BCHET-141

ANALYTICAL METHODS IN
Indira Gandhi National
Open University CHEMISTRY
School of Sciences

Block

3
THERMAL AND ELECTROANALYTICAL METHODS

UNIT 8
Thermal Methods of Analysis 7

UNIT 9
Potentiometry 30

UNIT 10
Conductometry 64
Course Design Committee

Prof. N.K. Kaushik, (Retd.) School of Sciences,

Department of Chemistry, IGNOU, New Delhi 110068
University of Delhi, New Delhi
Prof. M.S. Nathawat
Prof. B. S. Saraswat (Retd.)
School of Sciences, IGNOU, Prof. Sunita Malhotra
New Delhi Prof. B.I. Fozdar
Prof. Javed A. Farooqi
Prof. Nafisur Rehman, Prof. Sanjiv Kumar
Department of Chemistry, Prof. Lalita S. Kumar
A.M.U. Aligarh Prof. Kamalika Banerjee

Block Preparation Team

Prof. Bharat Inder Fozdar Prof. Nafisur Rehman (Editor)
School of Sciences, IGNOU Department of Chemistry,
New Delhi AMU, Aligarh

Course Coordinator: Prof. J. A. Farooqi

Print Production
Mr. Rajiv Girdhar Mr. Hemant Kumar Parida
Assistant Registrar (Pub), Section Officer (Pub),
MPDD, IGNOU, New Delhi MPDD, IGNOU, New Delhi

Acknowledgements: Sh. Sarabjeet Singh for CRC preparation

Material partially adapted from the MCH-004 Course of PGDAC Programme.

March, 2022
@ Indira Gandhi National Open University, 2022

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 BLOCK 3: THERMAL AND ELECTROANALYTICAL METHODS

In the preceding blocks of this course, you studied about the various chromatographic
techniques. In this block our focus will be on thermal and electroanalytical methods. This
block consists of three units. Unit 8: Thermal Methods of Analysis, deals with the methods
which are based on the determination of changes in chemical or physical properties of
material on heating. These analytical methods are known as thermal methods. These have
been developed based on the scientific study of changes in the properties of a sample which
occur on heating. In this unit our focus will be on therogravimetric methods of analysis. Unit 9
and Unit 10 deal with three important electroanalytical methods i.e. potentiometry, pH metry
and conductometry. In Unit 9, we are going to cover classification of electroanalytical
method, principle of potentiometry and pH metry, and different types of reference and
indicator electrodes. Procedural details of measurement of potential and pH along with
potentiomertic titation and pH metric titration have also been discussed in detail.

Unit 10, deals mainly with Conductometry is one of the oldest and in many ways simplest
among the other electroanalytical techniques. This technique is based on the measurement
of electrolytic conductance. In this unit we have covered principle and application of
conductometry in acid base titrations.

Both thermal methods and electroanalytical could be employed for the determination of
elemental concentration or compound in varying sample size of complex matrices of
geological, biological, environmental, forensic, pharmaceuticals and other industrial products.

Expected Learning Outcomes

After studying this block, you should be able to:

 describe the basic thermal methods of analysis;

 explain the basic principles of the thermogravimetric analysis;
 describe components of the instruments used for TGA;
 illustrate applications of the thermal methods in the characterizations of inorganic and organic
compounds;
 classify electroanalytical methods in different groups;
 describe the basic principles of potentiometry and pH metry;
 illustrate the applications of potentiometric and pH metric methods;
 describe the basic principle of conductometric methods of analysis;
 describe components of the instruments and their use in measurement of conductance.
Unit 8 Thermal Methods of Analysis

UNIT 8

THERMAL METHODS OF
ANALYSIS

Structure
8.1 Introduction 8.6 Factors Affecting TG Curve

Expected Learning Outcomes 8.7 Applications of

Thermogravimetric Analysis
8.2 Thermogravimetric Analysis
8.8 Summary
8.3 Instrumentation
8.9 Terminal Questions
8.4 Sources of Error in TGA
8.10 Answers
8.5 Interpretation of TG Curve

8.1 INTRODUCTION
In the preceding blocks you have studied various chromatographic methods.
These methods are commonly used to separate mixtures. We now turn our
attention to other analytical methods which are based on the determination of
changes in chemical or physical properties of material on heating. These
analytical methods are known as thermal methods. These have been
developed based on the scientific study of changes in the properties of a
sample which occur on heating. You may be familiar will the facts like, when
ice is heated, it melts at 0 oC and then boils at 100 oC, when sugar is heated; it
first melts, and then forms brown Caramel. In your undergraduate Organic
Chemistry lab you may have used melting points of organic solids in assessing
the purity and characterization of organic compounds. Melting points are
independent of experimental conditions whether we were using an oil bath or a
heating block. Basically in this process we are subjecting the organic sample
to a heating procedure and measuring a physical property (melting point) by
observing the physical change of the material, as it is heated. In fact, every
material behaves in a characteristic way when heated. The thermal methods
of analysis are based on the determination of change in chemical or physical
7
Block 3 Thermal and Electroanalytical Methods

properties of material as a function of temperature in a controlled atmosphere.

These methods are good analytical tools to measure:

 thermal decomposition of solids and liquids;

 solid-solid and solid-gas chemical reactions;

 material specification, purity and identification;

 adsorption behaviour of material;

 phase transitions.

These informations help us in the characterization of organic and inorganic

chemicals, polymers, metals, semiconductors and other common classes of
materials. Not only this, thermal methods also help us in understanding the
likely behaviour of chemicals and materials with change of temperature during
reactions, transport and storage. On that basis, one can suggest to take
possible precaution in handling the particular chemical or material.

Here we have summarized the variety of materials which can be usefully

studied by the thermal methods.

1. Organic and Inorganic compounds

2. Pharmaceuticals

3. Polymers and Plastics

4. Textiles and Fibers

5. Minerals, Soils and Clays

6. Ceramics and Glass

7. Building materials such as cement and concrete

8. Catalysts

9. Biological Materials e.g. kidney stone

10. Explosives

11. Fats, oils, soaps and waxes

12. Flame retardants

13. Foodstuffs and additives

14. Liquid crystals

15. Metals and alloys

The more frequently used thermal methods of analysis are shown in Table1,
with the brief names commonly used for them.
8
Unit 8 Thermal Methods of Analysis

Table 8.1: Thermal methods

Technique Abbreviat Property Uses
ion

Thermogravimetry or TG Mass Decompositions

(Thermogravimetric TGA Oxidations
analysis)
Differential thermal DTA Temperature Phase changes,
analysis difference reactions
Differential scanning DSC Power difference Heat capacity,
calorimetry or heat flow phase changes,
reactions
Thermometric Titration TT Enthalpy Acid-base and Non-
aqueous systems

Though in this unit our focus will be on thermogravimetric analysis, but a brief
description these techniques is given below.
TGA: This is a technique in which weight of a material is measured as a
function of temperature in controlled conditions. This technique provides
information regarding weight change of a material on heating and enables the
stoichiometry of the reaction involved during process. When we heat a
sample there may be two situations, sample either loses weight or gain weight,
which are shown below:
Sample (Solid) Product (Solid) + Gas (Loss of weight)
Gas + Sample (Solid) Product (Solid) (Gain of weight)

DTA & DSC: In DTA techniques, the difference in the temperature (  T)

between the material and an inert reference material is measured as function
of temperature under control conditions. DSC is very similar to DTA as both
shows an endotherm on melting and an endotherm (or exotherm) when
decomposition of material occurs. DSC differs from DTA in that instead of
allowing a temperature difference to develop between the sample and
reference, DSC measures the energy that has to be applied to keep the
temperature same. Beside these techniques thermometric titrations have
many applications in analytical chemistry. In such titrations we plot a graph of
change in temperature (  T) against the volume of titrant added. These
titrations are used for quantitative analysis.

Instrumentation for thermal methods

The modern instrumentation used for any experiment in thermal methods is

usually consists of five major parts:

 The sample and a container or holder,

 Sensor to detect and measure a particular property of the sample and to

measure temperature,

 An encloser within which the experimental parameters such as

temperature, pressure, gas atmosphere may be controlled,
9
Block 3 Thermal and Electroanalytical Methods

 A programmer to control the experimental parameters, such as the

temperature programmer,

 Recorder to collect the data from the sensors and to process the data to
produce meaningful results

Basic components of an instrument used for thermal methods are shown

schematically below.

Schematic of a typical instrument used to measure thermal properties

Expected Learning Outcomes

After studying this unit you should be able to:

 describe the basic thermal methods of analysis;

 explain the principle of TGA;

 describe the experimental setup of TGA;

 interpret the analytical information from TGA curves; and

 describe the applications of TGA in qualitative and quantitative analysis

of inorganic, organic and polymer materials.

8.2 THERMOGRAVIMETRIC ANALYSIS

Thermogravimetric analysis (TGA) is the most widely used thermal method. It
is based on the measurement of mass loss of material as a function of
temperature. In thermogravimetry a continuous graph of mass change against
temperature is obtained when a substance is heated at a uniform rate or kept
at constant temperature. A plot of mass change versus temperature (T) is
referred to as the thermogravimetric curve (TG curve). For the TG curve, we
generally plot mass (m) decreasing downwards on the y axis (ordinate), and
temperature (T) increasing to the right on the x axis (abscissa) as illustrated in
Fig. 8.1. Sometime we may plot time (t) in place of T. TG curve helps in
revealing the extent of purity of analytical samples and in determining the
mode of their transformations within specified range of temperature.

In thermogravimetry, the term ‘decomposition temperature’ is a complete

misnomer. In a TG curve of a single stage decomposition, there are two
characteristic temperatures; the initial Ti and the final temperature Tf (see Fig.
8.1). Ti is defined as the lowest temperature at which the onset of a mass
10 change can be detected by thermo balance operating under particular
Unit 8 Thermal Methods of Analysis

conditions and Tf as the final temperature at which the particular

decomposition appears to be complete. Although Ti has no fundamental
significance, it can still be a useful characteristic of a TG curve and the term
procedural decomposition temperature has been suggested. The
difference Tf – Ti is termed as reaction interval. In a dynamic
thermogravimetry a sample is subjected to continuous increase in temperature
usually linear with time whereas in isothermal or static thermogravimetry the
sample is maintained at a constant temperature for a period of time during
which any change in mass is noted. Now we will take up the instrumentation
commonly used to obtain TG Curve.

Fig. 8.1: A Typical TG Curve

8.3 INSTRUMENTATION
The instrument used in thermogravimetry (TG) is called a thermobalance. It
consists of several basic components in order to provide the flexibility
necessary for the production of useful analytical data in the form of TGA
curve as shown in Fig. 8.4.

Basic components of a typical thermobalance are listed below:

i) Balance

ii) Furnace: heating device

iii) Unit for temperature measurement and control (Programmer)

iv) Recorder: automatic recording unit for the mass and temperature
changes

These components may be represented by simple block diagram as in Fig. 8.2

Fig. 8.2: Block diagram of a Thermobalance. 11

Block 3 Thermal and Electroanalytical Methods

Balance

The basic requirements of an automatic recording balance are accuracy,

sensitivity, reproducibility, and capacity. Recording balances are of two types,
null point and deflection type. The null type balance, which is more widely
used, incorporates a sensing element which detects a deviation of the balance
beam from its null position. The sensor detects the deviation and triggers the
restoring force to bring the balance beam back to the null position. The
restoring force is directly proportional to the mass change. Deflection
balance of the beam type involve the conversion of the balance beam
deflection about the fulcrum into mass – change curves identified by (a)
photographic recoding i.e. change in path of a reflected beam of light
available of photographic recording, (b) recording electrical signals generated
by an appropriate displacement measurement transducer, and (c) using an
electro- mechanical device. The different balances used in TG instruments are
having measuring range from 0.0001 mg to 1 g depending on sample
containers used.

Furnace

The furnace and control system must be designed to produce linear heating
rate over the whole working temperature range of the furnace and provision
must be made to maintain any fixed temperature. A wide temperature range
generally from ambient temperature to 2000 °C of furnaces is used in
different instruments manufacturers depending on the models. The range of
furnace basically depends on the types of heating elements are used.

Temperature Measurement and Control

Temperature measurement are commonly done using thermocouples ,

chromel – alumel thermocouple are often used for temperature up to 180°C
whereas Pt/(Pt–8% Rh) is employed for temperature up to 1750°C.
Temperature may be controlled or varied using a program controller with two
thermocouple arrangement, the signal from one actuates the control system
whilst the second thermocouple is used to record the temperature.

Recorder

Graphic recorders are preferred to meter type recorders. X-Y recorders are
commonly used as they plot weight directly against temperature. The present
instrument facilitate microprocessor controlled operation and digital data
acquisition and processing using personal computer with different types of
recorder and plotter for better presentation of data.

In Fig. 8.3, we have shown a schematic diagram of the specific balance and
furnace assembly as a whole to better understand the working of a
thermobalance. In this diagram you can clearly see that the whole of the
balance system is housed in a glass to protect it from dust and provide inert
atmosphere. There is a control mechanism to regulate the flow of inert gas to
provide inert atmosphere and water to cool the furnace. The temperature
sensor of furnace is linked to the programme to control heating rates, etc. The
12
Unit 8 Thermal Methods of Analysis

balance output and thermocouple signal may be fed to recorder to record the
TG Curve.

Fig. 8.3: Schematic diagram of a typical balance and furnace assembly.

Thermogravimatic Curves

So far we have discussed the instrumentation of TG now we turn our attention

to quantitative aspects of TG. As discussed earlier TG curves represent the
variation in the mass (m) of the sample with the temperature (T) or time (t).
Normally, we plot mass loss downward on the ordinate (y) axis and mass gain
upwards as shown in Fig. 8.4.

Fig. 8.4: TG Curve. Note the plateau of constant weight (region A), the mass loss
portion (region B), and another plateau of constant mass (region C)
13
Block 3 Thermal and Electroanalytical Methods

Sometime we also record derivative thermogravimetric (DTG) Curves. A DTG

curve presents the rate of mass change (dm/dt) as a function of temperature,
or time (t) against T on the abscissa (x axis) as shown in Fig. 8.4 when
substance is heated at uniform rate. In this figure, the derivative of the Curve
is shown by dotted lines.

SAQ 1
List the different components of a thermobalance.

