrations or Oxidation-Reduction Titrations

(3). Precipitation Titrations

Acid-Base Titrations

Suppose an acid (say, HCl) is to be titrated with a base (say, NaOH). In the HCl solution is inserted a hydrogen electrode and this is coupled with a reference electrode, such as calomel electrode. So, the galvanic cell may be represented as---

Pt, H₂ (1 atm) | H⁺ || KCl sat. soln; Hg₂Cl₂ (s) | Hg

So, the EMF of the cell---

E = E_calomel – E_hydrogen

= 0.2422 – 0.0591 log [H⁺] (at 25⁰C)

= 0.2422 + 0.0591 P^H

Suppose 100 ml of 0.1 M HCl solution is to be titrated against the titrant 1 M NaOH solution. With the successive addition of alkali, the concentration of H⁺ goes on decreasing. So, the P^H of the solution goes on increasing and also EMF of the cell goes on increasing. It is found that, the EMF of the cell would increase by 0.0591 volt for every 10-fold decrease in the concentration of H⁺ ions or increase in the P^H of the solution by one unit.

Assuming that, there is no change in volume during the titration, it is found that, for the addition of first 9 ml of titrant NaOH, will give a change of 0.0591 volt. However, for the addition of next 0.9 ml of titrant NaOH, will produce the same change, and also for the addition of next 0.9 ml of titrant NaOH, will produce the same change and so on. So, the EMF of the cell changes slowly at first but more and more rapidly as the end point approaches.

Further addition of titrant NaOH solution, after the end point produces very little change in the H⁺ ion concentration. So, there is very little change in the EMF of the cell.

The plot of E against the volume of titrant NaOH is shown in the figure---

The EMF of the cell initially rises gradually, after that more rapidly near the equivalence point. After the equivalence point, the EMF of the cell again increases slightly on adding more of NaOH.

The plot of (ΔE/ΔV) against the volume of titrant NaOH is shown in the figure---

At the equivalence point, the resulting curve rises to a maximum. The volume of the titrant NaOH solution, at the equivalence point is determined by drawing a vertical line from the peak to the volume axis.

The plot of (Δ²E/ΔV²) against the volume of titrant NaOH is shown in the figure---

The derivation of the slope is zero, at the point where the slope ΔE/ΔV is a maximum. By drawing a vertical line from the point at which Δ²E/ΔV² is zero on the volume axis, the equivalence point is determined.

Redox Titrations or Oxidation-Reduction Titrations

Let us consider the titration of an acidified ferrous sulphate solution with an oxidising agent, say a dichromate solution. In a beaker, a known volume of ferrous sulphate solution is taken and a platinum wire is inserted in it. The titre dichromate solution is added from a burette. During the titration, at any instant, we have a mixture of Fe²⁺ and Fe³⁺ ions with a Pt-wire inserted in it, and this forms a reversible electrode. To form the cell, this electrode is coupled with a reference electrode, say a calomel electrode.

The galvanic cell is represented as---

Hg | HgCl₂ (s), KCl (sat. soln.) || Fe²⁺ | Fe³⁺; Pt

So, the EMF of the cell---

E = Constant + 0.0591 log ([Fe³⁺] / [Fe²⁺]) (at 25⁰C)

The progressive addition of titre, will cause a change in the EMF of the cell, as the ratio [Fe³⁺] / [Fe²⁺] increases. The Fe²⁺ ions concentration will be ultimately extremely small but not zero. When the EMF of the cell is plotted against the volume of titre added, the curve shows its greatest slope when the equivalence point is reached. Before the end point, the potentials are governed by the titrated system ([Fe³⁺] / [Fe²⁺]). After the equivalence point is passed, the potentials are governed by the titrant system ([Cr³⁺] / [Cr₂O₇^2-]).

The plot of E against the volume of titrant K₂Cr₂O₇ is shown in the figure---

Precipitation Titrations

Consider the estimation of chlorides with silver nitrate solution by potentiometric titrations. In a beaker, a known volume of KCl solution is taken, in which is inserted a silver electrode, called an indicator electrode. The titrant AgNO₃ is added from a burette in small amount. As a result, AgCl is formed as a precipitate. The reaction is---

Ag⁺ + NO₃^- + (K⁺ + Cl^-) ------> AgCl (s) + K⁺ + NO₃^-

So, we have a reversible electrode Ag | AgCl(s)|Cl^-. This electrode is coupled with a reference electrode, say a calomel electrode.

