Politechnika Gdańska

Wacław Grzybkowski

CONDUCTOMETRIC AND

POTENTIOMETRIC TITRATION

Gdańsk 2002

CONTENTS

1. TITRATION 3

2. CONDUCTOMETRIC TITRATION 5

3. POTENTIOMETRY 14

3.1 pH measurements 14 3.2 Potentiometric titration 16

3

TITRATION

Titration is process of chemical analysis in which the quantity, amount or

concentration, of some constituent of a sample, known as an analyte, is determined

by adding to the measured sample an exactly known quantity of another substance

with which the desired constituent reacts in a definite, known proportion. The process

is usually carried out by gradually adding a standard solution (i.e., a solution of

known concentration) of titrating reagent, or titrant, from a burette, essentially a

long, graduated measuring tube with a stopcock and a delivery tip at its lower end.

Titrations may be carried out by hand from the burette or automatically.

At the equivalence point of a titration, an exactly equivalent amount of titrant

has been added to the sample. The experimental point at which the completion of the

reaction is marked by some signal is called the end point. This signal can be the

colour change of an indicator or a change in some chosen, e.g., electrical property

that is measured during the titration. The difference between the end point and the

equivalence point is the titration error, which is kept as small as possible by the

proper choice of an end-point signal and a method for detecting it.

For many titration reactions it is possible to find a suitable visual colour

indicator that will signal the end point at, or very close to, the equivalence point. Such

titrations, classified according to the nature of the chemical reaction occurring

between the sample and titrant, include: acid-base titrations, precipitation

titrations, complex-formation titrations, and oxidation-reduction (redox) titra-

tions. In acid-base titration (i.e., the titration of an acid with a base, or vice versa), the

indicator is a substance that can exist in two forms, an acid form and a basic form,

which differ in colour. For example, litmus is blue in alkaline solution and red in acid

solution. Phenolphthalein is colourless in acid solution and pink in alkaline solution. A

wide choice of acid-base indicators is available, varying not only in the colours of the

two forms but also in the pH value at which the colour occurs.

Precipitation titrations may be illustrated by the example of the determination

of chloride content in a sample by titration with silver nitrate, which precipitates the

4

chloride in the form of silver chloride. The presence of the first slight excess of silver

ion (i.e., the end point) can be marked by the appearance of a coloured precipitate.

One way in which this can be done is by employing potassium chromate(VI) as the

indicator. Potassium chromate reacts with the first slight excess silver ion to form a

red precipitate of silver chromate. Another method involves the use of an adsorption

indicator, the indicator action being based on the formation on the surface of the

precipitate of an adsorbed layer of silver indicator salt, which forms only when an

excess of silver ions is present.

The most important titrations based upon complex-formation reactions are

those involving the titration of metal ions with the reagent disodium

ethylenediaminetetraacetate (a salt of edetic acid, or EDTA). The indicators are dyes

that have the property of forming a coloured complex with the metal ion. As the

titration proceeds, the reagent reacts first with uncomplexed metal ions, and, finally,

at the end point it reacts with the metal-indicator complex. The colour change

corresponds to the conversion of the metal-dye complex into the free dye. In

oxidation-reduction (redox) titrations the indicator action is analogous to the other

types of visual colour titrations. In the immediate vicinity of the end point, the

indicator undergoes oxidation or reduction, depending upon whether the titrant is an

oxidizing agent or a reducing agent. The oxidized and reduced forms of the indicator

have distinctly different colours.

Alternatively, for many titrations the end point can be detected by electrical

measurements. These titrations may be classified according to the electrical quantity

that is measured. Potentiometric titrations involve the measurement of the

potential difference between two electrodes of a suitable cell; conductometric

titrations, the electrical conductance or resistance of the solution being titrated; and

amperometric titrations, the electric current passing during the course of the

titration. In the titrations just mentioned the end point is indicated by a marked

change in the electrical quantity that is being measured.

5

CONDUCTOMETRIC TITRATION

In this experiment we shall be concerned with electrical conduction through

aqueous solutions. Although water is itself a very poor conductor of electricity, the

presence of ionic species in solution increases the conductance considerably. The

conductance of such electrolytic solutions depends on the concentration of the ions

and also on the nature of the ions present ( through their charges and mobilities ).