8.4 SOURCES OF ERRORS IN TGA

There are a number of sources of error in TGA, and they can lead to
inaccuracies in the recorded temperature and mass data. Some of the errors
may be corrected by placing the thermobalance at proper place and handling it
with great care. For understanding we are discussing some common source of
errors during operation of a thermobalance.

i) Buoyance effect: If a thermally inert crucible is heated when empty

there is usually an apparent weight change as temperature increases.
This is due to effect of change in buoyancy of the gas in the sample
environment with the temperature, the increase convection and possible
effect of heat from the furnace in the balance itself. Now, in most modern
thermobalances, this effect is negligible. However, if necessary, a blank
run with empty crucible can be performed over the appropriate
temperature range. The resultant record can be used as a correction
curve for subsequent experiment performed in the same condition.

ii) Condensation on balance suspension: Condensation of the sample

will also affect the mass of the sample and consequently the shape of
TG curve .This can be avoided by maintaining a dynamic atmosphere
around the sample in the furnace so that all the condensable product
may be driven by the flowing gases.

iii) Random fluctuation of balance mechanism

iv) Reaction between sample and container

v) Convection effect from furnace

vi) Turbulence effect from gas flow

vii) Induction effect from furnace

Errors of type (iii) can be avoided by proper placing of balance in the

laboratory and error (v) can be avoided by sensible choice of sample
container. Last three errors (v-vii) have to be considered in the design of the
furnace, the balance and its suspension system. By avoiding excessive
heating rate and proper gas flow rate some of above mentioned errors may be
avoided.

In the light of above discussion it is necessary to calibrate thermobalance

14 before to use.
Unit 8 Thermal Methods of Analysis

Calibration of thermobalance for the measurement of mass: It can be

done by adding known mass of the sample container and noting the reading of
the chart.
Temperature calibration: ferromagnetic standards are used for this purpose.
In a magnetic field these substances show detectable mass changes. The
ferromagnetic standards are quite suitable for the temperature range from 242
to 771° C.

SAQ 2
What are common source of errors in thermogravimetric analysis?

8.5 INTERPRETATION OF TG CURVES

TG curves of a pure compound are characteristic of that compound. Using TG
curve we can relate the mass changes to the stoichiometry involved. This can
often lead us directly to the quantitative analysis of samples whose
quantitative composition is known. To further illustrate, let’s consider the
example of TGA curve of CaCO3, (Fig. 8.5.) This curve indicates that CaCO3
decomposes in a single step between 600° C and 900° C to form stable
oxide CaO and the gas carbon dioxide. This can be explained the chemistry of
CaCO3 when it is heated:

CaCO3 (s)  CaO (s) + CO2 (g)

… (8.1)
Mr 100.1 56.1 44

Where Mr is relative mass. Now again consider the Fig. 8.5 (c), it indicates the
% mass lost by the sample is 44 (100.1–56.1) between 600 and 900° C. This
exactly corresponds to the mass changes calculations based on stoichiometry
of the decomposition of CaCO3 expressed by the chemical Eq. (8.1). As in this
case, percentage weight loss of CaCO3 will be
M
m

r (CO 2 )
M

% 100 … (8.2)
r (CaCO3 )

44×100
= = 44
100.1

o o
Fig. 8.5: TG and DTG Curve of CaCO3 at various heating rates (b =8 C, c = 3 C)
(DTG = Rate of Change of mass, dm/dt) curve. 15
Block 3 Thermal and Electroanalytical Methods

We have seen above how TG Curves is related to stoichiometry (quantitative

interpretation). Now we see in next example how it can be used to compare
thermal stability of materials (qualitative interpretation). Such information can
be used to select material for certain end-use application, predict product
performance and improve product quality. Fig. 8.6 gives TG Curves of some
polymers. TG Curves clearly indicate that polymer (PVC) is the least thermally
stable and polymer (PS) is most thermally stable. Polymer (PS) looses no
weight at all below about 500o C and then decomposes abruptly by about 600 o
C. The other three polymers have all decomposed by about 450 o C. Polymers
(PMMA) decomposes more slowly overall than the others as indicated by
slopes of TG curves. TG curve of polymer (PMMA) has less slope than the
others.

Fig. 8.6: TG Curves of some polymers: PVC = polyvinyl chloride; PMMMA =

polymethyl methacrylate, LDPE = low density poly ethylene; PTFF =
ploytetra fluoroethylene; and PS = polystyrene.

SAQ 3
Calculate the percentage mass change (m %) for the following reactions.
Δ
i) Ca(OH)2 (s) 
Heat
 CaO(s)+H2O(g)

Δ
ii) 6PbO (s) + O2 (g)  2Pb3O4 (s)

Δ
iii) NH4NO3 (s)  N2O(g) + 2H2O(g)

Δ
iv) CuSO 4 .5H2O  CuSO4 .4H2O +H2O

Δ
v) CuSO 4  CuO + SO3

SAQ 4
A thermogram of a magnesium compound shows a loss of 91.0 mg from a
total of 175.0 mg used for analyte. Identify the compound either as MgO,
MgCO3, or MgC2O4.

16
Unit 8 Thermal Methods of Analysis

8.6 FACTORS AFFECTING TG CURVE

In the beginning of this units we talked about the lowest temperature, Ti at
which the onset of a mass change can be detected by the thermobalance
operating under particular conditions and Tf is the final temperature at which
the decomposition completed. We may like to call this as decomposition
temperature, which is not correct. Actually in TGA experiments, both Ti and Tf
do not have fundamental significance, but they can still be a useful
characteristic of a TG curve and the termed procedural decomposition
temperature. It is often used for the temperature at which mass change
appears to commence. This indicates us that procedural decomposition
temperature does not have a fixed value, but depends on the experimental
procedure employed to get it. Similar to this there are many factors which
influence a TGA curve. These factors may be due to instrumentation or nature
of sample. We have listed the main factors which affects the shape, precision
and accuracy of the experimental results in thermogravimetry.

1. Instrumental factors:

i) Furnace heating rate.

ii) Recording or chart speed

iii) Furnace atmosphere

iv) Geometry of Sample holder/ location of sensors

v) Sensitivity of recording mechanism.

vi) Composition of sample container.

2. Sample Characteristics:

a) Amount of sample

b) Solubility of evolved gases in sample.

c) Particle size

d) Heat of reaction

e) Sample packing

f) Nature of sample

g) Thermal conductivity.

Now we will take up some important factors in some detail.

a) Furnace heating rate

At a given temperature, the degree of decomposition is greater the

slower the heating rate, and thus it follows that the shape of the TG
curve can be influenced by the heating rate. For a single stage
endothermic reaction it has been found that:

i) (Ti)F > (Ti)S

17
Block 3 Thermal and Electroanalytical Methods

ii) (Tf)F > (Tf)S

iii) ( Tf – Ti ) F > ( Tf – Ti ) S

where subscripts F and S indicate fast and slow heating rate

respectively. For example, polystyrene decomposes 10 % by mass
when heating rate is 1 °C per min by 357 °C and 10 % by mass when
heating rate is 5 °C per min by 394 °C. More specifically, it is observed
that the procedural decomposition temperature Ti, and also Tf (the
procedural final temperature) will decrease with decrease in heating rate
and the TG curve will be shifted to the left. This effect is illustrated in Fig.
8.5. The appearance of an inflection in a TG curve at a fast heating rate
may well be resolved into a plateau at a slower heating rate. Therefore,
in TGA there is neither optimum no standard heating rate, but a heating
rate of 3 °C per min. gives a TG curve with maximum meaningful
resolution.

b) Recording or Chart Speed

The chart speed on the recording of the TG curve of rapid or slow

reaction has pronounced effect on the shape of the TG curves. For a
slow decomposition reaction low chart speed is recommended for
recording the TG curve because at high chart speed the curve will be
flattened and it will not show the sharp decomposition temperature. For
a slow reaction followed by a rapid one at the lower chart speed the
curve will show less separation in the two steps than the higher chart
speed curve. For fast-fast reaction followed by slower one similar
observation was observed in shorter curve plateaus.

c) Furnace Atmosphere

The effect of atmosphere on the TG curve depends on (i) the types of the
reaction (ii) the nature of the decomposition products and (iii) type of the
atmosphere employed. The effect of the atmosphere on TG curve may
be illustrated by taking the example of thermodecomposition of a sample
of monohydrates of calcium oxalate in dry O2 and dry N2 as shown in
Fig. 8.7.

Fig. 8.7: TG Curve of Calcium Oxalate in O2 and N2

atmosphere: [ N2 ,----------------- O2]

18
The first step, which is dehydration is reversible reaction.
Unit 8 Thermal Methods of Analysis

Ca C2O4.H2O(s) Ca C2O4 (s) + H2O (g ) ... (8.3)

This is unaffected because both gases are equally effective in sweeping

the evolved water vapours away from the sample surface. For the
second step,

CaC2O4(s) CaCO3 (s) + CO (g) ... (8.4)

The curve diverges in O2 atmosphere because the oxygen reacts with

evolved CO, giving a second oxidation reaction which is highly
exothermic and so raises the temperature of the un-reacted sample.
The temperature accelerates the decomposition of the compound more
rapidly and completely at a lower temperature as shown in the above
diagram in dry O2 than in N2 atmosphere. The third step in
decomposition reaction is also reversible reaction.

CaCO3 (s) CaO (s) + CO2 (g) ... (8.5)

This step should not be influenced by O2 or N2. However there is a

slight difference in curves for the two gases as shown in diagram. The
small difference was due to the difference in the nature/composition of
CaCO3 formed in the two atmospheres. This is due to the particle size,
surface area, lattice defects or due to the other physical characteristics of
CaCO3 formed.

d) Sample Holder

The sample holders range from flat plates to deep crucible of various
capacities. The shape of the TG curve will vary as the sample will not be
heated in identical condition. Generally, it is preconditioning that the
thermocouple is placed on near the sample as possible and is not dipped
into the sample because it might be spoiled due to sticking of the sample
to the thermocouple on heating. So actual sample temperature is not
recorded, it is the temperature at some point in the furnace near the
sample. Thus it leads to source of error due to the thermal lag and partly
due to the finite time taken to cause detectable mass change. If the
sensitivity of recording mechanism is not enough to record the mass
change of the sample then this will also cause error in recording the
weight change of the sample. If the composition of the sample contains
is such that it reacts either with the sample, or product formed or the
evolved gases then this will cause error in recording the mass change of
the sample.
e) Effect of Sample Mass

The sample mass affects the TG curve in the following circumstances:

i) The endothermic and exothermic reactions of the sample will cause

sample temperature to deviate from a linear temperature change.

ii) The degree of diffusion of evolved gases through the void space
around the solid particles.

iii) The existence of large thermal gradients throughout the sample

particularly, if it has a low thermal conductivity. 19
Block 3 Thermal and Electroanalytical Methods

Thus, it is preferable to use as small a sample as possible depending on

the sensitivity of the balance.
f) Effect of Sample Particle Size
The particle size will cause a change in the diffusion of the evolved
gases which will alter the reaction rate and hence the curve shape. The
smaller the particle size, greater the extent of decomposition at any given
temperature. The use of large crystal may result in apparent rapid
mass loss during heating. This may be due to the mechanical loss of part
of the sample by forcible ejection from the sample container, when the
accumulated evolved gases within the coarse grains are suddenly
released.

g) Effect of Heat of Reaction

The heat of reaction will affect the extent to which sample temperature
proceeds or succeeds the furnace temperature. This depends on
whether the reaction is exothermic or endothermic and consequently the
extent of decomposition will also be affected.

The other sample characteristics such as sample packing, nature of the

sample and its thermal conductivity will also affect the shape of TG
curves. If the sample is packed loosely then the evolved gases may
diffuse more easily than if the sample packed tightly.

If the sample reacts with the sample container on heating then it will not
give the mass of the product formed so the sample will change. We can
avoid this effect by a sensible choice of sample container.

SAQ 5
What are the common instrumental factors affecting TG curves.

8.7 APPLICATIONS OF TERMOGRAVIMETRIC

ANALYSIS
In the previous section we have seen how TGA can be used to understand the
chemistry of decomposition of a particular compound. TGA also provides
information about the temperature range over which a particular sample
appears to be stable or unstable. We have also interpreted TG curves
qualitatively. Beside these there are many other applications of
thermogravimetric analysis. Some are listed below:

i) Purity and thermal stability.

ii) Solid state reactions.

iii) Decomposition of inorganic and organic compounds.

iv) Determining composition of the mixture.

20
Unit 8 Thermal Methods of Analysis

v) Corrosion of metals in various atmosphere.

vi) Pyrolysis of coal, petroleum and wood.

vii) Roasting and calcinations of minerals.

viii) Reaction kinetics studies.

ix) Evaluation of gravimetric precipitates.

x) Oxidative and reductive stability.

xi) Determining moisture, volatile and ash contents.

xii) Desolvation, sublimation, vaporizations, sorption, desorption,

chemisorptions.

It is not possible to discuss all these applications at this level; it is worth to

describe some of the applications which are more common.

Analysis of Inorganic and Organic Mixtures

We have already seen that single and pure compound gives characteristic TG
curves. Now, we will see how TG Curves can be used in predicting relative
quantities of the components of a mixture.

Binary mixtures

Consider a mixture of two compounds AB and CD having characteristic TG

Curves which are different from each other as shown in Fig. 8.8

Fig. 8.8: (a) Thermogravimetric curves of two compounds AB and CD and (b)
their Mixture.

The decomposition of pure compound AB and CD occur at T1, and labeled as

bc and temperature T2, and labeled as fg respectively, as illustrated in
Fig. 8.8 (a). The TG curve of mixture of AB and CD together is shown in
Fig. 8.8 (b). You can see in this figure, the plateaus (corresponding to the
regions of constant mass) commence at about the same temperature as they
21
Block 3 Thermal and Electroanalytical Methods

do in the TG Curves for the pure compounds AB and CD. You can also notice
that the mass loss overall up to T1 is x mg and from T1 to T2 it is an additional y
mg. By measuring these two quantities x and y from the TG curves of Fig. 8.8
(b), we can determine the relative quantities of AB and CD in the original
binary mixture. To understand further consider the mixtures of calcium and
magnesium carbonates.

i) Analysis of a mixture of calcium and magnesium carbonates

A typical TG curve of a mixture of calcium and magnesium carbonates is

shown in Fig. 8.9. You can notice that a significant mass loss occurs
before 28° C. This is due to the moisture present in the mixture. Another
mass loss at about 480° C is due to the following reaction:

MgCO3 (s)  MgO(s) + CO2 (g) … (8.6)

Earlier we mentioned that CaCO3 decomposes at about 800 °C. In Fig.

8.8 mass loss between about 600 °C and 900 °C can be interpreted due
to decomposition of CaCO3.

CaCO3 (s)  CaO (s) + CO2 (g) … (8.7)

Portion of the curve ab represents a mixture of MgO and CaCO3 and cd

represents a residue of the mixture of MgO and CaO. Both these
plateaus ab and cd represent weight m1 and m2, respectively. In fact
mass m1 is due to CaCO3 + MgO.

