Pabitra Kumar Mani; Assoc. Prof.; BCKV;

Class - 15

Potentiometric titrationsAndConductometric titrations

ACSS-501ACSS-501

Potentiometry

An electroanalytical technique based on the measurement of the electromotive force of an electrochemical cell comprised of a measuring and a reference electrode.

The simplest example of a measuring electrode is a metal electrode whose potential depends on the concentration of the cation of the electrode metal.

Indicator electrode

Electrochemical measuring system.

When a metal M is immersed in a solution containing its own ions Mn+, then an electrode potential is established, the value of which is given by the Nernst equation:

General Principles

Reference electrode | salt bridge | analyte solution | indicator electrode

Eref Ej Eind

Ecell = Eind – Eref + Ej

Reference cell :

a half cell having a known electrode

potential

Indicator electrode:

has a potential that varies in a

known way with variations in

the concentration of an analyte

A cell for potentiometric determinations.

1) Saturated calomel electrode (S.C.E.)

Hg(l) | Hg2Cl2 (sat’d), KCl (sat’d) | |

electrode reaction in calomel hal-cell

Hg2Cl2 (s) + 2e = 2Hg(l) + 2Cl–

Eo = + 0.268V

E = Eo – (0.05916/2) log[Cl–]2 = 0.244 V

Temperature dependent

Reference electrode: maintains a fixed potential :

a half cell having a known electrode potential

Fig. 21-2. Diagram of a typical commercial saturated calomel electrode.

Fig. 21-3. A saturated calomel electrode made from materials readily available in any laboratory.

2) Silver-silver chloride electrode

Ag(s) | AgCl (sat’d), KCl (xM) | |

AgCl(s) + e = Ag(s) + Cl–

Eo = +0.244V

E = Eo – (0.05916/1) log [Cl–]

E (saturated KCl) = + 0.199V (25oC)

Reference electrodes

Silver-Silver Chloride Reference Electrode

Calomel electrode

3) standard hydrogen electrode (SHE)

The most fundamental reference electrode in electrochemistry. "By definition" its equilibrium potential is considered zero at any temperature, because this electrode was chosen as an arbitrary zero point for electrode potentials. A zero point is needed since the potential of a single electrode cannot be measured, only the difference of two electrode potentials is measurable.

All electrode potentials are expressed on this "hydrogen scale." It is a hydrogen electrode with an electrolyte containing unit concentration of H ions and saturated with H2 gas at unit atmosphere pressure.

This electrode can be somewhat inconvenient to use because of the need to supply hydrogen gas. Therefore, other reference electrodes (e.g., calomel or silver/silver chloride) are often used instead, but the measured electrode potentials can be converted to the "hydrogen scale." Also called "normal hydrogen electrode."

Strictly speaking, one must use unit activity rather than concentration of hydrogen ions and unit fugacity rather than unit pressure of hydrogen gas.

Pt | H2(g, 1.0 atm)|H+(aq, A= 1.0M) ½ H2(g, 1.0 atm) = H+(aq, A= 1.0M) + e Eo = 0.000 V

Liquid-junction potentialA potential difference between two solns of different compositions separated by a membrane type separator. The simplest example is the case of two solns containing the same salt in different concns. The salt will diffuse from the higher concn side to the lower concn side. However, the diffusion rate of the cation and the anion of the salt will very seldom be exactly the same (mobility).

Let us assume for this example that the cations move faster; consequently, an excess positive charge will accumulate on the low concentration side, while an excess negative charge will accumulate on the high concn. side of the junction due to the slow moving anions. This sets up a potential difference that will start an electromigration of the ions that will increase the net flux of the anions and decrease the net flux of the cations.

In steady-sate conditions, the two ions will move at the same speed and a potential difference will be created between the two solns. This "steady-sate" potential difference seems constant, but this is misleading because it slowly changes as the concn between the two soln. equalize. The diffusion process will "eventually" result in equal concn of the salt in the two soln. separated by the membrane, and the liquid-junction potential will vanish. For a simple case, the value of the liquid junction potential can be calculated by the so called "Henderson" equation.

Junction potential :

a small potential that exists at the interface between two electrolyte solutions that differ in composition.

Development of the junction potential caused by unequal mobilities of ions.

