Politechnika Gdańska
Wacław Grzybkowski
CONDUCTOMETRIC
AND
POTENTIOMETRIC TITRATION
Gdańsk 2002
CONTENTS
1. TITRATION
3
2. CONDUCTOMETRIC TITRATION
5
3. POTENTIOMETRY
3.1 pH measurements
3.2 Potentiometric titration
14
14
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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) titrations. 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
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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.
4
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
i=
U
R
where R is the resistance of the body of solution in ohms [Ω] . The conductance G is
defined as the reciprocal of the resistance
G=
1
R
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 :
G=κ
A
l
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
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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
κ=
k
R
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
Λ=
1000 κ
c
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
Λ eq =
1000κ
c eq
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
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Λ = Λ0 − β c
is valid at low concentration range.
Fig.1. Plots of equivalent conductance of the strong electrolytes as a function of c 1/ 2 ,
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
:
Λ0 = λ0+ + λ0
It is known as the law of independent migration of ions. For hydrochloric acid we
can write
[ ]
[ ]
Λ0 [HCl] = λ0 H+ + λ0 Cl
while for sulphuric acid
[ ]
[
Λ0 [H2 SO 4 ] = 2 λ0 H + + λ0 SO 24−
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]
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:
[ ]
[
[ ]
[
Λ0 [CH3 COOH] = λ0 H + + λ0 CH3 COO −
]
]
[
]
[
]
[ ]
[ ]
= λ0 H + + λ0 CH3 COO _ + λ0 Na + − λ0 Na + + λ0 Cl − − λ0 Cl −
= Λ0 [HCl] + Λ0 [CH3 COONa] − Λ0 [NaCl]
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
Λ
Λ0
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
KC =
α 2c
1− α
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
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current, so that the quantity of the electricity carried during one half cycle is insufficient 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
H+ + OH → H2 O
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
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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
CH3 COOH + Na + + OH- → Na + + CH3 COO − + H2 O
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.
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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
H+ + OH →
H2 O
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.
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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 endpoint 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
H2C2O 4 → H+ + HC2O 4
−
HC2O 4 → H+ + C2O 4
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−
2−
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.
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POTENTIOMETRY
pH MEASUREMENT
Perhaps the most common potentiometric measurement is that of pH. pH was
defined originally as − lg CH+ or lg( 1/ C H+ ) , where CH+ is the concentration of hydrogen
ion. Today instead of CH+ one would write aH+ , 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
pH =
E + E(cal)
( −RT / F) ln10
pH =
E + E(cal)
(− 59,16 mV )
or at temperature of 250C
The practical definition of the pH of a solution X is
pH ( X) = pH (S) −
E
(RT / F) ln10
pH ( X) = pH (S) −
E
( 59.16 mV )
or
at 250C, where E is the potential of the cell
Pt | H2 (g) | s(aq) || 3.5 MKCl (aq) || X(aq) H2 (g) | Pt
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and S is a solution of standard pH while || 3.5 MKCl (aq) || 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
15
The
sensitivity
of
a
glass
electrode
towards
hydrogen
( H+ )
or
hydronium ( H3 O + ) 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,
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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.
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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
Ag + + Cl − → AgCl(s)
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.
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