Fig. 8.9: TG curve of mixture of calcium and magnesium carbonate.

22
Unit 8 Thermal Methods of Analysis

Thus, m1 – m2 is the loss of CO2 between 600° C and 900° C due to the
decomposition of CaCO3. Using TGA curve we can relate the mass of
different components formed during TGA experiment.

The mass of CaO (m3) formed can be calculated using following Eq. (8.8)

m3 = 1.27 (m1 – m2) … (8.8)

This equation can be obtained as follows:

The CaO is formed by the evolution of CO2 on the decomposition of

CaCO3,

CaCO3 (s)  CaO(s) + CO2 (g)

Mr 100.1 56.1 44

From the above equation 1mole of CaCO3 gives 1 mole of CO2 and
(m - m2 )
1mole of CaO. Thus, moles of CO2 in the given examples = 1
Mr (CO2 )
and this is equal to moles of CaO formed

(m1 - m2 )
Thus the amount of CaO must be, m3 = × Mr (CaO)
44

where, Mr(CaO) is the relative molar mass of CaO.

(m1 - m2 )
m3 = ×56.1 g
44

m3 = 1.27(m1 – m2) g

We know the mass of residue left, i.e., m2, the mass of MgO (m4) can be
calculated.

m4 = m2 – m3

Here m3 is the mass of CaO formed, which is equal to 1.27 (m1 – m2).
Thus

m4 = m2 – 1.27 (m1 – m2)

Mass of the Ca (mca) in the original sample can also be related to m1 and
m2 by the following formula

mca = 0.91 (m1 – m2)

This can be obtained as follows:

You know amount of Ca in CaCO3 and CaO will be equal in moles,

therefore amount of Ca in

Ar(Ca) Ar(Ca)
mCa = m3 × = 1.27 (m1 - m2 )×
Mr(CaO) Mr(CaO)

where, Ar(Ca) and Mr (CaO) are the relative atomic mass and relative
molar mass of Ca and CaO, respectively. Thus,
23
Block 3 Thermal and Electroanalytical Methods

= 1.27 (m1 – m2) × 40/56.1 = 0.91 (m1 – m2)

Similarly, mass of magnesium in the original sample can be related to m1

and m2:

Thus, the mass of Mg in original sample (mMg)

Ar (Mg)
= (mass of residue – mass of CaO)×
Mr (MgO)

Ar (Mg) 24.3
mMg = (m2 - m3 )× = (m2 - m3 )×
Mr (MgO) 40.3

mMg = 0.60 (m2 – m3)

ii) Mixture of calcium and magnesium oxalates

Calcium oxalate monohydrate is unsatisfactory weighing form for

determining calcium as oxalate because its tendency to retain excess
moisture even at 110 °C, co-precipitated ammonium oxalate remain un-
decomposed. The anhydrous calcium oxalate is hygroscopic but CaCO3
is excellent weighing form if heated to 500 ± 25 °C as can be seen in
TG curve of CaC2O4.H2O. Above 635 0C the decomposition of CaCO3
commences to become significant under usual laboratory conditions and
completely converted to CaO at 900 °C. Thus, calcium oxalate
monohydrate decomposes in three steps, first dehydration, second
removal of CO and formation of CaCO3 then third step CaCO3
decomposes to CaO (see Fig. 8.10).

CaC2O4.H2O → CaC2O4 + H2O at about 135-220 °C

CaC2O4 → CaCO3+CO at about 400-480 °C

CaCO3 →CaO+ CO2 at about 635-900 °C

But magnesium oxalate dihydrate decomposes in two steps instead of

three steps. First, dehydration then removal of CO and CO2
simultaneously and forming MgO, there is no horizontal corresponding to
MgCO3 as it is thermally unstable at this temperature.

MgC2O4.2H2O → MgC2O4+2H2O at about 135-220 °C

MgC2O4 → MgCO3 + CO→MgO+CO2 at about 500 °C

The TG curve for the mixture of CaC2O4.H2O and MgC2O4.2H2O shows

two mass losses up to 500 °C, first at about 200 °C due to loss of water
and the second mass loss occurs in the 390-500 °C range which is due
to decomposition of both calcium and magnesium oxalates. Thus, at
500°C, the composition of the mixture will be CaCO3 and MgO. Third
mass loss after 500 °C is due to only the decomposition of CaCO3. If m1
and m2 are the mass of the mixture at 500 °C and 900 °C then similar to
the previous example we can calculate the amount of calcium and
magnesium in the original sample.
24
Unit 8 Thermal Methods of Analysis

Fig.8.10: DTG/TG curve of calcium oxalate.

Organic Mixtures
TGA also provides quantitative information on organic compound
decompositions and is particularly useful for studying polymers. For example
TGA can be used in the determination of the amount of vinyl acetate in
copolymers of vinyl acetate and polyethylene. When vinyl acetate is heated it
looses acetic acid at about 340 °C. TG curves shown in Fig. 10.11 for several
vinyl acetate polyethylene copolymers are clearly indicating the loss of acetic
acid at about 340 °C due to the decomposition of vinyl acetate. Each mole of
vinyl acetate losses one mole of acetic acid. The amount of vinyl acetate in the
polymers can be calculated.

Fig. 10.11: TG curve of vinyl acetate copolym

SAQ 6
A mixture of CaO and CaCO3 is analysed by TGA. The result indicates that
mass of the sample decreases from 250.6 mg to 190.8 mg only between
600°C and 900°C. Calculate the percentage of calcium carbonate in the
mixture.
25
Block 3 Thermal and Electroanalytical Methods

8.8 SUMMARY
Thermogravimetric Analysis (TGA) technique has been described for its basic
principle, instrumentation and applications. The interpretation of results and
applications are discussed by taking different examples. The elementary
calculation are included to elaborate the topics. The probable cause of errors,
their remedies, interpretation of result are also discussed.

8.9 TERMINAL QUESTIONS

1. Formulate the solid state reaction of sodium bicarbonate when heated. It
decomposes between 80 and 225 °C with evolution of water and carbon
dioxide. The combined loss of water and carbon dioxide totaled 36.6%
by mass whereas the mass loss due to carbon dioxide alone was found
to be 25.4 %. Explain.

2. What types of standard are required to calibrate the mass variation

obtained with a TGA equipment?

3. What type of standards is required for temperature calibration of any

TGA?

4. A mixture of CaCO3 and CaO is analysed using TGA technique. TG

curve of the sample indicates that there is a mass change from 145.3 mg
to 115.4 mg between 500–900 °C. Calculate the percentage of CaCO3 in
the sample.

5. A 250 mg hydrated sample of Na2HPO4 decreases to a mass of 145.7

mg after heating to 150 °C. What is the number of water hydration in
Na2HPO4.

6. Draw a labeled diagram of the TG curve obtained by heating a mixture of

80 mg of CaC2O4.H2O and 80 mg of BaC2O4.H2O to 1200 °C. Calculate
the amount of all mass losses.

8.10 ANSWERS
Self Assessment Question
1. Balance; furnace; unit for temperature measurements and control; and
recorder.

2. Common source of error in thermogravimetric are listed in Sec. 8.3.

Δ
Ca(OH) 2  CaO  H 2 O
3. i)
Mr 74.1 56.1 18

Percentage loss =
 74.1- 56.1 = 24.3%
74.1

ii) 6PbO (s)  O 2 (g)  2Pb 3 O 4 (s)

26
Unit 8 Thermal Methods of Analysis

Mr 223.2 × 6 685.6 × 2

1339.2 1371.2

1371.2  1339.2 
  100
So, percent gain 1339.2
 2. 4 %

Δ
iii) NH 4 NO 3 (s)  N 2 O (g)  2H 2 O (g)

In this case, both the products are volatile when NH4NO3 is heated
at 300°C no solid residue is left. The percentage loss in this case is
80%.
Δ
iv) CuSO 4 .5H 2 O  CuSO 4 .4H 2 O  H 2 O

Mr 249.7 231.7 18

249.7  231.7  18
percen loss  100   100
249.7 249.7
 7. 2 %

Δ
v) CuSO 4  CuO  SO 3

Mr 231.7 151.7 80

231.7 - 151.7
%m × 100
231.7

80
%m  100  34.5%
231.7

4. Decomposition reaction of the MgO, MgCO3 and MgC2O4

MgO → No reactive

MgCO3 → MgO + CO2

MgC2O4 → MgO + CO2 + CO

44
% mass loss for MgCO3 = 100  52.2%
84.3

44  28 
% mass loss for MgC2O4 = 100  64.3%
112.3

91.0
% mass loss of the sample = 100  52%
175

Therefore, this compound is MgCO3.

5. Instrumental factors: Furnace heating rate, recording chart speeds,

furnace atmosphere, geometry of sample, holder/location of sensors,
sensitivity of recording mechanism, composition of sample container,
etc.
27
Block 3 Thermal and Electroanalytical Methods

6. The possible decomposition in the mixture may be written as

CaCO3 (s) → CaO (s) + CO2 (g)

Mr 100.1 56.1 44.0

Mass loss in the mixture is due to the formation of CO2 (g). We can
calculate the m moles of CO2, i.e. (250.6 – 190.8) mg/44 =1.359 mmol.
From the above chemical equation, 1 mole of CaCO3 give 1 mole of CO2.
Therefore the amount of CaCO3 in the mixture must be 1.359 mmol. This
will equal to = 1.359 × 100.1 mg = 135.9 mg.
135.9
So percentage of CaCO3 in the sample will be 100  54.2% by
250.6
mass.

Terminal Questions
1. Reaction proceed in following steps

Above 60 °C, it gradually decomposes into sodium carbonate and water

and carbon dioxide.

2NaHCO3 → Na2CO3 + H2O + CO2

Total calculated mass loss should be 36.9, dehydration is 8.71 and

decarbonylation is 26.19 . The observed mass loss is quite similar i.e.
total 36.6, dehydration 11.2 and decaroxylation is 25.4%.

2. There are no standards available for TGA calibration. It is only possible

to calibrate the balance using calibrated masses. However, it is possible
to use some materials with known mass variations, such as copper
sulphate pentahydrate or calcium oxalate, to check for good operation of
the thermobalance. The latter materials are generally agreed as working
standards but do not use the first mass loss, corresponding to the first
hydrate.

3. Temperature calibration of the TGA requires the use of a metal that is

99.99% pure and magnetic. A magnet has to be adjusted on the TGA
furnace.

4. Write the decomposition reaction of CaCO3

CaCO3 → CaO + CO2

Mr 100.1 56.1 44.0

This equation indicates that one mole of CaCO3 produces one mole of
CaO and one mole of CO2. Therefore,

m moles of CO2 = m moles of CaCO3

m moles of CO2 = mg lost/Mr (CO2)

= (145.3 – 115.4) mg/44.0

= 29.9/44.0
28
Unit 8 Thermal Methods of Analysis

= 0.682 m moles

A mount of CaCO3 in sample = m moles of CaCO3 × Mr (CaCO3)

= 0.682 × 100.1 mg

= 68.2 mg

68.2
% of CaCO3 = 100.  46.9 %
145.3

5. Molar mass of hydrated Na2HPO3 is 215.9. We can calculate mass loss

corresponding to each mole of hydrated water (n).

m % loss 8.8 16.7 25.0 33.3 41.7

n 1 2 3 4 5

250  145.7 
In this problem % mass loss =  100
250

= 41.7%

This corresponds to a mass loss of 5 moles of water of (hydration).

Therefore given sample must be of Na2HPO3.5H2O).

6. Table the help of Fig.8.12 to draw a labeled diagram of the TG curve for
mixture of CaC2O4.H2O and BaC2O4.H2O.

Total mass loss = 49.3 (CaC2O4.H2O) + 29.6 (BaC2O4.H2O)

= 78.9 mg.

29
Block 3 Thermal and Electroanalytical Methods

UNIT 9

POTENTIOMETRY

Structure
9.1 Introduction Measurement of Potential
Expected Learning Outcomes Direct Potential
9.2 Classification of Electrodes
Electroanalytical Methods
9.4 Potentiometric Titrations
Potentiometry
Types of Potentiometric
Voltammetry Titrations
Polarography 9.5 pH Metric Titration
Amperometry 9.6 Summary
Coulometry 9.7 Terminal Questions
Conductometry 9.8 Answers
9.3 Basic Principle of Potentiometry

9.1 INTRODUCTION
Electroanalytical methods find applications in all branches of Chemistry,
industries, engineering and a number of other technologies. The possibility of
the determination of low level of pollutants has prompted the use of these
methods in environmental studies.

An electroanalytical method can be defined as one, in which the electrical

response of a chemical system or sample is measured. These methods can
be classified into a number of types characterized by measuring the electrical
response in terms of different electrical quantities such as: potential, current,
quantity of current, resistance and voltage etc. and bear the corresponding
names as potentiometry, amperometry, coulometry, conductometry and
voltammetry etc. During the past few years, there has been sudden increase
in interest in electroanalytical techniques. This is partially attributed to the
development in instrumentation and partially due to the heavy demands by
environmental scientists for the determination of a large number of heavy
metal, organic and inorganic substances present in water and soil samples. In
this unit our focus will be on potentiometry.
30
Unit 9 Potentiometry

We hope you are already aware of the electrode potentials and how it can be
calculated using Nernst equation from your earlier studies. In this unit, we are
going further to discuss how the electromotive force developed in a cell can be
measured using a potentiometer. This method consists of measuring the
potential between any two electrodes immersed in the solution to be analysed.
For measuring the potential, we require two electrodes, an indicator electrode
and a reference electrode along with a device called potentiometer.

Potentiometric methods have many applications in the area of analytical

chemistry. These methods can be used for direct and selective measurement
of analyte concentrations, for determining end point in various types of
titrations and for the determination of several types of equilibrium constants.

In this unit, first we study the classification of electro analytical methods. After
that you will describe different types of reference and indicator electrodes.
There will be a brief description about instrumentation and potentiometric
titrations and pH titrations too.

Expected Learning Outcomes

After studying this unit, you should be able to:

 describe the classification of the electroanalytical techniques;

 explain the principle of potentiometric methods of analysis;

 describe some common types of reference and indicator electrodes;

 describe chemical reactions involved in potentiometric

titrations;

 explain the principle of potentiometric titration; and

 state the experimental details of pH titrations.

9.2 CLASSIFICATION OF ELECTROANALYTICAL

METHODS
Although the variety of electrochemical methods may seem to be large, all of
them are based on a rather limited number of percepts, the particular
combination of which determines the nature of the technique. A general
classification of electroanalytical methods is based on

i) the particular electrical property or properties measured by keeping the

other quantities constant and

ii) the mode of mass transport as: diffusion, convection and migration.