The cell is represented as---

Ag | AgCl(s) | Cl^- || KCl sat. soln; Hg₂Cl₂(s) | Hg

So, the EMF of the cell---

E = Constant – 0.0591 log [Ag⁺] (at 25⁰C)

The solubility of AgCl is quite small, with the progress of the titration the concentration of Ag⁺ ions in solution will change very slightly, so the EMF of the cell will change but little. When the equivalence point is reached, the addition of a drop of AgNO₃ would bring about a large increase in the Ag⁺ ion concentration, so the EMF of the cell change sharply. That is, when the sharp change in EMF is detected, the end point is reached.

The plot of E against the volume of titrant AgNO₃ is shown in the figure---

The plot of (ΔE/ΔV) against the volume of titrant AgNO₃ is shown in the figure---

 TRANSITION STATE THEORY

Transition state theory or theory of absolute reaction rate was developed by Eyring considering statistical mechanics. It is known as theory of absolute reaction rate, because it was fundamental properties such as vibrational frequency of the reactant molecules to calculate the rate of reaction.

According to this theory---

(1) In order for only chemical reaction to take place the reactant molecules possessing sufficient energy must approach each other, to form a lose association known as activated complex. This complex is in equilibrium with the reactant molecules. The configuration of this complex is such that energetically it corresponds to the top of energy barrier separating the reactants from the product.

(2) The activated complex is an aggregate of atoms, it may be thought of being similar to a molecule except that it has one special vibration with respect to which it is unstable. This vibration leads to dissociation of the complex into products. If the frequency of this vibration is v then rate in molecules per unit volume per second at which products are formed as---

Rate = v x concentration of activated complex

Now let us consider the following reaction---

A + B <=====> [ AB] ^#

Where is [AB]^# activated complex.

Since reactant molecules and activated complex are in equilibrium, the equilibrium constant---

K^# = [AB]^# / [A][B]

Or, conc of activated complex, [AB]^# = K^# [A][B]

Now, if v is the frequency of the vibration of the unstable degree of freedom, then vibrational energy is hv, but from statistical mechanics, vibrational energy per degree of freedom is KT, so ---

hv = KT

Or, v = KT / h 

[where K= Boltzmann’s constant]

Hence the rate of reaction---

Rate = v [AB]^#

Rate = (KT / h) K^# [A][B] ------ (a)

Now simple kinetic study for the reaction---

A + B ------> Products states 

Rate = K_r [A][B] ------ (b)

where K_r is rate constant

Comparing (a) and (b), we get---

K_r = (KT / h) K^# ------ (1)

Now from Vant Hoff’s isotherm---

-ΔG^# = RT lnK^#

(Where, ΔG^# = free energy change during an activated formation)

Or, K^# = e^{- ΔG#/RT}

Or, K^# = e^-ΔH#/RT . e^ΔS#/R

ΔS^# and ΔH^# are entropy and enthalpy of activation.

So, from equation (1) ---

K_r = (KT / h) e^-ΔH#/RT . e^ΔS#/R ------ (2)

Thus, experimentally measuring rate constant (K_r) at two different temperature, enthalpy and entropy of activation can be known. This is the most important success of transition state theory, because with the knowledge of ΔH^# and ΔS^# for a reaction, knowledge about its mechanism can be obtained. 

 FRIEDEL CRAFTS REACTION

The carbon atom of alkyl halides R^δ+―X^δ- is electrophilic but is so weak that to effect the substitution of aromatic species. So, the electrophilicity of carbon may be enhanced by the addition of a species which is able to  accept electrons from halogen, that is X and the reaction then occurs with less reactive aromatic compounds. This principle may be applied to the formation of bonds between aromatic and aliphatic carbon atoms by Friedel-Crafts alkylation and acylation.

ALKYLATION

Alkylating agents are halides, alcohols, esters, alkenes, aldehydes and ketones. Reactions of the first four classes are normally catalysed by Lewis acids and those of the last three by proton acids. In alkylation AlCl₃ is employed as the catalyst. The order of effectiveness of the Lewis acid catalysts has been shown to be---

AlCl₃>FeCl₃>BF₃>TiCl₃>ZnCl₂>SnCl₄

With primary and secondary halides, it is believed that an ion-pair is formed with the Lewis acid, the carbocation part of which then effects substitution.