Mobilties of ions in water at 25oC:

Na+ : 5.19 × 10 –8 m2/sV K+ : 7.62 × 10 –8 Cl– : 7.91× 10 –8

Fig. 21-5. Schematic representation of a liquid junction showing the source of the junction potential, Ej. The length of the arrows corresponds to the relative mobilities of the ions.

Fig 21-4 Diagram of a silver/silver chloride electrode showing the parts of the electrode that produce the reference electrode potential Eref and the juction

potential Ej

Liquid junction potential

Cells without liquid junction

Pt/H2(g), HCl/AgCl/Ag

Rare to have this type of cell

Cells with liquid junction

Glass frit

Salt bridge

Develop a potential by differential migration rates of the cation and anion.

Junction potential

HCl(0.1)/HCl(0.01) Ej = 40 mV (H+ faster than Cl– )

KCl(0.1)/KCl(0.01) Ej = –1.0 mV (K+ slower than Cl– )

Usually experimentally determine instrument response

Indicator electrodes

Metallic indicator electrode responds to analyte activity.

Electrode of the first type

Direct equilibrium with analyte

Ag for Ag+, Au for Au3+, etc

Potential described by Nernst equation.

As [M] , E

Note potential linearly related to log of the concentration !

Remember - indicator BY DEFINITION cathode

measurement theoretically under zero-current (steady state)

Electrode of the second type

Indirect equilibrium with analyte

M/MX/X–

Silver/Silver chloride for chloride

also Nernstian response

as [X–] , E

Inert Metallic electrode for Redox systems

Provides a surface for the electrochemistry to occur

Pt, Au, Pd, C

Xn+(aq) + ne = X(s)

Eind = Eo – (0.5916/n) log (1/[Xn+])

AgCl(s) + e = Ag(s) + Cl–

(aq)

Eind = Eo – 0.5916 log [Cl–]

A plot of Equation 21-3 for an electrode of the first kind.

A plot of Equation 21-4 for an electrode of the second kind for Cl–.

Indicator electrodes

Indicator electrodes for potentiometric measurements are of two basic

types, namely, metallic and membrane.

1) Metallic indicator electrodes :

develop a potential that is determined by the equilibrium position of redox half-reaction at the electrode surface.

First-order electrodes for cations :

A first order electrode is comprised of a metal immersed in a solution of its ions, such as silver wire dipping into a silver nitrate solution. Only a few metals such as silver, copper, mercury, lead , zinc, bismuth, cadmium and tin exhibit reversible half- reactions with their ions and are suitable for use as first order electrodes.

Other metals, including iron, nickel, cobalt, tungsten, and chromium, develop nonreproducible potentials that are influenced by impurities and crystal irregularities in the solid and by oxide coatings on their surfaces. This nonreproducible behavior makes them unsatisfactory as first-order electrodes.

Example of First-order electrode

Ag+ + e = Ag(s) Eo = + 0.800V

E = 0.800 – (0.05916/1) log {1/[Ag+]}

Second-order electrodes for anions

A metal electrode can sometimes be indirectly responsive to the concn of an anion that forms a precipitate or complex ion with cations of the metal.

Ex. 1. Silver electrode

The potential of a silver electrode will accurately reflect the concentration of iodide ion in a solution that is saturated with silver iodide.

AgI(s) + e = Ag(s) + I– Eo = – 0.151V

E = – 0.151 – (0.05916/1) log [I–] = – 0.151 + (0.05916/1)pI2.Mercury electrode :

for measuring the concentration of the EDTA anion Y4–. Mercury electrode responds in the presence of a small concn of the stable EDTA complex of mercury(II). HgY2– + 2e = Hg(l) + Y4– Eo = 0.21V E = 0.21 – (0.05916/2) log ([Y4–] /[HgY2–])

K = 0.21 – (0.05916/2) log (1 /[HgY2–]) E = K – (0.05916/2) log [Y4–] = K +(0.05916 / 2) pY

Ag(s) | AgCl[sat’d], KCl[xM] | | Fe2+,Fe3+) | Pt

Fe3++e = Fe2+ Eo = +0.770V

Ecell = Eindicator – Ereference

= {0.770 – (0.05916/1) log [Fe2+]/[Fe3+]} – {0.222 – (0.05916/1) log [Cl–]}

Inert electrodes Chemically inert conductors such as gold, platinum, or carbon that do not participate, directly, in the redox process are called inert electrodes.