Further many of these techniques may be divided into two types on the basis
of the procedures adopted for the analytical determination:

1. methods in which little or no chemical transformation occurs and the

measurement of an electrical quantity gives a direct measure of
31
Block 3 Thermal and Electroanalytical Methods

concentration, this is sometimes indicated by prefixing ‘direct, before the

name of the technique (such as direct potentiometery)

2. the second type involves methods based on titration procedures in that

the analyte undergoes a stoichiometric chemical transformation affected
by an electrochemical reaction, however, the end point may or may not be
determined electrochemically. These methods are named by adding
titration after the original name of the technique, such as, potentiometric
titration, amperometric titration, etc.

On the basis of above consideration the various electonalytical methods are

classified and discussed briefly as below.

9.2.1 Potentiometry
This technique involves the measurement of potential at zero current flow.
Analytical use of this technique is made in two ways. In one, known as direct
potentiometry, in this technique, we utilize the single measurement of potential
and the Nernst Equation is used to relate cell potential to the concentration of
analyte. The liquid-junction potentials and activity coefficients influence the
value of cell potential. In the other technique, known as potentiometric titration,
a set of measured potential is used to detect the changes in concentration that
occur at the equivalence point of a titration. In these titrations the change in
the potential is of importance and thus the influence of junction potentials and
activity coefficients may be ignored. Let us discuss more about these
techniques.

a) Direct Potentiometry

In direct potentiometry, we measure a potential difference between two

electrodes immersed in a solution and connecting the cell so formed to a
voltage measuring device (potentiometer, vacuum tube voltmeter). The cell
formed by two electrodes (half-cells) and the solution is known as an
electrochemical cell (a galvanic cell). The net cell reaction can be considered
as the sum of the two half-cell reactions in which the each half-cell reaction is
the representation of the actual chemical process that occurs at the individual
electrode of the galvanic cell. A half-cell reaction always include the electrons
transferred.

Usually, one of the electrodes (half-cell) is chosen such that its potential is
invariant and is termed as reference electrode. The potential of the other
electrode is then a function of the concentration (more correctly activity) of the
species involved in the electron transfer process (a redox reaction), through
the Nernst Equation. This electrode is termed the indicator electrode. Under
these conditions the cell emf is given by

Ecell = (Eind - Eref ) + E j ...(9.1)

where

Ecell is emf of galvanic cell,

Eind = half-cell potential of the indicator electrode,

32
Unit 9 Potentiometry

Eref = half-cell potential of the reference electrode,

Ej = liquid-junction potential developed at the interface between two

electrolytes.

Concentration of the solution is determined by a single measurement of cell

potential applying the Nernst Equation.

pH-metry is also based on direct potentiometry, in this case the glass

electrode commonly used for pH measurement. Glass electrode is an ion
selective membrane electrode. Further details of these methods will be
discussed in Section 9.3, 9.4 and 9.5.

Potentiometric Titrations

By far the most common application of potentiometry is in the potentiometric

titrations. In these titrations, the potential between appropriate indicator and
reference electrode immersed in the sample is monitored during the titration.
The titrations can be performed manually or with automatic titration equipment.
The cell potential (or in pH titrations the pH) is plotted as a function of the
volume of titrant.

Further details of these methods will be discussed in Section 9.3, 9.4 and 9.5.

9.2.2 Voltammetry
In voltammetry an electroactive species is consumed (oxidized or reduced
only at the surface layer of the indicator electrode in an electrolytic cell. The
resulting current, due to the electron transfer process is measured as a
function of applied potential. Such electrolysis is carried out under controlled
conditions of diffusion (or/and convection). In diffusion layer electrolysis
methods only a thin layer of solution immediately adjacent to the electrode
undergoes electrolysis. In these methods, the electrical variable is related to
the concentration of the bulk, and usually, the time of electrolysis is short that
only a negligible fraction of the reactant is electrolysed and the reactant
concentration in the bulk solution is not altered (theoretically).

In voltammetry we study the relationship between the current and electrode

potential and their applications to chemical analysis. The voltammetric curves
are known as current-volts curves or current-potential curve. The shape of the
I-E curve depends on the polarization of the indicator electrode, when the
other electrode known as the reference electrode remain unpolarized and
does not influence the shape of the I-E curve.

9.2.3 Polarography
Various types of electrodes can be used in voltammetry, but one of them, the
dropping mercury electrode (dme), is particularly useful and the corresponding
voltammetric method is referred to as polarography.

The use of dme in chemical analysis was originated at the Charles University
in Prague, Czechoslovakia in the early 1920s by Heyrovsky who coined the
name polarography to designate this technique. The dropping mercury
33
Block 3 Thermal and Electroanalytical Methods

electrode is essentially composed of a capillary connected to mercury

reservoir. The bore of the capillary, the length of the capillary, and the head of
mercury are adjusted in such a way that a drop is dislodged every 2-6 sec. A
platinum wire is immersed in the mercury reservoir, and the dme is coupled
with unpolarized electrode.

Polarography consists of electrolysing a solution of an electroactive substance

between a dme (cathode) andand some reference electrode (anode). The area of
the anode is large correspondingly so that it may be regarded as unpolarized
and the potential of such electrode remains fairly constant.

The current-potential characteristics can be studied with the type of an

apparatus (Fig.9.1) in a simple manner in which the voltage applied to the cell
C is adjusted by means of a potentiometer P and the current through the cell
is read on a galvanometer G.

Fig. 9.1: Manual polarographic circuit

On applying the potential between two electrodes and increasing its value in a
stepwise manner the following processes take place. At first only a small
current flow-the so called residual current. This continues until the
decomposition potential of the reducible
reducible ionic species is reached. At this point
the following reaction takes place,

Mn+ +ne ⇌ M(Hg) (Reducible)

Afterward a steep rise in current is observed and will continue to rise with
increasing potential till the current reaches a limiting value (Fig. 9.2).

34
Unit 9 Potentiometry

Fig. 9.2: I-E curve for Mn+ (Polarogram)

The conditions are set such that the diffusion is the main process of mass
transfer. This can be done by minimising convection and migration. The
limiting current under these conditions is known as the diffusion current (Id ).

The factors affecting the diffusion current were examined by D. Ilkovic and he
gave the following equation which is known as the Ilkovic equation.

Id = 708 nm 2/3 D ½ t1/6 c … (9.2)

where I d is the diffusion current, n is the number of electrons consumed in the

reduction of M n + , D is the diffusion coefficient, m is the rate of flow of mercury,
t is the time and c is the concentration of Mn+ in the solution and 708 is the
combination of constants and conversion factors involved in changing in units
taken into account.

Equation 9.2 gives a direct relation between Id and concentration, hence can
be applied for quantitative measurements, we can write from equation 9.4,

Id  c or Id = Kc … (9.3)

where K can be evaluated by noting the current with a standard solution of the
substance of interest.

The curve shown in Fig.9.3 is called I-E or polarogram or polarographic wave.

Two important features of a polarogram are (i) the half wave potential E1 2 ,
and (ii) the diffusion current.

SAQ 1
Distinguish between voltammetry and polarography.

9.2.4 Amperometry
In Polarography, we have seen that in a particular polarogram, the limiting
current of an electroactive substance, at a suitable (fixed) potential depends
on the substance concentration only. If we reduce the concentration of the
electroactive substance by its interaction with another substance, the current
will be reduced. This principle is made to get the equivalence point by
measuring the current flowing at an indicator electrode. This technique is
35
Block 3 Thermal and Electroanalytical Methods

known as amperometric titration. Thus, amperometry named after the unit of

current, “ampere” is based on the measurement of current when the voltage
across the electrodes of a cell is kept constant. In amperometric titrations the
current passing through the cell (containing the analyte) at a suitable constant
voltage is measured as a function of the volume of titrant (or of time if the
titrant is generated by a constant current coulometric process). By far, the
application of amperometry is in amperometric titrations.

Amperometric titrations are more accurate than voltammetric methods.

Furthermore, this titration can be performed even when the substance being
determined is not reactive, since an equally satisfactory equivalent point can
be located with either a reactive titrant or when the product is reactive.

9.2.5 Electrogravimetry and Coulometry

Faraday’s law of electricity gives a direct proportion between quantity of
electricity and the amount of substance consumed or obtained after oxidation
and reduction taking place when a current is passed for a sufficient period
through an electrochemical cell. Two electroanalytical techniques are based
on the above statement, they are electrogravimetry and coulometry. These are
the bulk electrolysis methods.

Electrogravimetry

It is the oldest of electroanalytical techniques and was well established by the

end of nineteenth century. It involves the controlled potential reduction of a
solution of a metal salt which is continued till the current falls near to zero.
Thus, electrolysis is used as a means of chemical transformation (reduction of
the metal ion). The product of analysis (i.e., after electrolysis) is weighed as a
deposit on one of the electrodes (working electrode). The increase in the
weight of the previously weighed working electrode leads to the determination
of the metal context of the sample solution. Since the reaction product after
electrolysis is determined ordinarily by weighing, hence the name
“electrogravimetry”.

The method is very simple to apply in the analysis of a single element in the
absence of any other substance which might be deposited. For this analytical
method the appropriate electrode potential is essential. The potential for the
selective deposition of a metal can be calculated from the Nernst equation or it
can be determined from data obtained by voltammetry.

Coulometry

In the bulk electrolysis method, when the amount of the constituent to be

determined is not weighed but calculated by measuring the quantity of
electricity and making use of Faraday’s law the technique is called coulometry,
the term derived from coulomb, the quantity of current. In these methods, the
analyte is quantitatively converted to a different oxidation state by passing the
current through the electrolytic cell.

In primary coulometric analysis the substance being determined may directly

undergo reaction at one of the electrodes. In secondary coulometric analysis
36 the substance being determined may react in solution with another substance
Unit 9 Potentiometry

which is generated by an electrode reaction. Further, in coulometric analysis

which consider the reactions proceeding with 100% current efficiency, so that
the quantity of the species reacted can be calculated via Faraday’s law from
the quantity of electricity passed.

According to Faraday’s law, a given amount of chemical change caused by

electrolysis is direct proportional to the amount of electricity passed through
cell. For a general reaction,

O + ne R

where n is the number of electrons in the involved reaction, O is the reactant

to be reduced and R the reduction product. Faraday’s law relate the number of
moles of the analyte nA to the charge

Q
nA = … (9.4)
nF

where, n = the number of moles of electrons in the analyte half-reaction,

F = Faraday, this is the quantity of charge that corresponds to one mole or

6.022×1023 electrons. Since each electron has charge of 1.6022×10-19 C, the
faraday also equals 96,485C, and

Q = Quantity of electricity consumed in coulomb.

The value of Q can be determined as:

i) for a constant current, I amperes, operate for t seconds , Q = It, and

t
ii) for a variable current, i, Q = 0 idt
In coulometry we can directly calculate the amount of the reactant/product by
the relation (9.4) and the calibration or standardisation is not ordinarily
required.

Coulometry can be classified as (a) potentiostatic coulometry, and (b)

amperostatic coulometry.

a) Potentiostatic Coulometry

In potentiostatic coulometry, that is, coulometry at constant potential, the

potential of the working electrode is maintained at a constant level, so that
only analyte gets quantitatively oxidized or reduced there is no involvement of
the less reactive species. Here the current is initially high but decreases
exponentially with time and approaches zero at a time required to attain a
reaction position that is quantitatively complete (~10-6 M).
t
Q may be evaluated by a current time integrator or graphical, Q = 0 idtas
shown in Fig. 9.3.
t
Area = Q = 0 idt
37
Block 3 Thermal and Electroanalytical Methods

Fig. 9.3: Current and time relationship in potentiostatic coulometry

b) Amperostatic Coulometry or constant-current coulometry

The current, in a coulometric titration is carefully maintained at a constant and

accurately known level by means of an amperostat, (It=Q (It=Q) required to reach
an end point. Q is proportional to the quantity of the analyte involved in the
electrolysis. The essential requirement is 100% current efficiency to a single
change in the analyte.

In these titrations, the titrant is generated at one of the electrodes. The

reaction may take place directly on the same electrode or on the other
electrode. To remove the interferences, when may occur, the reagent is
separated from the solution by the use of sinter glass.

The reagent can be generated externally also, which removes the

interferences. Such a cell has mainly been used to generate H+/OH- ions.

SAQ 2
Differentiate between potentiostatic coulometry and amperostatic coulometry.

SAQ 3
A 9.65 ampere current is passed through a solution of AgNO3 for 50 minutes.
Calculate the amount of Ag deposited at the cathode.

9.2.6 Conductometry
In conductometry we examine the transport of electricity in solution and
application of this phenomenon to chemical analysis. The principle advantage
of this technique is its simplicity and relatively good sensitivity. It is, one of the
earliest techniques to study the behaviour of electrolytic solutions. Since the
conductance (which is reciprocal of resistance) of an electrolytic solution
depends on the number of ions present, their charge, their mobility, and
applications of conductometry are thus possible. More
temperature; analytical applications
detail discussion on the methods is given in Unit 10.

RELATIONSHIPS OF ELECTROANALYTICAL METHODS

As we have seen there are a wide variety of electroanalytical methods

available for the analytical purposes. Some of these methods differ only in
38 very few aspects but often the differences are important and require a good
Unit 9 Potentiometry

understanding of the techniques. For the most of methods discussed so far,

we are interested in the relationships between four variables: current, emf,
analyte concentration and time. The only exceptions to this is the
conductometric techniques. These methods are based on conductance of the
solution. For the purpose of classification, these methods can be divided into
interfacial methods and bulk methods, former are based upon phenomena that
occur at the interface between electrode and solution and latter are based
upon phenomena that occur in the bulk of the solution. Further interfacial
methods can be divided into major sub-group, static and dynamic, based upon
whether electrochemical cells are operated in the absence or presence of
current flow. Potentiometry and potentiometric titrations come under the
category of static (zero current) methods. In dynamic interfacial methods
current play important roles. These methods are further divided in several
categories like voltammetry, amperometry, coulometry and electrogravimetry
as shown in Fig. 9.4. Polarography name is given to voltammetric methods
when a dropping mercury electrode is used. Details of all these techniques will
be discussed in subsequent units

Fig. 9.4: Classification of electroanalytical methods. Quantity measured

is given in parentheses. Where I = current; E = potential; R = resistance;
G = conductance; Q = quantity of charge, t = time; V = volume of a
standard solution, m = mass of an electrolyte

9.3 BASIC PRINCIPLE OF POTENTIOMETRY

Potentiometry deals with the measurement of difference in potential between
two electrodes which have been combined to form an electrochemical cell.
The difference in potential between the two electrodes in electrochemical cell
is known as cell potential. The cell potential depends on the composition of the
electrodes, concentration of the solution or more correctly activity of a species
in solution (or pressure of gases) and the temperature. Relationship
connecting the cell potential with the activity of the species involved in the
39
Block 3 Thermal and Electroanalytical Methods

concerned chemical reaction, known as Nernst equation, can be derived

using thermodynamic principles. A detailed discussion is given regarding this
in earlier semester course. Based on the dependence of cell potential on the
activity or concentration of the species in the electrochemical cell, we use this
concept to obtain the activity or concentration, and pH of a species in solution
from potential difference measurements using potentiometer or pH meter.