Conductance behaviour as a function of concentration is different for strong and

weak electrolytes.

Electrolytic solutions obey Ohm’s law just as metallic conductors do. Thus the

current i passing through a given body of solution is proportional to the potential

difference U, and

RUi =

where R is the resistance of the body of solution in ohms [ ]Ω . The conductance G is

defined as the reciprocal of the resistance

R1G =

and is expressed in siemens [S], that is in ohms-1 [Ω−1] or mhos. The conductance of

a homogeneous body of uniform cross section is proportional to the cross section A

and inversely proportional to the length l :

lAG κ=

where κ is the conductivity or the specific conductivity expressed in S·cm-1 or in

Ω−1·cm-1. The conductivity is thus the reciprocal of the resistivity. The conductivity of

6

a solution in a cell of an arbitrary design and dimensions can be obtained by first

determining the cell constant k, being the effective value of l/A, by measuring the

resistance of a cell filled with the solution of known conductivity. One of the standards

solution that can be used for making this calibration is 0.02000 molar solution of

potassium chloride, with conductivity equal to 0.002768 S·cm-1 at 25ºC. Once the cell

constant has been found, conductivity can be calculated from the experimental

resistance by using equation

Rk

=κ

The conductivity of a solution depends on the concentrations and mobilities of

the ions present. It is convenient to define a new quantity, the molar conductance Λ,

by

c1000κ

=Λ

where c is the molar concentration, that is expressed in mol·dm-3. 1000 is the factor

arising from the fact that 1 dm3=1000 cm3. Thus, the molar conductance is expressed

in S·cm2·mol-1. The molar conductance is sometimes described as the actual

conductance of that volume of solution which contains one mol of solute when placed

between parallel electrodes 1 cm apart with a uniform electric field between them. In

order to compare the conductances of the electrolytes differing in the ionic

composition the equivalent conductance Λeq is defined

eqeq c

1000κ=Λ

where c is the equivalent concentration, that is expressed in equiv.·dm-3

For a strong electrolyte the molar and/or equivqlent conductances are roughly

constant, decreasing to some extent owing to changes in mobilities with increasing

concentration but approaching a finite value Λο at infinite dilution.

Typical plots of equivalent conductance against square root of the salt

concentration are presented in Figure 1. As is seen, if the conductance is plotted

against the square root of the concentration a linear relationship

7

c0 β−Λ=Λ

is valid at low concentration range.

Fig.1. Plots of equivalent conductance of the strong electrolytes as a function of 2/1c , at low concentrations the plots are linear as is indicated by broken lines.

It was first described by Kohlrausch (1900) and is found to be universal for

strong electrolytes. Moreover, this relationship known as Kohlrausch’s law was

deduced from the effect of ion attraction on the mobilities. Using this relation, Λο for

strong electrolytes can be obtained experimentally from conductance measurements.

At infinite dilution the ions act altogether independently, and it is then possible to

express Λο as the sum of the limiting conductances of the separate ions

: 000 λ+λ=Λ +

It is known as the law of independent migration of ions. For hydrochloric acid we

can write

[ ] [ ] [ ]ClHHCl 000 λ+λ=Λ +

while for sulphuric acid

[ ] [ ] [ ]−+ λ+λ=Λ 24

0042

0 SOH2SOH

8

For weak electrolytes, thus for weakly ionized solutes, Λ varies markedly with

concentration because the degree of dissociation varies strongly with concentration.

The limiting molar conductances of weak electrolytes we can calculate with the help

of the law of independent migration of ions. Thus, for acetic acid, we can write:

[ ] [ ] [ ]−+ λ+λ=Λ COOCHHCOOHCH 300

30

[ ] [ ] [ ] [ ] [ ] [ ]−−+++ λ−λ+λ−λ+λ+λ= ClClNaNaCOOCHH 0000_3

00

[ ] [ ] [ ]NaClCOONaCHHCl 03

00 Λ−Λ+Λ=

For sufficiently weak electrolytes, the ionic concentration is small and the

effect of ion attraction on the mobilities is slight; thus we may assume the mobilities

to be independent of concentration and obtain the approximate equation

0ΛΛ

=α

which may be used to calculate the value of fractional ionization α, known also as

the degree of dissociation. If one measures Λ for a weak electrolyte at concentration

c and calculates Λο from conductometric data for strong electrolyte or from known

values of the limiting conductances of the individual ions, it is possible to obtain the

actual degree of ionization of the weak electrolyte at this concentration. Then the

value of respective equilibrium constant, KC, can be estimated using the Ostwald’s