The potential developed at an inert electrode depends on the nature and concentration of the various redox reagents in the solution.

2) Membrane indicator electrodes

The potential developed at this type of electrode results from an unequal charge buildup at opposing surface of a special membrane. The charge at each surface is governed by the position of an equilibrium involving analyte ions, which, in turn, depends on the concentration of those ions in the solution.

The electrodes are categorized according to the type of membrane they employ :

glass,

polymer,

crystalline,

gas sensor.

The first practical glass electrode. (Haber and Klemensiewcz, Z. Phys. Chem, 1909, 65, 385.

Membrane indicator electrodes Glass membrane pH electrodes

The internal element consists of silver-silver chloride electrode immersed in a pH 7 buffer saturated with silver chloride. The thin, ion-selective glass membrane is fused to the bottom of a sturdy, nonresponsive glass tube so that the entire membrane can be submerged during measurements. When placed in a solution containing hydrogen ions, this electrode can be represented by the half-cell :

Ag(s) | AgCl[sat’d], Cl–(inside), H+(inside) | glass membrane | H+(outside)

E = Eo – (0.05916/1) log [Cl–] + (0.05916/1) log ([H+(outside)]/[H+(inside)])

E = Q + (0.05916/1) log [H+(outside)]

How a pH meter works When one metal is brought in contact with another, a voltage difference occurs due to their differences in electron mobility. When a metal is brought in contact with a solution of salts or acids, a similar electric potential is caused, which has led to the invention of batteries. Similarly, an electric potential develops when one liquid is brought in contact with another one, but a membrane is needed to keep such liquids apart. 

A pH meter measures essentially the electro-chemical potential between a known liquid inside the glass electrode (membrane) and an unknown liquid outside. Because the thin glass bulb allows mainly the agile and small hydrogen ions to interact with the glass, the glass electrode measures the electro-chemical potential of hydrogen ions or the potential of hydrogen.

To complete the electrical circuit, also a reference electrode is needed. Note that the instrument does not measure a current but only an electrical voltage, yet a small leakage of ions from the reference electrode is needed, forming a conducting bridge to the glass electrode.

Most often used pH electrodes are glass electrodes. Typical model is made of glass tube ended with small glass bubble. Inside of the electrode is usually filled with buffered solution of chlorides in which silver wire covered with silver chloride is immersed. pH of internal solution varies - for example it can be 1.0 (0.1M HCl) or 7.0 (different buffers used by different producers).Active part of the electrode is the glass bubble. While tube has strong and thick walls, bubble is made to be as thin as possible. Surface of the glass is protonated by both internal and external solution till equilibrium is achieved. Both sides of the glass are charged by the adsorbed protons, this charge is responsible for potential difference. This potential in turn is described by the Nernst equation and is directly proportional to the pH difference between solutions on both sides of the glass.

The majority of pH electrodes available commercially are combination electrodes that have both glass H+ ion sensitive electrode and additional reference electrode conveniently placed in one housing.

In principle it should be possible to determine the H+ ion activity or concn. of a soln by measuring the potential of a Hydrogen electrode inserted in the given soln. The EMF of a cell, free from liquid junction potential, consisting of a Hydrogen electrode and a reference electrode, should be given by,

E = E ref – RT/F ln aH+ E = E ref + 2.303 RT/F pH R= 8.314 J/mol/°K

pH = ( E- Eref )F/2.303 RT F= faraday constant ,96,485

T= Kelvin scaleSo, by measuring the EMF of the Cell E obtained by combining the H electrode with a reference electrode of known potential, Eref , the pH of the soln. may be evaluated.

The electric potential at any point is defined as the work done in bringing a unit charge from infinity to the particular point

Reduced state Oxidised state + n Electron⇋ M = Mn+ + nE E(+) = E0 – (RT/F) ln aM

n+ Nernst Equation

Typical electrode system for measuring pH. (a) Glass electrode (indicator) and saturated calomel electrode (reference) immersed in a solution of unknown pH. (b) Combination probe consisting of both an indicator glass electrode and a silver/silver chloride reference. A second silver/silver chloride electrode serves as the internal reference for the glass electrode.