In order to understand the above concept, we shall study the galvanic cell in
some detail. For example, consider the simple galvanic cell illustrated in
Fig.9.5. In this cell there are two half cells. Where a half cell is the
combination of an electrode and the solution with which it is in contact. In one
half cell zinc gets oxidized to Zn2+ ions.

Zn(s) Zn2+ (a1) + 2e (Oxidation)

This electrode is negatively charged relative to the solution and is referred to

as anode i.e. oxidation always occurs at the anode. On the other hand, in
second half cell Copper (II) ions get reduced to copper.

Fig. 9.5: Simple galvanic cell having Cu2+/Cu and Zn2+/Zn half cells.

Cu2+(a2) + 2e Cu(s) (Reduction)

This electrode is, therefore positively charged relative to the solution and, this
is referred to as cathode. Note that reduction always occur at the cathode.

As shown in the Fig.9.6 both electrodes of half cells are connected externally
via an electric circuit and the circuit is completed by ionic conduction through
the solution and KCl salt bridge. The voltmeter will then measure the
difference in potential between the two electrodes.

Note that the one half cell involves an oxidation process and the other half cell
a reduction process. These are then combined in the cell to give a redox
reaction represented below by Equation,

Zn(s) + Cu2+(a2) Zn2+(a1) + Cu(s) …(9.5)

Using IUPAC convention this can be represented by

Zn(s)  Zn2+(a1) ║ Cu2+(a2)  Cu(s)

This notation starts with the left hand electrode and move to the right through
40 the solution to the right hand electrode. The simple vertical bars signify phase
Unit 9 Potentiometry

boundary, whilst the double vertical bar the salt bridge. a1 & a2 are the
activities of two ions.

Measurement of Potential Difference

The potential difference between the electrode and solution in a half cell is
referred to as the electrode potential. It is impossible to determine the potential
of a single electrode and rather it is the potential difference that is measured.
A number of conventions have been established in order to compare the
potential of different half reactions. The half-reaction is written as a reduction
process i.e. for the metal, M and its own ion Mn+, it is written as

Mn+ + ne ⇌ M(s)

If the constituents in the half-cell are present at unit activity, the potential
difference is measured at 25ºC with respect to a standard hydrogen electrode
(SHE), which has been arbitrarily assigned the zero potential. Under these
conditions the potential difference or electrode potential is known as the
standard electrode potential, Eº. We will take up standard hydrogen electrode
in detail in the next section.

In general, the potential difference of a cell is given by the difference between

the two electrode reduction potentials E1 and E2, of the cathode and anode,
respectively

Ecell = E1  E2

The junction potential developed at the junction between the two half cells are
also contributing to the cell potential, the Ecell calculation can be rewritten as:

E(cell) = [E1  E2] + Ej

Where Ej is the liquid junction potential and can be a positive or negative

quantity. By using salt bridge between two half cell the liquid junction potential
can be minimized.

Using Nernst equation, the relationship between cell potential and activity of
species involved can be developed.

The Nernst equation is:

RT a(reduced)
E = Eº  ln ..… (9.6)
nF a(oxidised)

Where R is the universal gas constant, T is the absolute temperature, n is the

numbers of electron involved in the transfer, F is Faraday’s constant and
a(reduced) and a(oxidized) are the activities of the reduced and oxidized
species of each half cell.

For the Copper half cell of the galvanic cell mentioned earlier it is written as

RT a(Cu)
E 2+ = E0 - ln

Cu 
Cu 
 2+ 
 Cu Cu 
 
2F a(Cu2+ )
 

But we can take the activity of a pure substance to be unity, so

41
Block 3 Thermal and Electroanalytical Methods

RT 1
E Cu = E0 - ln
 2+
Cu   Cu2+



Cu  2F 2+
a(Cu )

Above equation can be simplified by introducing the known values of R, F, and

T, and converting natural logarithms to base 10 by multiplying by 2.3; it then
becomes:

0.
0591 1
E Cu = E0 + log
 2+
Cu   Cu2+



Cu  n a(Cu2+ )

For most purposes in quantitative analysis, it is sufficiently accurate to replace

cu2+) with [Cu ], the concentration of the copper ions in mol/dm .
2+ 3
a(

0.
0591 1
E Cu = E0  log
 2+
Cu   Cu2+



Cu  n [Cu2+ ]

0.
0591
Or E Cu = E0  log [Cu2+ ]
 2+
Cu   Cu2+



Cu  n

A similar expression could be written for the left-hand half-cell:

0.0591 1
E Zn = E0  log 2+
 2+
Zn   2+ 
 Zn Zn 
 
n [Zn ]

0.0591
Or E Zn = E0  log [Zn2+ ]
 2+
Zn   2+ 
 Zn Zn 
 
n

If the liquid junction potential is negligible, the potential of the cell is then given
by:

Ecell = E - E Zn
 Cu2+



Cu   2+
Zn 
Clearly the potential of the cell will depend upon the concentration of both the
copper(II) and zinc(II) ions. In such situation it is not possible to determine the
activity or concentration of the two ions from the cell potential. In practice, we
determine the activity or concentration of a single substance, rather than a
combined value for two or more substances. For this reason if we keep the
concentration of zinc(II) ions at a fixed value so that its potential also remain
constant. Then,

0.0591
Ecell = E0 + lna(Cu2+ ) - E Zn
 Cu2+



Cu  2  2+
Zn 
As E0 and E Zn are both constant, they can be combined into one
 Cu2+



Cu   2+
Zn 
value K. Then,

0.0591
Ecell = K + log [Cu2+ ]
2

Now, the measurement of cell potential is clearly proportional to the natural

logarithm of the concentration of the Copper(II) ion. This equation relates the
42
Unit 9 Potentiometry

concentration (activity) of the oxidized form of the metal to potential. However,

a general equation can be written for both oxidized and reduced forms of
electrodes.

0.0591
Ecell = K ± log [I]n 
n
0.0591
Or Ecell = K ± log aM I+ ..… (9.7)
n

Where n is the charge on the ion, I, and K is a constant incorporating the

potential of first half cell which is kept constant, standard potential of the
second half cell containing the solution under investigation, the first half cell
anf junction potential if any. Note the ± sign in the equation is used to signify
that it will be positive if I is a cation and negative if I is an anion. This equation
can be applied to a typical cell used in potentiometric analysis and shown in
Fig. 9.6. This is the common practice in potentiometric measurements.

Fig. 9.6: Diagrammatic representation of a cell used for potentiometric

analysis.

The first half cell which is having constant potential is referred to as a

reference electrode. The second electrode in combination with the reference
electrode is called an indicator electrode and its response should be
dependent upon changes in activity or concentration of the species of interest.

Before considering electrodes in detail, let us now discuss the measurement of

cell potential. If a current is drawn from a cell as discussed above, in the
course of measurement of cell potential, the cell reaction proceeds and the
concentration of the solutions will change in the two half-cells. Hence, it is
important to measure the cell potential without allowing current to flow. The
cell potential measured nearly less than zero or negligible current flow is called
electromotive force (e.m.f) of the cell. The instruments which used for
accurate measurement of potential are potentiometer and pH meter. These
instruments draw only negligible current.

SAQ 4
Calculate the potential of a copper electrode immersed in 0.044 M CuSO4

43
Block 3 Thermal and Electroanalytical Methods

SAQ 5
Calculate the potential of a zinc electrode immersed in 0.060 M ZnSO4.

SAQ 6
Calculate the cell potential for the cell made by combining the half-cell in
SAQs 4 and 5 in the following way:

Zn Zn2+ (0.060 M ) Cu2+ (0.044 M ) Cu

9.3 1 Direct Potentiometry

For direct potentiometric measurement, the potential of the cell can be
expressed in terms of the potential developed by the indicator electrode and
the reference electrode:

Ecell = (Eind – Eref ) + Ej …(9.8)

Consider the indicator electrode whose potential vary with cation activities or
concentrations, we can write Nernst Equation similar to Eq. 9.7.

o 0.0591
(a) Eind = Eind + log a n+ … (9.9)
n M

Substitution of Eq. 9.9 into Eq. 9.8 yields:

o 0.0591
Ecell = ( Eind + log a n+ ) – Eref + Ej
n M

On rearrangement
n(Ecell - K )
log a = … (9.10)
Mn + 0.0591

n(Ecell - K )
or pM = – log a = – … (9.11)
Mn + 0.0591
(b)
For anion An- Eq. 9.11 will have reversed sign

n(Ecell - K )
pA = – log a = … (9.12)
An- 0.0591

where pM and pA are the negative logarithm of the metal ion activity a and
Mn +
an anion a , respectively. These terms are more general forms of the
An-
familiar term pH. K is summation of several constants, including standard
electrode potential of metal ion or anion, potential of reference electrode,
junction potential, asymmetrical potential if membrane electrode is involved.

All direct potentiometric methods are based on Eqs 9.11 and 9.12. Both these
equations in terms of Ecell may be written as
44
Unit 9 Potentiometry

0.0591
Ecell = K – pM … (9.13)
n

0.0591
Ecell = K + pA … (9.14)
n

Using Eqs. 9.11 and 9.12,we can determine concentration of metal ions or
cations and anions in terms of pM and pA, respectively. Further, Eq. 9.13 also
indicates that for a metal ion-selective electrode, an increase in pM results in
decrease in Ecell as shown in Fig. 9.7. But before that constant K should be
known to us. As you know K is made up of several constants, including the (a)
junction potential, which cannot be measured directly or calculated from theory
without assumptions. This problem can be overcome by electrode calibration
method using standard solution of the analyte. Though calibration methods are
simple, take less time and convenient to the continuous monitoring of pM or
pA, but suffer somewhat limited accuracy because of uncertainty in junction
potential.

In the electrode-calibration method, K is determined by measuring Ecell for one

or more standard solution of known pM or pA. The calibration is performed just
before the determination of pM or pA for the unknown. There is an assumption
that K is unchanged when standard is replaced by the unknown analyte (b)
solution. Some time instead of calculating K using emf value of standard Fig. 9.7: (a) A plot of
Eq. 9.13 for a metal ion
solution, a calibration graph is plotted using measured emf of standard electrode; (b) A plot of
solutions against log a/(concentration), pM or pA. The sample is then treated Eq. 9.14 for an anion
electrode
in the same way as the standards and the concentration (or activity) read
directly from the calibration graph. For getting fast results, a graph between
cell potential and log a is plotted and for this we can use graph paper called
semi-log paper for drawing calibration curve and concentration of a sample
can be read off directly from the graph. To further understand this let’s try
following SAQ.

SAQ 7
Following emf readings are obtained for the standard solutions of Ca2+ ions in
a potentiometry experiment. What is the concentration of a sample if its emf 33
mV?
Concentration of Ca2+/mol dm-3 (M) emf/mV
1.00 × 10-4 –2
5.00 × 10-4 +16
1.00 × 10-3 +25
5.00 × 10-3 +43

9.3.2 Electrodes
In previous part we saw that a electrochemical cell were composed of two
electrodes: indicator and reference electrodes. A reference electrode must be
easy to construct, and must maintain a constant, reproducible potential even if
small currents are passed. An indicator electrode responds to change in 45
Block 3 Thermal and Electroanalytical Methods

activity of the species to be measured. Now we are going to consider some

systems which can be used as reference electrodes.

Reference Electrode

There are three common reference electrodes used for potentiometric

analysis:

 Standard Hydrogen Electrode

 Calomel Electrode

 Silver-Silver Chloride Electrode

Standard Hydrogen Electrode (SHE)

The standard hydrogen electrode (Fig. 9.8) is constructed from a platinum foil
plate, which has been platinized, that is coated with platinum black (finely
divided platinum) by chemical or electrochemical reduction of chloroplatinic
acid. The finely divided layer of platinum black helps in achieving the largest
possible surface area. Its composition can be formulated as
Pt, H2 (1 atm) 1 H+ (a =1)

Fig.9.8: Common design of Hydrogen Electrodes

The half cell reaction, may occur in either direction depending upon the type of
electrode which is coupled with it.

2H+ + 2e ⇌ H (g)
2

The potential of a hydrogen electrode is given by the Nernst equation:

2

E=E +02.303 RT a+
log H
  ..… (9.15)
2F p H2

where E0, the standard electrode potential for hydrogen electrode is zero. For
the standard hydrogen electrode, having H+ activity, aH+ equal to one and
pressure exerted by hydrogen gas PH2 also equal to one atmosphere, the
(9.15) becomes equal to zero and E = E0 =
logarithmic term on the right of Eq. (9.15)
46
Unit 9 Potentiometry

0. By convention, the potential of SHE is assigned the value of exactly zero

volt at all temperatures.

The SHE was selected as a primary reference electrode for several reasons
as given below:

(i) It can be used for the entire pH range.

(ii) The accuracy in measurement is high.

(iii) The reagents used in its preparation can easily be purified.

(iv) The potential of the electrode is not affected by mechanical stress of

the electrode.

Besides these advantages, the use of SHE has certain limitations as:

(i) It can not be used in solutions containing strong oxidizing and reducing
substances.

(ii) It is not handy and hence transfer from one place to another is not
easy.

(iii) The platinum surface is poisoned in presence of species like H2S, CN
and Hg.

However, for experimental measurement of the electrode potential the use of

SHE requires many precautions, therefore, other electrodes of simpler design
whose potentials are well known with respect to the SHE e.g. Saturated
Colomel Electrode (SCE) and Ag/AgCl electrodes. Such electrodes are known
as secondary reference electrodes and are generally preferred.

Saturated Calomel Electrode (SCE)

A saturated calomel electrode is the most frequently used reference electrode.

Many designs of saturated calomel electrodes have been reported in literature.
One of those is shown in Fig. 9.9.

Fig.19.9: A commercial calomel electrode.