Dilution Law

α−α

=1

cK2

C

For determining electrolytic conductance by measuring the resistance of the

solution in a conductivity cell, the use of direct current circuitry is impractical, since

the electrodes would quickly become polarized; that is, electrode reactions would

take place. Polarization can be prevented by (1) using high frequency alternating

9

current, so that the quantity of the electricity carried during one half cycle is insuffi-

cient to produce any measurable polarization, and at the same time by (2) employing

platinum covered with platinum black, having an extremely large surface area, to

facilitate the adsorption of the tiny quantities of electrode reaction products produced

in one-half cycle, hence, reducing the polarization effect.

Classical circuit employed to such measurements is a Wheatstone Bridge

adapted for use of a high frequency alternating current. However, a variable

capacitance is necessary to achieve a true balance and eliminate the non-ohmic

effects.

Determination of the ac impedance can be also carried out with an automatic

bridge that employs a frequency generator and gives a direct read-out. Such an

equipment is employed for measurements during conductometric titration.

In all measurements of impedance, careful temperature control is essential,

since viscosity of water, for example, changes in the region near room temperature

by about of 3% per degree.

It was mentioned above that the measured conductance of an electrolyte

solution depends primarily on the concentration and types of the ions. Conductivity

measurement can thus provide a sensitive measure of the changes taking place in

ionic composition in the course of chemical reaction occurring in the solution during

conductometric titration.

Consider a solution of a strong acid, hydrochloric acid, HCl for instance, to

which a solution of a strong base, sodium hydroxide NaOH, is added. The reaction

OHOHH 2→++

occurs. For each amount of NaOH added equivalent amount of hydrogen ions is

removed. Effectively, the faster moving H+ cation is replaced by the slower moving

Na+ ion, and the conductivity of the titrated solution as well as the measured

conductance of the cell fall. This continues until the equivalence point is reached, at

which we have a solution of sodium chloride, NaCl. If more base is added an

increase in conductivity or conductance is observed, since more ions are being

added and the neutralization reaction no longer removes an appreciable number any

of them. Consequently, in the titration of a strong acid with a strong base, the

10

conductance has a minimum at the equivalence point. This minimum can be used

instead of an indicator dye to determine the endpoint of the titration. Conductometric

titration curve, that is a plot of the measured conductance or conductivity values

against the number of milliliters of NaOH solution, is shown in Fig. 2.

Fig.2. Conductometric titration curve for hydrochloric acid titrated using solution of sodium hydroxide.

The position of the equivalence point may be localized precisely as the point of

intersection of two straight-lines both determined using readings obtained before and

after the minimum observed, respectively. It makes the conductometric titration more

objective and independent of a nature of an indicator used in the end-point method.

This is one of advantages of the instrumental method.

The same reaction of neutralization takes place when a solution of strong base

is titrated using a solution of strong acid. Thus, analogous effects and very similar

shape of conductometric titratration curve are observed.

Consider the titration of solution of weak acid, such as acetic acid CH3COOH,

using a solution of strong base, NOH. As we know, the weak acids, as well as other

weak electrolytes, are dissociated into very small extent and they exist in solution

essentially in form of the neutral acid molecules. When a solution of NaOH is added

the reaction occurs

OHCOOCHNaOHNaCOOHCH 233 ++→++ −++ -

and, as is seen, the undissociated molecules of acetic acid are transformed into

dissociated molecules of potassium acetate. The changes are accompanied by

increase in conductivity of the solution, Figure 3.

11

Fig.3. Conductometric titration curve for acetic acid titrated using solution of sodium hydroxide.