The two electrodes are arranged concentrically with the internal reference in the center and the external reference outside. The reference makes contact with the analyte solution through the glass frit or other suitable porous medium.

Combination probes are the most common configuration of glass electrode and reference for measuring pH.

pH0591.0EE G0 Glass electrode:

The value of E0 G depends upon the composition of glass membrane and it includes asymetry potential which is residual emf when identical solns and electrodes are placed inside and outside the glass membrane.

It varies from day to day on the exposure of the surface to dryness or putting in very strong acid or alkali. The glass electrode usually operates in the pH range 1-10 without much deviation in pH due to asymetry potential

To measure the hydrogen ion concentration of a solution the glass electrode must be combined with a reference electrode, for which purpose the saturated calomel electrode is most commonly used, thus giving the cell:

Owing to the high resistance of the glass membrane, a simple potentiometercannot be employed for measuring the cell e.m.f. and specialised instrumentationmust be used. The e.m.f. of the cell may be expressed by the equation:

In these equations K is a constant partly dependent upon the nature of the glass used in the construction of the membrane, and partly upon the individual character of each electrode; its value may Vary slightly with time. This variation of K with time is related to the existence of an asymmetry potential in a glass electrode which is determined by the differing responses of the inner and outer surfaces of the glass bulb to changes in hydrogen ion activity; this may originate as a result of differing conditions of strain in the two glass surfaces. Owing to the asymmetry potential, if a glass electrode is inserted into a test solution which is in fact identical with the interna1 hydrochloric acid solution, then the electrode has a small potential which is found to Vary with time. On account of the existence of this asymmetry potential of time-dependent magnitude, a constant value cannot be assigned to K, and every glass electrode must be standardised frequently by placing in a solution of known hydrogen ion activity (a buffer soln)

or at a temperature of 250C by the expression:

the operation of a glass electrode is related to the situations existing at the inner and outer surfaces of the glass membrane. Glass electrodes require soaking in water for some hours before use and it is concluded that a hydrated layer is formed on the glass surface, where an ion exchange process can take place. If the glass contains sodium, the exchange process can be represented by the equilibrium

The concn of the soln within the glass bulb is fixed, and hence on the inner side of the bulb an equilibrium condition leading to a constant potential is established. On the outside of the bulb, the potential developed will be dependent upon the hydrogen ion concentration of the soln in which the bulb is immersed. Within the layer of 'dry' glass which exists between the inner and outer hydrated layers, the conductivity is due to the interstitial migration of sodium ions within the silicate lattice.

Composition of glass membranes

70% SiO2

30% CaO, BaO, Li2O, Na2O,

and/or Al2O3

Ion exchange process at glass membrane-solution interface:

Gl– + H+ = H+Gl–(a) Cross-sectional view of a silicate glass struture. In addition to the three Si│O bonds shown, each silicon is bonded to an additional oxygen atom, either above or below the plane of the paper. (b) Model showing three-dimensional structure of amorphous silica with Na+ ion (large dark blue) and several H+ ions small dark blue incorporated.

Potentiometric titration:

Ag+/Ag Ag+NO3-/Ag , NH4NO3

+Agar Calomel electrode Half cell Salt Bridge Satd KCl soln, Hg2Cl2,Hg Indicator Electrode to remove ljp Reference Electrode Agln

nFRT

EE AgAg0 E calomel = -0.246 V

(SCE)

E cell = EAg –E SCE = AglnnFRT

E Ag0

SCEE

0.591

EE- cell E Ag log SCE

o Ag

[Ag+]= 2.51 x 10-3 E cell = -0.4 VE0 Ag = -0.8 VESCE = -0.246 V

E calomel = -0.246 V (SCE)E cell = EFe+3/Fe+2 –E SCE

2

30

FeFe

log0591.0E 2/3

SCEEFeFe

0.591

EE cell E-

FeFe

log SCE

23

o

2

3 /FeFe

E cell = - 0.4 VE0 (Fe+3/Fe+2) = 0.77VESCE = -0.246 V

Fe+2 /Fe+3 , Pt KCl +Agar Calomel electrode Half cell Salt Bridge Satd KCl soln, Hg2Cl2,Hg Indicator Electrode to remove ljp Reference Electrode