47
Block 3 Thermal and Electroanalytical Methods

It consists of an outer glass tube with a crack in the end of the tube. A crack is
made by an asbestos filament or fitted porcelain plug or quartz fiber. A
mercury and mercurous chloride paste is filled in the inner tube, which is
connected to the saturated potassium chloride solution in the outer tube
through a small opening. The saturated potassium chloride solution in the
outer tube can be easily renewed through a lateral hole. Calomel, i.e.,
mercurous chloride is a sparingly soluble salt. Its solubility product (Ksp) is
given as:

Ksp = aHg  (aCl )2 = 1.1  1018

2+ - ..… (9.16)
2

A calomel electrode may be symbolised as:

Hg2Cl2 (satd.), KCl (x M)  Hg

Where x represents the concentration of potassium chloride and must be

specified in describing the electrode. Commonly, 0.1 M, 1 M, and saturated
solutions of potassium chloride have been employed and the calomel
electrodes are named as decimolar, molar and saturated calomel electrodes,
respectively.

The half cell reaction is

Hg2Cl2 (s) + 2e ⇌ 2Hg (l) + 2Cl

and the potential at 250 C is given by the equation:

0.0591
E = E0 + log a
Hg 2 Hg 2+
2

Substituting for a Hg from Eq.9.16. gives:

2+
2

0 0.0591 K sp
or E = EHg + log ..… (9.17)
2 a Cl-

The activity of chloride ions (by excess of chloride ions obtained from
potassium chloride) remains constant for a particular electrode. The
experimental value of the potential of the saturated calomel electrode is 0.244
V at 250 C.

Silver-Silver Chloride Electrode

The silver-silver chloride electrode is another frequently used reference

electrode. It is prepared by plating a layer of silver chloride onto a metallic
silver wire and immersing in a solution containing chloride ions (usually KCl) of
known concentration which is also saturated with silver chloride (see Fig.
9.10).

Silver chloride is a sparingly soluble salt. Its, solubility product, Ksp, is:

Ksp = aAg+ aCl- = 1.77×10-10 at 250 C … (9.18)

The silver-silver chloride electrode may be symbolised as:

48
Unit 9 Potentiometry

AgCl (satd.), KCl (x M)  Ag

Fig. 9.10: Silver-silver chloride electrode.

Where x represents the molarity of potassium chloride solution. Normally, a

saturated potassium chloride solution is taken.

The half cell reaction is:

AgCl (s) + e  Ag (s) + Cl-

and the potential at 250C is given by the equation

E = E 0 A g + 0 .0 5 9 1 lo g a A g +

Substituting for a Ag+ from Eq.9.18 gives:

K sp
E = E 0 Ag + 0.0591 log ...(9.19)
a Cl -

When a large excess of chloride ion (potassium chloride) is present, the

contribution of chloride ions obtained from dissolution of silver chloride can be
(in the half cell) controlled by the concentration of potassium chloride (which
remains constant). The experimental value of potential for an electrode
prepared by saturated solution of potassium chloride is 0.199 V.

Indicator Electrodes

As described earlier, electrodes that respond to a specific ion are referred to

as indicator electrodes and the selection and use of such electrodes is the key
to modern potentiometry. Several metals like silver, copper, mercury, lead and
cadmium can be served as indicator electrodes. Usually these metal
electrodes are constructed from coils of wire, flat metal, metal plates or button
set in plastic or glass (see Fig. 9.11). Large surface area is preferable because
of rapid attainment of equilibrium. Metal surface is to be thoroughly cleaned.
Usually it is achieved by dipping in concentrated nitric acid followed by
repeated rinsing with distilled water.
49
Block 3 Thermal and Electroanalytical Methods

Fig. 9.11: Typical indicator electrode designs

Metal indicator electrodes are not selective as these electrodes can respond to
its own ions and can also respond to a number of other metal ions. There are
several other indicator electrodes which are selective to particular ions. Many
of them are very valuable in potentiometric analysis and are collectively
referred to as ion selective electrodes (ICE). The most common of these is the
glass electrode, which is selective to H+ ions and, consequently, pH.

Glass Electrode

The most convenient way for determining pH has been by the use of the glass
electrode. It is an ion-selective electrode. Glass electrode is a membrane type
electrode whose membrane is made by a special type of glass. A potential
develops across a thin glass membrane separating two solutions of different
acidities. The measurement of potential difference can thus be related to
hydrogen ion concentration. This phenomenon was first recognized by
Cremer in 1906 and systematically explored by Haber in 1909 with the
construction of a glass bulb electrodes. After the work of Sorenson (1909) to
determine hydrogen ion concentration in terms of pH and the use of vacuum
tube voltmeter by A. Beckmann (1930) made the use of glass pH electrodes
more practical. Development of transistor based pH meters and the special
purpose glass for the measurement of high pH values has further improved
the technology.

The glass electrodes of various sizes, shapes and for different pH ranges are
commercially available. Fig. 9.12 illustrates the construction of a common type
of glass electrode. It consists of a thin, H+ sensitive glass membrane bulb at
the end of a heavy-walled glass tubing. A buffer solution (or 0.1M HCl) is filled
in the glass membrane bulb. A reference electrode (usually silver-silver
chloride electrode) is placed in contact with the inner solution. It is connected
to one terminal of the pH meter. The bottom portion (bulb) of the glass
electrode is immersed in the external solution whose pH is to be measured.
An external reference electrode (usually an SCE) is immersed in the external
solution and is connected to the other terminal of the pH meter.

50
Unit 9 Potentiometry

Schematic diagram of cell containing a pH glass electrode can be represented

as below:
+
Internal Internal H sensitive External External

Reference buffer glass solution reference

+ +
Electrode (aH )1 membrane (aH )2 electrode

Fig.9.12: A typical glass electrode for pH measurements.

Potential of this cell:

Ecell = E1 - E2 + Emembrane + Ej

The potential for this cell response is related to the logarithm of hydrogen ion
activities on the two sides of the glass membrane and is given by Nernst
equation:

(aH )1
+
Ecell = Easym - 0.0591 log
(aH )2
+

Where Easym is asymmetry potential. This is due to the potential difference

between internal and external surface of glass membrane. Now Ecell can be
written as

(aH )1
+
Ecell = k - 0.0591 log ...(9.20)
(aH )2
+

Where k is a constant. The constant includes the difference in junction

potential between the reference electrode and solution and the asymmetry
potential for the glass membrane. The asymmetry potential is due to the
difference in surface of the inner and outer layers of the glass membrane.

Since the pH on the internal side of the glass membrane is held constant using
a buffer, the potential of the glass membrane electrode will depend upon the
pH of the external solution (aH )2 . Now Eq. 9.20 can be written as:
+

Ecell = k1 + 0.0591 log (aH )2 +

Since pH =  log aH+ 51

Block 3 Thermal and Electroanalytical Methods

Ecell = k1 + 0.0591 pH … (9.21)

Where k1 now includes the constant factor related to aH+. Thus, the emf
produced in the glass electrode system varies linearly with pH. From the
Eq.18.18 the constant k1 can be eliminated by measuring potential, first with
standard buffer solution whose pH is precisely known and then with known
solution. Thus for the standard buffer

(Ecell)s = k1 + 0.0591 (pH)s

For unknown sample solution

(Ecell)u = k1 + 0.0591 (pH)u

Then the difference in both the cell potentials

(Ecell)u  (Ecell)s = 0.0591 (pH)u  0.0591 (pH)s

or

(pH)u = (pH)s + (E c e ll) u - ( E c e ll) s ...(9.22)

0 .0 5 9 1

This is the operational definition of the pH.

As said above, the constant k1 includes the asymmetry potential which exists
across the glass membrane even if the two sides of the cell are of identical
composition. For this reason, a pH meter is to be calibrated from time to time
(preferably every time when pH measurements are done) with standard
buffers.

In pH meter voltmeter is used to measure the potential of the cell. The voltage
scale is calibrated in pH units so that 0.0591V correspond to 1pH Unit at 25C.
This value will change with temperature and modern pH meters have a
temperature compensation device. This may be set before taking pH readings.

Combination Electrodes

For the purpose of convenient both an indicator and a reference electrodes

(with salt bridge) can be combined into a single probe to make a complete cell
or combination electrodes. For such electrodes only small volume is needed
for potentiometric measurements. A typical assembly of combination
electrodes is shown in Fig.9.13. It consists of a tube within a tube, the inner
one having the pH indicator electrode and the outer one having the reference
electrode and its salt bridge.

pH determination using glass electrode is most accurate and widely used

method despite a few disadvantages viz. the glass membrane being very
fragile, it requires great care while using. The ordinary potentiometer cannot
be used for measuring the potential of the glass electrode. Thus, the electronic
potentiometers are required to be used, needs frequent standardization and,
cannot be employed in pure ethyl alcohol, acetic acid and gelatin. The
following features of glass electrode have made it more versatile to be used be
as indicator electrode for pH measurement.

52
Unit 9 Potentiometry

 It may be used in the presence of strong oxidizing and reducing

solutions in viscous media and in presence of proteins which interfere
with operation of other electrodes.

Fig.9.13: Combination pH reference electrode.

 It can be used for solutions having pH values 2 to 10 with some special

glass, measurements can be extended to pH values greater than 10.

 It is simple to operate and immune to poisoning.

 The equilibrium is reached quickly

While measuring pH you should be little care full as there are few factors
which limit the accuracy of pH measurements. We are listing few of them
below:

1. The alkaline error: It is noticed that the ordinary glass electrode

becomes sensitive to alkali ions and gives low reading in high pH range
– above 9 or 10 pH units. The reason for the error is that whilst the
glass membrane is selective to hydrogen ion, it also responds to other
ions. This becomes more significant when the activity of the other ions is
higher to activity of the hydrogen ion.

2. The acid error: At low pH range – less than 0.5, the values determined
by the glass electrode tend to be somewhat higher. This error is due to
the activity of water which we have ignored while writing Nernst equation
for the indicator electrode. We have assumed that activity of water may
be taken to be unity as it is in large excess in the solution and it behaves
as a pure substance. However, in highly acidic solution, the activity of
the water becomes less than unity because a good amount is used in
hydrating the protons.

3. Variation in junction-potential: In most of the cases the composition of

the standard buffer solution and test solution are different. In such
situation, the liquid junction potential will be different.

53
Block 3 Thermal and Electroanalytical Methods

4. Error in the pH of the standard buffer: There may be possibility that

buffer solution is not prepared with full care or its composition may
change during storage. All All these factors will cause an error in
subsequent pH measurements.

5. Temperature: A change in temperature may affect on pH

measurements, because change in temperature affects the activities of
the ions as well as the liquid-junction potentials. Therefore, it is advised
to calibrate the electrode at the temperature of the test solution.

6. Calibration procedures: Buffer solution cannot be prepared more

accurately than ± 0.01 pH units. Therefore, we cannot calibrate the
electrode better than this.

7. Equipment related: These errors may be due to the power fluctuations,

parallax errors in reading analogue scales, etc.

With this theoretical background now we will see how the pH is measured
using pH meter, but before that try following SAQs.

SAQ 8
Why is it necessary to calibrate the glass electrode before use?

SAQ 9
List some factors which may cause errors in pH measurements.

9.4 POTENTIOMETRIC TITRATIONS

In a potentiometric titration, the equivalence point is detected by measuring
the potential change during the titration. Fig. 9.14 shows the usual apparatus
for a potentiometric titration.

Electric potential (E)

is measured in volts
(V). The smaller unit d
potential is millivolt
(mV).
-3
1 mV = 10 V

54 Fig. 9.14: Typical apparatus for potentiometric titration

Unit 9 Potentiometry

The potential between the reference electrode half cell (whose potential is
known) and the indicator electrode half cell (whose potential varies with
concentration of the solution) is measured at the start and after the addition of
small amounts of titrant, say each 1 cm3, and more closely near the
equivalence point, when &dings start to change by larger values. After each
addition the solution is stirred well and the reading is allowed to become
steady.

For detecting the equivalence point in a potentiometric titration, a graph is

plotted between the potential and the volume of the titrant to give a titration
curve such as shown in Fig. 9.15(a)

Fig. 9.15 : Methods of equivalence point determination (a) normal plot (b)
first derivative (c) second derivative

Once the titration curve is at hand, we must determine where the curve is
steepest, normally by some sort of inspection. We may draw a vertical line
through the steep portion of the curve and find the intersection of this line with
the volume axis. To overcome the uncertainty in this procedure, we plot
another graph as shown in Fig. 9.15(b). This is a plot of the slope of a titration
curve, that is, the change in potential with change in volume (∆E/∆V) against
volume of the titrant. The resulting curve rises to a maximum height at the
equivalence point. The volume at the equivalence point (V) is determined by
drawing a vertical line from the peak to the volume axis. Fig. 9.15(c) shows a
plot of the change in the slope of a titration curve (  E/  V2) against the
2

volume of titrant. At the point where the slop  E/  V2 is a maximum, the

2

derivative of the slope is zero. The end-point is located by drawing a vertical

line from the point at which  E/  V2 is zero to the volume axis.
2

In contrast to direct potentiometric measurements, potentiometric titrations

generally offer increased accuracy and precision. Accuracy is increased
because; measured potentials are used to detect rapid changes in activity that
occurs at equivalence point of the titration. Furthermore, it is a change in emf
versus titre volume rather than absolute value of emf. Thus, the influence of
liquid-junction potentials and activity coefficients is minimised.

Potentiometric titrations may be applied to a variety of systems including those

involving oxidation-reduction, precipitation, acid-base, and complexation
equilibria reactions. We will discuss all these systems in detail in subsequent
sections. Further, potentiometric end-point detection also provides more
accurate result than the corresponding method employing indicators. It is
55
Block 3 Thermal and Electroanalytical Methods

particularly useful for titration of coloured or opaque solutions and for detecting
the presence of unsuspected species in a solution. Titrations of more dilute
solutions are possible using potentiometry. Unfortunately, it is more time
consuming than a titration performed with an indicator.

9.4.1 TYPES OF POTENTIOMETRIC TITRATIONS

The majority of potentiometric titrations involve chemical reactions such as
neutralisation, oxidation-reduction, precipitation and complexation. Here we
will discuss neutralization and oxidation-reduction titration methods as these
are most common titration methods.