Free carbocations are thought to be involved with tertiary halides. For example, benzene tertiary butyl chloride, FeCl₃ give tertiary butyl benzene in 80% yield via the tertiary butyl cation.

Some Examples:

Alkenes react via the carbocations which the form with proton acids.

REACTIVITY

Aromatic compounds whose nuclear reactivity is comparable with or greater than that of benzene can be successfully alkylated but strongly deactivated compounds do not react. For example, chloro benzene reacts but nitro benzene is inert. Phenol do not react satisfactorily because they react with the Lewis acids at oxygen (ArOH + AlCl₃ ---> ArOAlCl₂ + HCl) and the resulting compound is usually only sparingly soluble in the reaction medium so that it reacts slowly. Aromatic amines are not suitable for alkylations because aromatic amines form strong complex with Lewis acids.

PROBLEMS OF FRIEDEL CRAFTS ALKYLATION

Since alkyl groups are activating in electrophilic substitutions, the product of alkylation is more reactive than the starting material and further alkylation occurs. For example, the methylation of benzene with methyl chloride in the presence of AlCl₃ gives a mixture containing toluene, the xylenes, tri and tetra methyl benzenes, penta methyl benzenes and hexa methyl benzene.

Many alkyl groups rearrange during alkylation.

The reason probably comes from the fact that the initial electrophilic complex being polarized enough to allow the rearrangement.

The explanation is that the complex with the weaker Lewis acid, FeCl₃ is not now polarized enough to allow the isomerisation taking place.

However, in some instances, during alkylation, rearrangement of tertiary halides occurs.

A probable explanation is that although the tertiary ion is the more stable of the two, it is also the less reactive, so that the faster reaction of the secondary ion dominates, even though this ion is present in smaller concentration.

Tertiary butyl halides do not undergo rearrangement during alkylation, probably this would involve formation of the highly energetic carbonium ion.

SYNTHETIC UTILITY

Alkylation is reversible, so that the reaction is thermodynamically controlled. For example, a monosubstituted benzene usually gives mainly meta-alkyl derivative, since this is thermodynamically most stable.

Just as tertiary alkyl groups are the most readily introduced during alkylation, they are also readily removed by the reverse reaction, departing as the relatively stable tertiary carbocations.

This enables the tertiary butyl group to be used as a protective group, to protect the most reactive position, in a compound in order to effect reaction elsewhere.

ACYLATION

The acylation can be brought about by an acid chloride or anhydride in the presence of a Lewis acid or by a carboxylic acid in the presence of a protic acid. In the Lewis acid catalysed methods, two electrophiles are involved, one is an oxygen-bonded complex.

The other is an acylium ion.

There are a number of differences between acylation and alkylation.

1. In the alkylation does not require stochiometric quantities of the Lewis acid, because this is regenerated in the last stage of the reaction, but in case of acylation, requires greater than equivalent quantities because the ketone which is formed complexes with the Lewis acid.

2. In the electrophilic substitution acyl groups deactivate aromatic nuclei, so the products of acylation are less reactive as compare to the starting materials and so the monoacylated product is easy to isolate. This makes acylation a more useful procedure than alkylation, and alkyl derivatives are often more satisfactorily obtained by acylation followed by reduction of carbonyl to methylene than by direct alkylation.

3. One limitation attempted acylation with derivatives of tertiary acids may lead to alkylation.

The driving force for the decarboxylation resides in the relative stability of tertiary carbocations. However, more reactive aromatic compounds can react before decarboxylation occurs.

CHLOROMETHYLATION

With the appropriate halogen acid other halogen methylation such as fluoromethylation, bromomethylation and iodomethylation may be carried out.

The chloromethylated product can be alkylate another molecule of the aromatic compound in the presence of the acid catalyst.

This secondary reaction is of the particular significance when the aromatic compound is strongly activated and for this reason chloromethylation is not a suitable procedure for phenols and anilines.