To determine the Fe+2 /Fe+3 in soln

Pt inert electrode, Pt has polarisation effect

= 42.2

3

2

3

103.6 FeFe

x

Basics

It is therefore usually considered preferable to employ analytical (or derivative) methods of locating the end point, these consist in plotting the first derivative curve (ΔE/ΔV against V), or the second derivative curve (Δ2E/ΔV2 against V). The first derivative curve gives a maximum at the point of inflexion of the titration curve, i.e. at the end point, whilst the second derivative curve (Δ2E/ΔV2) is zero at the point where the slope of the ΔE/ΔV curve is a maximum.

CONDUCTOMETRY

Ohm's Law States that the current I (amperes) flowing in a conductor is directly proportional to the applied electromotive force E (volts) and inversely proportional to the resistance R (ohms) of the conductor

The reciprocal of the resistance is termed the conductance (G): this is measured in reciprocal ohms (or Ω –), for which the name Siemens (S) is used. The resistance of a sample of homogeneous material, length l, and cross-section area a, is given by:

where ρ is a characteristic property of the material termed the resistivity (formerly called specific resistance). In SI units, l and a will be measured respectively in metres and square metres, so that ρ refers to a metre cube of the material, and

The reciprocal of resistivity is the conductivity, κ (formerly specific conductance), which in SI units is the conductance of a one metre cube of substance and has the units Ω – m - , but if ρ is measured in Ωcm, then κ will be measured in Ω - cm - '.

The conductance of an electrolytic solution at any temperature depends only on the ions present, and their concentration. When a solution of an electrolyte is diluted, the conductance will decrease, since fewer ions are present per millilitre of solution to

carry the current. If all the solution be placed between two electrodes 1 cm apart and large enough to contain the whole of the solution, the conductance will increase as the solution is diluted. This is due largely to a decrease in inter-ionic effects for strong electrolytes and to an increase in the degree of dissociation for weak electrolytes.The molar conductivity (Λ) of an electrolyte is defined as the conductivity due to one mole and is given by:

For strong electrolytes the molar conductivity increases as the dilution is increased, but it appears to approach a limiting value known as the molar conductivity at infinite dilution(Λ∞). The quantity Λ∞ can be determined by graphical extrapolation for dilute solutions of strong electrolytes.

For weak electrolytes the extrapolation method cannot be used for the determination of Λ∞ but it may be calculated from the molar conductivities at infinite dilution of the respective ions, use being made of the 'Law of Independent Migration of Ions‘. At infinite dilution the ions are independent of each other, and each contributes its part of the total conductivity, thus:

THE BASlS OF CONDUCTIMETRIC TlTRATlONS

principle underlying conductimetric titrations, i.e. The substitution of ions of one conductivity by ions of another conductivity.

Conductimetric TitrationsThe principle of conductimetric titration is based on the fact that during the titration, one of the ions is replaced by the other and invariably these two ions differ in the ionic conductivity with the result that conductivity of the solution varies during the course of titration. The equivalence point may be located graphically by plotting the change in conductance as a function of the volume of titrant added.

In order to reduce the influence of errors in the conductometric titration to a minimum, the angle between the two branches of the titration curve should be as small as possible . If the angle is very obtuse, a small error in the conductance data can cause a large deviation. The following approximate rules will be found useful.

The smaller the conductivity of the ion which replaces the reacting ion, the more accurate will be the result. Thus it is preferable to titrate a silver salt with lithium chloride rather than with HCl. Generally, cations should be titrated with lithium salts and anions with acetates as these ions have low conductivity.The larger the conductivity of the anion of the reagent which reacts with the cation to be determined, or vice versa, the more acute is the angle of titration curve.

The titration of a slightly ionized salt does not give good results, since theconductivity increases continuously from the commencement. Hence, the salt present in the cell should be virtually completely dissociated; for a similar reason; the added reagent should also be as strong electrolyte.The main advantages to the conductimetric titration are its applicability to very dilute, and coloured solutions and to system that involve relative incomplete reactions.