It should be noted, however that an initial decrease in a conductivity of the

solution may be observed after addition of the first drops of titrant. This minor

importance effect is related to neutralization reaction of the protons resulting from a

dissociation and existing even in a solution of the weak acid

OHOHH 2→++ Thus, an mild increase in conductivity of a titrated solution is observed until the

equivalence point is reached, at which we have a solution of sodium acetate,

CH3COONa. If an excess of titrant, that is the potassium hydroxide solution, is added

a sharp increase in conductivity is observed. This distinct difference in a rate of

increase is related to the fact that the excess OH- anions, as well as the protons,

exhibit particular mechanisms of charge migration More detailed inspection of the

conductometric titration curve presented in Fig.3. indicates that the equivalence point

is less sharp than that observed for the strong acid. Thus, it should be localized as

the intersection point of two lines determined by two section of the conductometric

curve. The slope of the first part of the conductometric curve is dependent on a

strength of the acid. It means that it is positive for very weak acid only.

12

The method of conductometric titration is thus well adapted to the estimation

of mixtures of acids of differing strengths. When a mixture of strong and weak acid is

titrated a plot of conductance against alkali added takes form of Fig.4.

Fig.4. Conductometric titration curve for the hydrochloric acid – acetic acid mixture titrated using solution of sodium hydroxide.

As is seen, the conductometric titration curve is a combination of the diagrams

obtained during the titration of strong and weak acid respectively, where the first end-

point corresponds to a neutralization of the strong acid present in the sample and the

second one is associated with a neutralization of the weak acid in the solution under

investigation. The volume of the alkali consumed by the latter is given by a difference

of the respective volumes.

Analogous conductometric titration curve is obtained for an oxalic acid,

solution titrated using a solution of strong base, NaOH. Oxalic acid, chemical formula

H2C2O4 or (COOH)2, is the simplest dibasic, i.e. diprotic carboxylic acid. As is seen,

its molecule consists of two carboxylic groups only and a dissociation equilibria are

described by the following two equations

−+ +→ 42422 OHCHOCH

−+− +→ 24242 OCHOHC

13

The dissociation constant for the second proton is significantly smaller, and so

pK2 > pK1. Hence, the solution of the oxalic acid may be considered as an equimolar

mixture of two acids of differing strength.

The dissociation constant for the second proton is significantly smaller, and so

pK2 > pK1. Hence, the solution of the oxalic acid may be considered as an equimolar

mixture of two acids of differing strength.

It seems to be rather obvious that an analogous conductometric titration curve

describes a conductometric titration of solution of weak base, such as ammonia,

using a solution of strong acid.

The conductometric titration method can also be employed in other volumetric

estimations, e.g. the determination of halides by titration with silver nitrate.

Correction for the relatively small change of volume during the titration is

readily made by plotting not the measured conductance or conductivity, but the

values of product of the conductance and total volume of the sample, against the

volume of titrant added.

14

POTENTIOMETRY

pH MEASUREMENT

Perhaps the most common potentiometric measurement is that of pH. pH was

defined originally as +− HClg or ( )+HC/1lg , where +HC is the concentration of hydrogen

ion. Today instead of +HC one would write +Ha , the activity of hydrogen ion. The

experimental determination of pH potentiometrically leads to a value which is neither

strictly concentration nor activity of hydrogen ion but something in between.

The measurement of the pH of a solution is simple in principle, fo it is based

on the measurement of the potential of hydrogen electrode immersed in the solution.

The left-hand, i.e. the reference electrode of the cell is typically a saturated calomel

electrode (SCE) with potential E(cal). The pH of the cell is therefore

10ln)F/RT()cal(EEpH

−+

=

or at temperature of 250C

( )mV16,59)cal(EEpH

−+

=

The practical definition of the pH of a solution X is

10ln)F/RT(E)S(pH)X(pH −=

or

)mV16.59(E)S(pH)X(pH −=

at 250C, where E is the potential of the cell

Pt|)g(H)aq(X||)aq(KClM5.3||)aq(s|)g(H|Pt 22

15

and S is a solution of standard pH while ||)aq(KClM5.3|| denotes the salt bridge. The

currently recommended primary standards include a saturated solution of potassium

hydrogen tartrate, which has pH =3.557 at 250C and 0.0100 mol kg-1 disodium

tetraborate, which has pH=9.180 at that temperature.