The principal value of chloromethylation lies in the ease of displacement of benzylic chloride by nucleophiles. Conversion into the corresponding alcohols PhCH₂OH, ethers PhCH₂OR, nitriles PhCH₂CN and amines PhCH₂-NR₂.  

INTERHALOGEN COMPOUNDS

Halogen atoms have different electronegativity. Therefore, they combine with one another to form a class of compounds known as interhalogen compounds. These may be regarded as the halides of the more electronegative halogens. Since F is the most electronegative of the halogens, it can not form any interhalogen compounds. While the most electropositive iodine has the maximum tendency to form interhalogen compounds.

These compounds can be classified into four groups.

AX type: ClF (g), BrF (g), BrCl (g), ICl (l), IBr (s), IF (unstable)

AX₃ type: ClF₃ (g), BrF₃ (l), ICl₃ (s), IF₃ (unstable)

AX₅ type: ClF₅ (g), BrF₅ (l), IF₅ (l)

AX₇ type: IF₇ (g)

[Where A = central halogen atom, X = other halogen atom]

Interhalogens are generally prepared by the direct combination of halogens. These are never than two different halogens in a molecule. Interhalogens are essentially covalent because of small difference in electronegativities between the two halogen atoms. The melting point and the boiling point of the interhalogen compound increases as the difference in electronegativity of two halogens increases.

In general, reactivity of interhalogens are more than  halogens (except F₂). This is because A―X bond in interhalogen is weaker than the X―X bond in the halogens.

The central halogen atom A has to expand its octet in order to accommodate more than one X group. F is most electronegative and it is devoid of d orbitals. Therefore, it can not serve as the central atom. But F serves strongly as the constituent atom and helps the central atom to attain a high coordination number. Its high electronegativity helps to reduce accumulation of excessive charge density on the central atom.

In interhalogens the number of X atoms is always odd. This is due to the fact that the valence shell of A has or produce odd number of electrons through unpairing.

The melting and boiling points of interhalogens increases regularly with the increase of their molecular weights. This is a proof of their covalent character.

Hydrolysis of an interhalogen produces halide and oxohalide ions. The smaller and the more electronegative halogen forms the halide, while the other forms the oxohalide. The larger and more electropositive halogen serves as the central atom.

The interhalogens are all potential non-aqueous ionizing solvents. This property arises due to their---

1.Convenient liquid range.

2.Good fluorinating behaviour.

3.Considerable self ionisation.

BrF₃ is more widely used as a solvent than the others.

2 BrF₃ <====> [BrF₂] ⁺ + [BrF₄]^-

ICl, IBr, ICl₃, IF₅ can also be used as non-aqueous ionizing solvents. They have appreciable electrical conductivity in their molten state and in solutions.

2 ICl <====> I⁺ + [ICl₂]^-

2 ICl₃ <====> [ICl₂] ⁺ + [ICl₄]^-

2 IF₅ <====> [IF₄] ⁺ + [IF₆]^-

2 ClF₅ <====> [ClF₄] ⁺ + [ClF₆]^-

2 ClF₃ <====> [ClF₂] ⁺ + [ClF₄]^-

The interhalogens are good fluorinating agents. They are also good oxidants. They fluorinate many metal oxides, metal halides, metals and nonmetals. Interhalogen compounds are reactive. The order of reactivity is---

ClF₃>BrF₃>IF₇>ClF>IF₅>BrF>IF₃>IF

INDIVIDUAL CATEGORY

AX type compounds

All six compounds such as ClF, BrF, IF, BrCl, ICl, and IBr are known.

General properties

1.These are essentially covalent.

2.The melting points and boiling points of these interhalogens are intermediate between two free halogens which made the interhalogen.

3.Their thermal stability falls in the order—

IF>BrF>ClF>ICl>IBr>BrCl

Corresponding to the electronegativity difference between the two atoms. The thermal stability of the molecule increases when the polarity increases.

4.Lewis acid strength decreases in the order---

ICl>BrCl>IBr

5.When molten ICl is electrolyzed, a mixture of I₂ and Cl₂ is liberated at anode and only I₂ is liberated at cathode. This mode of electrolysis suggests that ICl ionizes as---

2 ICl <====> I⁺ + ICl₂^-

At cathode:

2 I⁺ + 2 e^- ------> I₂

At anode:

2 ICl₂^- - 2 e ------> I₂ + 2 Cl₂

6.With alkali halides they form ionic poly halides.