For example, which neither a potentiometric, nor indicator method can be used for the neutralization titration of phenol (Ka = 10–10) a conductimetric endpoint can be successfully applied.

The electrical conductance of a solution is a measure of its currents carrying capacity and therefore determined by the total ionic strength. It is a non-specific property and for this reason direct conductance measurement are of little use unless the solution contains only the electrolyte to be determined or the concentrations of other ionic species in the solution are known. Conductimetric titrations, in which the species in the solution are converted to non-ionic form by neutralization, precipitation, etc. are of more value.

Consider how the conductance of a solution of a strong electrolyte A+ B- will change upon the addition of a reagent C+D-, assuming that the cation A+ (which is the ion to be determined) reacts with the ion D- of the reagent.If the product of the reaction AD is relatively insoluble or only slightly ionised,the reaction may be written:

Thus in the reaction between A+ ions and D- ions, the A+ ions are replaced by C+ ions during the titration. As the titration proceeds the conductance increases or decreases, depending upon whether the conductivity of the C + ions is greater or less than that of the A+ ions.

During the progress of neutralisation, precipitation, etc., changes in conductance may, in general, be expected, and these may therefore be employed in determining the end points as well as the progress of the reactions. The conductance is measured after each addition of a small volume of the reagent, and the points thus obtained are plotted to give a graph which ideally consists of two straight lines intersecting at the equivalence point.

Ostwald derived a relationship between the molar conductivity and limiting molar conductivity. The molar conductivity of weak electrolyte

can be expressed as the product of degree of dissociation of the electrolyte and its limiting molar conductivity.This relationship is known as Ostwald relation. Substituting this in Eq. 6.3 gives.

Rearrange Eq. (6.10) gives

Thus, we can use this method for the determination Ka. of weak acids and bases. To

further understand this, let us consider the dissociation of nitric acid in methanol over a wide range of concentration (see Table 6.1). In methanol nitric acid acts as a weak electrolyte and therefore, we can use Eq. (6.12) to determine the dissociation constant Ka

Strong Acid with a Strong Base, e.g. HCl with NaOH: Before NaOH is added, the conductance is high due to the presence of highly mobile hydrogen ions. When the base is added, the conductance falls due to the replacement of hydrogen ions by the added cation as H+ ions react with OH− ions to form undissociated water.

This decrease in the conductance continues till the equivalence point. At the equivalence point, the solution contains only NaCl.After the equivalence point, the conductance increases due to the largeconductivity of OH- ions.

Conductimetric titration of a strong acid (HCl) vs. a strong base (NaOH)

The conductance first falls, due to the replacement of the H+ (Λ∞ 350, Table 13.1) by the added cation (Λ∞ 40-80) and then, after the equivalence point has been reached, rapidly rises with further additions of strong alkali due to the large Λ∞ value of the hydroxyl ion (198).

Strong Acid with a Weak Base, e.g. H2SO4 with dilute NH3 (Kb=10-5 )

Initially the conductance is high and then it decreases due to the replacement of H+. But after the endpoint has been reached the graph becomes almost horizontal, since the excess aqueous ammonia is not appreciably ionised in the presence of ammonium sulphate.

Conductimetric titration of a strong acid (H2SO4) vs. a weak base (NH4OH)

The first branch of the graph reflects the disappearance of the H ions during the neutralisation,

Weak Acid with a Strong Base, e.g. acetic acid (Ka= 1.8 x10-5 )with NaOH:

Initially the conductance is low due to the feeble ionization of acetic acid. On the addition of base, there is decrease in conductance not only due to the replacement of H+ by Na+ but also suppresses the dissociation of acetic acid due to common ion acetate.

But very soon, the conductance increases on adding NaOH as NaOH neutralizes the un-dissociated CH3COOH to CH3COONa which is the strong electrolyte. This increase in conductance continues raise up to the equivalence point. The graph near the equivalence point is curved due the hydrolysis of salt CH3COONa. Beyond the equivalence point, conductance increases more rapidly with the addition of NaOH due to the highly conducting OH− ions .As the titration proceeds, a

somewhat indefinite break will occur at the end point, and the graph will become linear after all the acid has been neutralised. Some curves for acetic acid-sodium hydroxide titrations are shown in Fig.clearly it is not possible to fix an accurate end point

Weak acids with weak bases. The titration of a weak acid and a weak base can be readily carried out, and frequently it is preferable to employ this procedurerather than use a strong base.