1. Neutralisation Titrations: Potentiometric neutralisation titrations are

particularly useful for the analysis of mixture of acids or polyprotic acids or
bases because discrimination between the end-points can often be made.
An approximate numerical value for dissociation constant of the reactant
species can also be estimated from potentiometric titration curves in
theory. This quantity can be obtained from any point along the curve as a
practical matter. It is most easily calculated from the pH at the point of
half-neutralisation e.g. in the titration of weak acid HA, we may ordinarily
assume that at the mid-point [HA]  [A¯ ] + [H+] and therefore :

[H+ ] [A - ]
Ka = … (9.23)
[HA]

[A - ]
log Ka = log H+ + log
[HA]

[A - ]
– log Ka = – log H+ – log
[HA]

[A - ]
pKa = pH – log
[HA]

At half neutralization of the acid

[A- ] (salt) = [HA] (acid)

Therefore, pKa = pH – log 1 (log 1 = 0)

or pKa = pH … (9.24)

This is the midway point to the equivalence pint. Therefore, pKa values can
also be directly read from the titration curves.

It is important to note that a dissociation constant determined from a

potentiometric titration curve may differ from that shown in the table of
dissociation constant in the literature by a factor of 2 or more because the
latter is based upon the activities while the former is not.

2. Oxidation-Reduction Titrations: Indicator electrodes for oxidation-

reduction are generally fabricated from platinum, gold mercury or silver.
The metal chosen must be un-reactive with respect to the components of
56
Unit 9 Potentiometry

the reaction. It is merely a site for electron transfer. Platinum electrode is

most widely used for oxidation-reduction titrations.

The determining factor in the values of potential is the ratio of the activity
or concentration of the oxidised and reduced forms of certain ion
species.

Take a general equation

Oxidised form + ne reduced form … (9.25)

the potential acquired by the indicator electrode at 25 oC is given by

0.0591 aoxidised form

E = Eo + log ... (9.26)
n areduced form

where Eo is the standard potential of the system. The potential of the

immersed electrodes are controlled by the ratio of these activities or
concentration. In redox reactions, reducing agent is oxidised or oxidising
agent is reduced and the ratio and the potential therefore changes more
rapidly at the end point of the reaction. Thus titrations involving such
reactions like Fe (II) with potassium permanganate or potassium
dichromate or ceric sulphate may be followed potentiometrically and
equivalence points can be obtained.

Automatic Titrations

Now-a-days large number of automatic titrators based on the principle of

potentiometry have come into the market. These are highly useful in those
places, where a large number of routine analysis are required. These may not
be more accurate than the manual techniques, but are quite rapid and
decrease the time needed to perform the experiment and thus offer some
economic advantages. Two different automatic titrators are available:

1. The first type gives titration curves of V vs E or  E/ Δ V vs V. The end

point is obtained from the curve by inspection.

2. In the second type of titrators, the titration is stopped automatically when

the potential of the electrode system reaches a predetermined value and
the volume of reagent delivered is read at the operators convenience or
printed on a tape. These titrators usually employ a burette system with a
solenoid-operated value to control the flow or alternately it makes use of
a syringe, the plunger of which is activated by a motor driven micrometer
screw.

9.5 pH TITRATION
Similar to potentiometric titrations, in contrast to direct pH measurements, pH
titrations generally offer increased accuracy and precision. Accuracy is
increased because, measured pH are used to detect rapid changes in activity
that occur at equivalence point of the titration. Furthermore, it is the change in
pH versus titre volume rather than absolute value of pH that is of interest.
Thus, the errors due to liquid-junction potentials and activity coefficients are
minimized. pH titrations may be applied to a variety of systems including those 57
Block 3 Thermal and Electroanalytical Methods

involving weak acids and weak bases. In such titration, it is difficult to get end
point using indicator method. A typical acid-base titration using pH metry is
briefed as follows.

It is known that the neutralization

neutralization of acids and bases is always accompanied

by the changes in the concentration of H+ and OH ions. It is evident that
hydrogen electrode may be employed in these titrations. The reference
electrode used in these titrations is 1 M calomel electrode. The apparatus
used for acid-base titrations is as shown in Fig. 9.16.

The critical problem in titration is the recognition of point at which the

quantities of reacting species are presented in equivalent amounts, i.e. the
equivalence point.
point. The titration curve can be followed point by point plotting as
the ordinate successive values of the pH versus the corresponding volume of
titrant added as the abscissa. Addition of the titrant should be the smallest
accurately measurable increments that provide an adequate density of points,
particularly in the vicinity of equivalence point.

 Over most of the titration range the pH varies gradually, but near the end
point the pH changes very abruptly. The resulting titration curve
resembles Fig. 9.17(a).

Fig. 9.16:
9.16: Typical Instrumental set up for pH titration

 By inspection, the end point can be located from the inflection point of the
titration curve.

 This is the end point that corresponds to maximum rate of change of pH

per unit volume of titrant added (0.05 cm3 or 0.1 cm3).

 The distinction of the end point increases as the reaction involved

becomes more nearly quantitative.

 Once the pH has been established for a given titration, it can be used to
indicate subsequent end points for the same chemical reaction.

58
Unit 9 Potentiometry

 The equivalence point can be more precisely located from the 1st and 2nd
derivative curves as illustrated in Fig. 9.17(b) and 9.17(c). Solutions more
dilute than 10-3 M generally do not give satisfactory end points. This is
limitation of pH metry and potentiometric titrations.

(a) (b) (c)

Fig. 9.17: pH titration curves; (a) Normal curve; (b) First derivative curve; and
(c) second derivative curve `

9.6 SUMMARY
In this unit, you have learnt that about electrode potentials, principles of
potentiometer and measurement of potential, different types of reference
electrodes : such as Hydrogen Electrode, Calomel Electrode, Silver-Silver
Chloride Electrode and different types of indicator electrodes. You have also
learnt about the measurement of potential and location of end points from the
graphs obtained from the experimental values of emf and volume of titrant.
Different types of titration such as acid-base titrations and redox titrations were
also explained in detail. You have also learnt that pH tells the acidic or basic
nature of an aqueous solution and is defined as negative logarithm of
hydrogen ion concentration. pH can be readily measured in an accurate
manner with the help of a pH meter. There is also detail discussion on pH
titration.

9.7 TERMINAL QUESTIONS

1. What is an electrode potential?

2. Why the absolute value of electrode potential cannot be determined?

3. What is a indicator electrode? Give some examples.

4. Explain liquid-junction potential. How can it be eliminated?

5. Calculate the EMF of the following electrochemical cell at 25°C:

Cu, Cu2+ (a = 0.1 M)|| H+ (a = 0.01 M) H2 (0.95 atm.), Pt.

6. What is the source of the asymmetry potential in a glass membrane

electrode?

7. What are the advantages of a pH metric titration over a direct pH metry?

59
Block 3 Thermal and Electroanalytical Methods

8. Drive an expression for the ‘operational definition of pH’.

9.8 ANSWERS
Self Assessment Questions

1. Voltammetry is an analytical technique that is based on measuring the

current that develops at a small electrode as the applied potential is
varied. Polarography is a particular type of voltammetry in which a
dropping mercury electrode is used.

2. In potentiostatic coulometry (coulometry at constant potential), the

potential of the working electrode is maintained at a constant level, so
that only analyte gets quantitatively oxidized or reduced there is no
involvement of the less reactive species. In amperostatic coulometry or
constant-current coulometry, the cell is operated so that the current is
maintained at a constant value.

3. According to Faraday’s law

nA=Q/nF where Q = It

Half-reaction for silver deposition

Ag+ + e Ag (s)

Thus, 1 mole of silver is equivalent to 1 mol of elecrtons

Q = 9.6 5×50×60 C = 28950C

Further n=1 and F = 96490 C

We can find the number of moles of Ag from Faraday’s law

28950 C
nAg = =0.300 mol Ag
1 e / molAg× 96485 C / mole e

Mass of Ag = 0.300 mol × 108 g /mol = 32.40 g

4. Half-cell reaction : Cu2+ + 2e -  Cu(s)

0.0591 1
Nernst equation : E = E o - log
2 [Cu2+ ]

No term of elemental Cu is included in the logarithmic term because it is

a pure solid.

0.0591
or E = Eo + log Cu2+ 
2  

Eo for Cu electrode is + 0.337 (from Table 1 Appendix 1), therefore,

0.0591
E = 0.337 + log0.044
2

E = 0.297 V
60
Unit 9 Potentiometry

5. You have to follow the same steps as shown for SAQ 4.

E = – 0.799 V

6. For this cell chemical reaction is:

Zn + Cu2+ ⇌ Zn2+ + Cu

Ecell = E -E
Cu2+ /Cu Zn2+ /Zn

= 0.297 – (– 0.799) = 1.096 V

7. Draw a calibration graph using the data given in SAQ 7 on special type
of graph paper called semi-log (or log/mm) paper. The calibration graph
is shown in Fig. 9.18. You can find the concentration of sample from this
graph is 2.1 × 10-3 M.

Fig. 9.18 : Calibration curve for calcium ion selective electrode

8. It is not possible to determine the values of asymmetry potential as well

as liquid- junction potential in glass/calomel electrode, therefore, it is
necessary to calibrate glass membrane electrode with suitable buffer
solutions before use.

9. i) Alkaline error

ii) Acid error

iii) Variation in junction potential

iv) Error in the pH of the standard buffer

v) Temperature

vi Calibration procedures

vii) Equipment related

Terminal Questions
1. This is the tendency of an electrode to get oxidised or reduced. But as
per the IUPAC conventions, it is the reduction potential of the electrode.

2. Because oxidation or reduction cannot take place independently.

61
Block 3 Thermal and Electroanalytical Methods

3. A standard electrode with reference to which the potential of an indicator

electrode is determined is called "reference electrode." Some examples
are Standard Hydrogen Electrode (S.H.E.); Saturated Calomel Electrode
(S.C.E.).

4. This is the potential which is set up at the junction of two solutions

because of difference in the speeds of ions moving across the boundary.
It can be eliminated by using a salt bridge containing KCl, since K+ and
Cl¯ move with almost equal speeds.

5. The half-cell reactions are :

R.H.E. 2H+ + 2e- ⇌ H2 (g)

L.H.E. Cu (s) ⇌ Cu2+ (aq) + 2e-

Overall reaction : Cu(s) + 2H+ ⇌ Cu2+ (aq) + H2 (g)

E°cell = E° = E°R – E°L = – 0.34 V

The EMF of the cell is given by,

0.0591 a 2+ × aH2
E = Eo - log cu at 25o C
2 (a + )2
H

0.0591 (0.1) (0.95)

= - 0.337 - log
2 (0.01)2

= – 0.337 - 0.088 = – 0.425 V

6. The asymmetry potential in a membrane arises from difference in the

structure of the inner and outer surfaces. These difference may be due
to the manufacture reason or due to its use.

7. pH titrations generally offer increased accuracy and precision. Accuracy

is increased because measured pH are used to detect rapid changes in
activity that occur at equivalence point of the titration. Furthermore, it is
the change in pH versus titre volume rather than absolute value of pH
that is of interest. Thus, the errors due to liquid-junction potentials and
activity coefficients are minimized.

8. Cell potential for the standard buffer can be expressed as

(Ecell )s = E* – 0.0592 (pH)s … (i)

Cell potential for unknown solution will be expressed as

(Ecell )u = E* – 0.0592 (pH)u …(ii)

To eliminate E* subtract Eq. (i) from Eq. (ii), we find

(Ecell )u - (Ecell )s
(pH)u = (pH)s – … (iii)
0.0591

Eq. (iii) is the operational definition of pH.

62
Unit 9 Potentiometry

Appendix I
Standard Electrode Potentials*
0
Reaction E at 25° C,V
MnO 4 + 8 H + 2e ⇌ Mn + 4H2O + 1.51
+ 2+

+ 1.359
Cl2(g)+ 2e⇌ 2Cl 
Cr2O
2– +
+ 14 H + 6e ⇌ 2Cr
3+
+ 7 H2O + 1.33
+
O2(g)+4H + 4e ⇌ 2H2O + 1.229
+ 1.087
Br2(aq) + 2e ⇌ 2Br 
+ 1.065
Br2(l) +2e ⇌ 2Br 
+
Ag + e ⇌ Ag (s) + 0.799

Fe
3+
+ e ⇌ Fe
2+ + 0.771
+ 0.536
I 3 + 2e ⇌ 3I 
-

Cu
2+
+ 2e ⇌ Cu (s) + 0.337

UO
2 + +
+ 4H +2e⇌ U
4+
+ 2H2O + 0.334
2

+ 0.268
Hg2Cl2 (s) + 2e ⇌ 2Hg (l) + 2Cl 
+ 0.222
AgCl(s) + e ⇌ Ag(s) + Cl 
+ e ⇌ Ag (s) + 2S2O 32  + 0.017
3-
Ag(S2O3) 2

+
2H + 2e ⇌ H2(g) 0.000
– 0.151
AgI(s) + e ⇌ Ag(s) + I 
PbSO4 + 2e ⇌ Pb(s) + SO 24  – 0.350

Cd
2+
+ 2e ⇌ Cd (s) – 0.403

Zn
2+
+ 2e ⇌ Zn(s) – 0.763

Ce
4+
+ e ⇌ Ce
3+ – 1.70 V
– 2.363
Mg 2  + 2e ⇌ Mg (s)

63
Block 3 Thermal and Electroanalytical Methods

UNIT 10

CONDUCTOMETRY

Structure
10.1 Introduction The Wheatstone Bridge Principle
Expected Learning Outcomes Measurement of Conductance of
a Solution
10.2 Electrolytic Conductance
10.4 Application of Conductometry
Molar Conductivity
10.5 Summary
Variation of Conductance with
Concentration 10.6 Terminal Questions
Limiting Molar Conductivity 10.7 Answers
Effect of other Factors on 10.8 Further Reading
Conductance
10.3 Measurement of Electrolytic
Conductance

10.1 INTRODUCTION
So far we have discussed potentiometric methods. In these methods we
measure the emf of a galvanic cell which is operating near zero current.
Because this emf is a function of the ionic activities within the cell, it can be
used to measure ionic concentrations in titration, water samples, biological
samples and other industrial and environmental samples. We have also seen
that both potentiometry and pH metry are most widely used electroanalytical
technique. In this unit you will study another electroanalytical technique called
the conductometry, which is one of the oldest and in many ways simplest
among the other electroanalytical techniques. This technique is based on the
measurement of electrolytic conductance.

An application of electrical potential across the solution of an electrolyte

involves the transfer of mass and charge from one part of the solution to the
other. Such transport processes, enable an insight into the structure of such
solution. A transport property of great significance, which can be easily
measured, is the conductance. Since, an electrolytic solution consists of ions
and the nature of interaction existing in the medium could be better
understood in terms of the conducting power of these ions, it is more
convenient to speak of conductance rather than resistance. The conducting
64 ability of electrolytic solutions provides a direct prove of the existence of ions
Unit 10 Conductometry

in solutions. The experimental determinations of the conducting properties of

electrolytic solutions are very important as they can be used to study

quantitatively the behaviour of ions in solutions. They can also be used to

determine the values of many physical quantities such as solubilities and
solubility product of sparingly soluble salts, ionic product of self ionizing
solvents, hydrolysis constant of salts, dissociation constants of weak acids and
bases and to form the basis for conductometric titration methods.