NaBr + ICl ----> Na⁺[BrICl]^-

KCl + ICl ----> K⁺[ICl₂]^-

7.AlCl₃, SiCl₄, SnCl₄, SbCl₅ produce I⁺ ion in liquid ICl and hence are acidic.

AlCl₃ + ICl -----> I⁺ + AlCl₄^-

SiCl₄ + ICl ----> I⁺ + SiCl₅^-

SbCl₅ + ICl ----> I⁺ + SbCl₆^-

8.ClF is a good fluonating agent. It can fluorinate metals and non-metals.

6 ClF + 2 Al -----> 2 AlCl₃ + 3 F₂

6 ClF + S ------> SF₆ + 3 Cl₂

It can simultaneously chlorinate and fluorinate a compound.

ClF + SF₄ ------> SF₅Cl

ClF + SO₂ -----> ClSO₂F

ClF + CO -----> COFCl

Structure

Structure of ClF

The AX type of interhalogen has linear structure.

AX₃ type of compounds

Known compounds are ClF₃, BrF₃, (ICl₃)₂, IF₃. ClF₃ and BrF₃ are well known. These are covalent. ClF₃ is the most reactive but BrF₃ is most useful as a fluorinating agent since it is a liquid and is not too violent in its action.

All the trifluorides are powerful oxidants and fluorinating agents. The oxidising power increases in the order---

IF₃<BrF₃<ClF₃

Their thermal stabilities are in the order---

BrF₃>ClF₃>ICl₃>IF₃

The order of their reactivity---

ClF₃>BrF₃>IF₃

These undergo self ionisation considerably; these have high electrical conductivity.

2 ClF₃ <=====> [ClF₂] ⁺ + [ClF₄]^-

2 BrF₃ <====> [BrF₂] ⁺ + [BrF₄]^-

2 ICl₃ <=====> [ICl₂] ⁺ + [ICl₄]^-

Fluorinating behaviour:

ClF₃ + BF₃ -----> [ClF₂] ⁺ [BF₄]^-

ClF₃ + SbF₅ -----> [ClF₂] ⁺ [SbF₆]^-

ClF₃ + PtF₅ -----> [ClF₂] ⁺ [PtF₆]^-

4BrF₃ + 3SiO₂ ----> 3SiF₄ +2Br₂ +3O₂

Structure

The X-ray structure of crystalline ClF₃ shows that the molecule is T-shaped, with bond angle of 87⁰40'.

Structure of ClF₃

The distortion from 90⁰ is due to repulsion between the lone pairs. The structure is trigonal bipyramid arising out of the sp³d hybridization of Cl.

The structure of BrF₃ is also T-shaped. ICl₃ in the solid state is a dimeric planar molecule, (ICl₃)₂. Here two T-shaped ICl₃ molecules join together forming the dimer.

Structure of I₂Cl₆

AX₅ type of molecules

Three interhalogen compounds such as ClF₅, BrF₅, and IF₅ are known.

The order of reactivity is---

BrF₅>ClF₅>IF₅

They fluorinate compounds, react violently with water.

ClF₅ + 2H₂O = FClO₂ + 4HF

BrF₅ + AsF₅ = [BrF₄] ⁺ [AsF₆]^-

BrF₅ + CsF = Cs⁺[BrF₆]^-

IF₅ + KF = K⁺ [IF₆]^-

IF₅ + SbF₅ = [IF₄] ⁺ [SbF₆]^-

Liquid IF₅ self ionizes and therefore conducts electricity.

2 IF₅ <====> [IF₄] ⁺ [IF₆]^-

Structure

Structure of IF₅

AX₅ compounds all have square pyramidal structures (octahedral with one position occupied by a lone pair).

AX₇ type of compounds

Only known compound is IF₇. It is a gas at ordinary temperature and is highly reactive. It is a violent fluorinating agent.

IF₇ + 6H₂O <====> H₅IO₆ + 7HF

IF₇ + CsF <====> Cs⁺ [IF₈]^-

IF₇ + SbF₅ <====> [IF₆] ⁺ [SbF₆]^-

Structure

Structure of IF₇

The structure of IF₇ is unusual. It is pentagonal bipyramidal in shape.