In practice, indirect methods are much more convenient, and the hydrogen

electrode is replaced by the glass electrode. This electrode is sensitive to hydrogen

ion and its potential is proportional to pH. It is filled with hydrochloric acid or

phosphate buffer containing −Cl anions. Conveniently, the glass electrode has E=0

when the external medium is at pH=7.The glass electrode is much more convenient

to handle than the gas electrode itself, and can be calibrated using solutions of

known pH. The glass electrode is usually used in conjunction with a calomel

electrode that makes contact with the test solution through a salt bridge.

Fig.1. Glass electrode and its cell schematic in association with a reference electrode

16

The sensitivity of a glass electrode towards hydrogen )H( + or

hydronium )OH( 3+ ion is a result of complex processes at the interface between the

glass membrane and the solutions on either side of it. The membrane itself is

permeable to Na+ and Li+ cations but not to H+ ions. Therefore, the potential

difference across the glass membrane must arise by a mechanism that is different

from that responsible for biological transmembrane potentials. A clue to the

mechanism comes from a detailed inspection of tee glass membrane, for each face

is coated with thin layer of hydrated silica. The hydrogen ion in the test solution

modify this layer to an extent that depends on their activity or/and concentration in

the solution, and the charge modification of the outside layer is transmitted to the

inner layer by the Na+ and Li+ cations in the glass. The hydronium ion activity give

rise to a membrane potential by this indirect mechanism.

POTENTIOMETRIC TITRATION

If, during a chemical reaction, there is a change in the concentration of an ion

which can be sensed through the change in potential of a suitable electrode, then the

progress of the reaction can be followed through this potential change. It follows the

electromotive force measurements, like conductivity measurements, can serve to

determine the equivalence point or end point of titration. Both conventional

electrodes and the types of ion-sensitive electrodes can be used to follow the

process and the change of potential in the case of acid-base, precipitation,

complexation and red-ox titration.

To follow an acid-base titration a hydrogen electrode or a pH-sensitive glass

electrode may be used as the indicator electrode. In both cases, as the titration is

carried out, for example, by addition of alkali to an acid solution, the potential

difference measured will decrease at the rate of 59.1 mV per decade lowering in

H3O+ concentration. As long as the acid is in excess, then the pH, as well as the

electromotive force of the studied cell, will vary only slightly with addition of base.

However, near the equivalence point, concentration of the H3O+ cation falls rapidly

before levelling out again in excess base. Thus, the measured potential difference

will show a step-like behaviour, as is seen in Figure 1,

17

in which the change in potential of the pH-electrode is calculated for titration of 100

cm3 of 0.01 M solution of strong acid, HCl, with 0.1 M solution of strong base. The

end-point of the titration corresponds to the point at which the potential changes most

rapidly.

Fig.2. Potentiometric acid-base titration: (a) schematic representation of titration of 100 cm3 of a strong acid of concentration 0.01 M with a stronge base of concentration 0.1 M; (b) differential potential change on addition of aliquots of titrant, showing a marked peak at the end point.

18

A more precise measure of the end-point than the position of the steepest

change in the potential difference, i.e. the change in the electromotive force, can be

obtained by plotting the derivative of the potential difference with the volume of titrant

added. This is shown as the dotted line in Figure 2, and it can be see to have a nice,

sharp maximum indicating a position of the end-point.

As an example of the precipitation titration, consider the determination of the

chloride ions by silver nitrate, making use of the reaction

)s(AgClClAg →+ −+

here, the equilibrium-potential of the Ag|Ag+ electrode can be followed as a function

of addition of the titrant. At the beginning of the titration, the concentration of silver in

solution will, in effect, be determined by the solubility product of silver chloride, and,

at the end-point, the Ag+ concentration will rise very rapidly as the last of the chloride

is precipitated. The height of the potential step can be further enhanced if the

titrations is carried out in a water-acetone mixture, in which the solubility of silver

chloride is lower.

The change of potential in the case of complexation and redox titrations is

very similar to that observed in case of potentiometric acid-base and precipitation

titration.

Potentiometric titrations have the great advantage, in common with

conductometric titrations, of being possible in turbid, coloured and very dilute

solutions. Further advantages of potentiometric titrations are the generally very sharp

end points and the ease of automation, and a large number of commercial rigs are

available. The range of applications is enormous, and accurate methods have been

developed for many electroanalytical processes.