Curve (c) is the titration curve of 0.003 M acetic acid with 0.0973 M aq. NH3 solution. The neutralisation curve up to the equivalence point is similar to that obtained with NaOH solution, since both Na and ammonium acetates are strong electrolytes;

after the equivalence point an excess of aq. NH3 solution has little effect upon the conductance, as its dissociation is depressed by the ammonium Salt present in the solution. The advantages over the use of strong alkali are that the end point is easier to detect, and in dilute solution the influence of CO2 may be neglected.

Mixture of a strong acid and a weak acid with a strong baseUpon adding a strong base to a mixture of a strong acid and a weak acid (e.g. HCl and acetic acids), the conductance falls until the strong acid is neutralised, then rises as the weak acid is converted into its salt, and finally rises more steeply as

excess alkali is introduced. Such a titration curve is shown as S in Fig.(d).

The three branches of the curve will be straight lines except in so far as:(a) increasing dissociation of the weak acid results in a rounding-off at the first end-point, and (b) hydrolysis of the Salt of the weak acid causes a rounding-off at the second end point. Usually, extrapolation of the straight portions of the three branches leads to definite location of the end points. Here also titration with a weak base, such as aq NH3 soln, is frequently preferable to strong alkali for reasons already mentioned in discussing weak acids: curve W in Fig. (d) is obtained by substitutingaqueous ammonia solution for the strong alkali.

The procedure may be applied to the determination of mineral acid in vinegar or other weak organic acids (K < 4 and can be used to analyse 'aspirin' tablets.

Displacement (or Replacement) Titrations:

When a salt of a weak acid is titrated with a strong acid, the anion of the weak acid is replaced by that of the strong acid and weak acid itself is liberated in the undissociated form. Similarly, in the addition of a strong base to the salt of a weak base, the cation of the weak base is replaced by that of the stronger one and the weak base itself is generated in the undissociated form. If for example, 1M-HCl is added to 0.1 M soln of sodium acetate, the curve shown in Fig. is obtained, the acetate ion is replaced by the chloride ion after the endpoint.

The initial increase in conductivity is due to the fact that the conductivity of the Cl- is slightly greater than that of acetate ion. Until the replacement is nearly complete, the solution contains enough sodium acetate to suppress the ionization of the liberated acetic acid, so resulting a negligible increase in the conductivity of the solution.

However, near the equivalent point, the acetic acid is sufficiently ionized to affect the conductivity and a rounded portion of the curve is obtained. Beyond the equivalence point, when excess of HCl is present (ionization of acetic acid is very much suppressed) therefore, the conductivity arises rapidly.

Care must be taken that to titrate a 0.1 M-salt of a weak acid, the dissociation constant should not be more than 5×10–4, for a 0.01 M -salt solution, Ka < 5 ×10–5 and for a 0.001 M-salt solution, Ka < 5 ×10–6, i.e., the ionization constant of the displace acid or base divided by the original concentration of the salt must not exceed above 5 ×10-3.

Fig. 6.6. Also includes the titration of 0.01M- ammonium chloride solution versus 0.1 M - sodium hydroxide solution. The decrease in conductivity during the displacement is caused by the displacement of NH4 ion of grater conductivity by sodium ion of smaller conductivity

Precipitation Titration and Complex Formation Titration: A reaction may be made the basis of a conductimetric precipitation titration provided the reaction product is sparingly soluble or is a stable complex . The solubility of the precipitate (or the dissociation of the complex) should be less than 5%. The addition of ethanol is sometimes recommended to reduce the solubility in the precipitations. An experimental curve is given in Fig. 6.8 (ammonium sulphate in aqueous-ethanol solution with barium acetate). If the solubility of the precipitate were negligibly small, the conductance at the e.p should be given by AB and not the observed AC.The addition of excess of thereagent depresses the solubility of the precipitate and, if the solubility is not too large, the position of the point B can be determined by continuing the Straight portion of the two arms of the curve until they intersect.

Precipitation titration. Conductimetric titration of (NH4)2 SO4 vs. bariumacetate