Expected Learning Outcomes

After studying this unit you should be able to:

 define electrolytic conduction;

 distinguish between the electrolytes and non-electrolytes solutions; and
strong and weak electrolytes,;
 explain conductance of solutions, molar and equivalent conductivities;
 describe different factors effecting conductance; and
 explain various application of conductometry.

10.2 ELECTROLYTIC CONDUCTANCE

An electrolytic solution contains free ions in addition to other kinetically
identifiable species. When electrical potential is applied across the solution the
macroscopic observations are, the flow of current through the solution and the
chemical changes generally resulting in the liberation or dissolution of the
electrode material at the points where the current enters or leaves the solution.
This phenomenon of decomposition of the solutions by electrical current is
termed as electrolysis.

Electrolytic conduction, in which charges carried by ions, will not occur unless
the ions of the electrolyte are free to move. Hence, electrolytic conduction is
exhibited principally by molten salts and by aqueous solutions of electrolytes.
The principle of electrolytic conduction is best illustrated by reference to an
electrolytic cell such as that shown in Fig. 10.1 for the electrolysis of molten
NaCl between inert electrodes. The entire assembly except that of the external
battery of Fig. 10.1 is known as the cell.

Fig. 10.1: Electrolysis of molten sodium chloride. 65

Block 3 Thermal and Electroanalytical Methods

The electrons are received from the negative end of the external battery by the
negative electrode of the cell. These are used up in the reduction reaction at
this electrode. The numbers of electrons received at the negative electrode
are given back to the positive end of the external battery from the positive
electrode of the cell where electrons are released as the result of oxidation
reaction. Within the cell, current is carried by the movement of ions; cations
moves towards negative electrode called the cathode and anions towards the
positive electrode called anode. This movement of ions give rise to what is
known as the electrolytic conduction. The latter, thus, depends on the mobility
of ions and anything that inhibits the motion of ions causes resistance to
current flow. Factors that influence the electrical conductivity of solutions of
electrolytes include interionic attraction, solvation of ions, and viscosity of
solvents. These factors depend on the attraction i.e. solute-solute, solute-
solvent and solvent-solvent respectively. The average kinetic energy of the
solute ions increases as the temperature is raised and, therefore, the
resistance of electrolytic conductors generally decreases, that is, conduction
increases as the temperature is raised.

Electrolytes and non-electrolytes

The ionic compounds, which furnish ions in solution and conduct electric
current, are electrolytes e.g. NaCl, KCl etc. There are covalent compounds,
which also conduct electric current in solutions. These include HCl, CH3COOH
etc. All other substances which do not produce ions in solutions are called
non-electrolytes, e.g. cane sugar, benzene, carbon tetrachloride etc.

Sometimes electrolytes are also called as true electrolytes and potential

electrolytes. In true electrolytes the cations and anions do exist even in the
molten states, e.g. NaCl, KCl. They are true electrolytes because they exist as
Na+ Cl  and K+ Cl  in their normal states and in the molten states. Also when
they are dissolved in water they ionize and conduct current.

Na+ Cl   Na+ (aqueous) + Cl  (aqueous)

The potential electrolytes do not conduct electricity in the pure normal state
rather they conduct electricity when dissolved in water, e.g. HCl, CH3COOH
and NH3.

Strong and weak electrolytes

Electrolytes can be classified as strong or weak. This has nothing to do with

their concentration but related to their extent of ionisation.

Strong electrolytes: The substances, which are completely ionized in aqueous

solutions, are called strong electrolytes, e.g. NaCl, NH4Cl, KNO3, HCl, HBr etc.

Weak electrolytes: The substances which ionize only to a certain extent are
called weak electrolytes, e.g. CH3COOH, HCN etc.

The terms strong and weak are relative. The behaviour of electrolytes also
depend on the nature of solvents, e.g. NaCl behaves as strong electrolyte
where as acetic acid as a weak electrolyte in water. On the other hand, when
dissolved in ammonia both NaCl and acetic acid show comparable behaviour
towards electricity.
66
Unit 10 Conductometry

Conductance of solutions

The ease of flow of electric current through a body is called its conductance.
In metallic conductors it is caused by the movement of electrons, while in
electrolytic solutions it is caused by applied electrical field. The electrolytic
conductance, G, of a medium is equal to the reciprocal of its electrical
resistance R in ohms:

1
G … (10.1)
R

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:

E
I or I  EG … (10.2)
R

Since a solution is a three dimensional conductor, the exact resistance will

depend on the spacing (l) and area (A) of the electrodes. The resistance of a
solution in such situation is directly proportional to the distance between the
electrodes and inversely proportional to the electrode surface area.

2 2
Am Am

Consider the electrolytic cell shown above, its two electrodes are having a
cross-sectional area of A m2 and separated by l m. The resistance (R) of the
electrolyte solution present between the two electrodes is:

R l

1
R 
A

l
R 
A

l
R= ρ … (10.3)
A

Where  (rho) is proportionality constant is called resistivity (formerly called

specific resistance). It is a characteristic property of the material and it is the
resistance offered by a conductor of unit length and unit area of cross section. 67
Block 3 Thermal and Electroanalytical Methods

A
= R … (10.4)
l

In SI units, l and A are measured in meters and square meters respectively,

and the resistance is expressed in ohm,  (omega). Therefore, the unit of 
is ohm meters ( m). Formerly, resistivity measurements were made in terms
of a centimetre cube of a substance, giving  the units  cm.

Substitute the value R in Eq. 10.1 The expression for the conductance, G is

1 1 A
G=  κ … (10.5)
R ρ ( A/l ) l

where K (kappa) is reciprocal of specific resistance called as specific

conductance or conductivity. It is measured in -1 m-1. This quantity may be
considered to be the conductance of a cubic material of edge length unity.
However, in SI system, the unit for conductance is ‘Siemens’ and, given the
symbol ‘S’. Hence, the unit for conductivity will be S m1 (1S = 11) or S cm1.
It may be remembered that S m1 = 1/100 S cm1. However specific
conductance is customarily reported in smaller units as milli Siemens per
meter (mS m1) and micro Siemens per cm (S cm1).

Cell constant: For a given cell, l and A are constant, and the quantity (l/A) is
called the cell constant (Kcell).

l
Kcell =
A

Substitute this value in Eq. (10.5)

 = G Kcell … (10.6)

Conductivity = observed conductance  cell constant

To obtain the value of the cell constant, it is not necessary to determine l and
A directly. Instead, it is measured by a solution of known conductivity.
Potassium chloride solutions are invariably used for this purpose, since their
conductances have been measured with sufficient accuracy in cells of known
dimensions. A given solution of potassium chloride of conductivity K' is placed
in the cell and its resistance R' is measured. The cell constant is then equal to
K'R'. Therefore,

Cell constant = conductivity of KCl solution  measured resistance

Conductance is an additive property, e.g. in an aqueous solution containing

several electrolytes, the total conductance is

G(total) = Gi + G (water) … (10.7)

Where the summation is to be carried over all the electrolytes present in the
solution and G (water) is the conductance of water, which is utilized for making
the solution. G (water) is often negligible in comparison to Gi as repeatedly
distilled water (known as conductivity water) of very low conductance is
68 employed for making the solutions.
Unit 10 Conductometry

SAQ 1
The resistance of a conductivity cell containing 0.01 mol dm 3 KCl is 150 Ω.
The same conductivity cell gives the resistance of 0.01 mol dm 3 HCl 51.4 Ω.
The conductivity of the KCl solution is 1.41 × 10–3 -1 cm-1 Calculate the
following values:

(i) cell constant, and

(ii) conductivity of the HCl solution.

10.2.1 Molar Conductivity

In order to compare quantitatively the conductivities of electrolytes, a quantity
called molar conductivity is frequently used. The molar conductivity, m
(capital lambda) is the conductivity per unit molar concentration of a dissolved
electrolyte. It is related to conductivity,  by the relation:


m = … (10.8)
c

where c is the concentration mol m3. The molar conductivity is usually

expressed in S m2 mol1 or S cm2 mol1. It may be remembered that S m2
mol1 = 10,000 S cm2 mol1.

It is to be remembered that c in Eq. 10.8 is to be expressed in mol m3 unit. If

the concentration is given in terms of Molarity (mol dm3), then the following
conversion is to be carried out

c (mol m3) = Molarity  1000 … (10.9)

Earlier equivalent conductivity (eq), which is given by the following

expression, was in use

1000  
eq = … (10.10)
c

Where c is the concentration expressed in terms of normality of the solution.

Unit of eq is  1 cm 2 eq 1 . However, IUPAC recommends the use of molar
conductivity only.

SAQ 2
Write the units of the following:

(a) Specific conductance

(b) Equivalent conductivity

(c) Cell constant

(d) Molar conductivity

69
Block 3 Thermal and Electroanalytical Methods

SAQ 3
From the following data, calculate the molar conductivity of KCl in aqueous
solution:

Conductivity of 5.0 × 10 4 mol dm 3 KCl = 7.44 × 10 3 S m–1

Conductivity of the water = 0.06 × 10 3 S m–1

10.2.2 Variation of Conductance with Concentration

The conductivity of an ionic solution increases with increasing concentration.
For strong electrolytes, the increase in conductivity with increase of
concentration is sharp. However, for weak electrolytes, the increase in
conductivity is more gradual. In both cases the increase in the conductivity
with concentration is due to an increase in the number of ions per unit volume
of the solution. For strong electrolytes, which are completely ionized, the
increase in conductivity is almost proportional to the concentration. In weak
electrolytes, however, the increase in specific conductance is not large due to
the low ionization of the electrolytes, and consequently the conductivity does
not go up so rapidly as in the case of strong electrolytes. Table 10.1 shows the
variation of molar conductivity of a number of electrolytes at various
concentrations at 298 K.

Table 10.1: Molar conductivity (104  S m2 mol-1) of electrolytes in

aqueous solutions at 298 K

–3
c/mol dm KCl NaCl HCl AgNO3 CH3COOH CH3COONa

1.0 111.9 89.9 332.8 - - 49.1

0.1 129.0 106.7 391.3 109.1 5.2 72.8

0.05 133.4 111.1 399.1 115.7 7.4 76.9

0.01 141.3 118.5 412.0 124.8 16.3 83.8

0.005 143.5 120.6 415.8 127.2 22.9 85.7

0.001 146.9 123.7 421.4 130.5 49.2 88.5

0.0005 147.8 124.5 422.7 131.4 67.7 89.2

It is observed that in contrast to the conductivity, the molar conductivity, m

invariably increases with decreasing concentration for both weak and strong
electrolytes. If we plot the molar conductivities of a large number of
electrolytes against the square root of the concentrations we find that these fall
into two distinct categories. In the case of strong electrolytes (for example KCl,
NaCl or acids such as HCl, H2SO4 etc), there is a small increase in molar
conductivities with the decrease in concentration. Since these electrolytes
dissociate almost completely even in concentrated solution, the number of
ions do not change much with concentration. The conductivity should not vary
much since it is directly related to the number of ions present in solution. The
70
Unit 10 Conductometry

minor changes observed are due to interionic interactions. In the case of weak
electrolytes (for example CH3COOH, ammonia, organic fatty acids etc), the
ionization will increase with dilution, and hence, the molar conductivity
increases with dilution. Thus the conductivity is directly proportional to the
degree of dissociation of a weak electrolyte.These above results are depicted
in Fig. 10.2 in which the molar conductivity, m, of two electrolytes (KCl and
acetic acid) at a constant temperature is plotted against c. It may be seen
from the figure that two different types of behaviours are exhibited by these
electrolytes. The strong electrolyte, KCl shows a linear plot (almost straight
lines). On the other hand, the weak electrolyte, CH3COOH seems to approach
the dilute solution limit almost tangentially. It is, however, impossible to draw a
sharp line of demarcation between the two categories as many substances are
known to exhibit intermediate behaviour, e.g., nickel sulphate. Such
electrolytes are sometimes called moderately strong electrolytes.

0
(a)

KCl


(b)
CH3COOH

0
c

Fig. 10.2: Variation of molar conductivity on dilution (a) for aqueous solution of
potassium chloride (strong electrolyte) (b) acetic acid (weak
electrolyte).

The conductance of a solution depends on the number of ions and the speed
with which the ions move in solution. In case of strong electrolytes, the number
of ions is the same at all dilutions (since strong electrolytes are completely
ionized) and the variation of equivalent conductance with dilution is therefore
due to the change in the speed of the ions with dilution. In a concentrated
solution of such electrolytes, the interionic attractions among the oppositely
charged ions would be quite appreciable. The ions may also form some ion-
pairs of the type A+B  that would not contribute to the conductance. These
interionic forces considerably lower the speed of the ions and hence the
conductivity of the solution. As the dilution is increased the interionic
attractions decrease with the result that the ions will move more freely and
independently of their co-ions and thus increasing the molar conductivity with
dilution. At infinite dilution, the ions are quite far apart, the interionic attractions
are almost absent and each ion moves completely independent of its co-ions.
The molar conductivity then approaches a limiting value at infinite dilution and
represents the conducting power of 1 mole of the electrolyte when it is
completely split up into ions. It is denoted by .

It can be conclude that in case of weak electrolytes, the increase in molar

conductivity with dilution is mainly due to (a) an increase in the number of ions
in the solution (degree of ionization increases with dilution), and (b) smaller
interionic attractions at higher dilutions.
71
Block 3 Thermal and Electroanalytical Methods

10.2.3 Limiting Molar Conductivity

An important relation can be obtained by extrapolating the curve for strong
electrolytes (Fig. 10.2) to c  0 where all interionic effects are absent. The
limiting value obtained by this extrapolation is called the molar conductivity at
infinite dilution.

Observing the linearity of m versus c for strong electrolytes in dilute

solutions, Kohlrausch suggested the following empirical relation for the
variation of molar conductance of strong electrolytes with dilution.

m =   – bc … (10.11)

where b is a constant for the given electrolyte and   is the molar

conductivity of the electrolyte at infinite dilution. The validity of this equation
may be seen from the plot for electrolytes like HCl, KCl etc. To obtain   of
such electrolytes the curve is extrapolated to c  0 and the intercept so
obtained gives the value of   . The same method cannot be used for
obtaining   for weak electrolytes because of the steep increase in  at high
dilutions.   may also be computed from the molar conductivities at infinite
dilution of the respective ions, since at infinite dilution, the ions are
independent of each other according to the law of independent migration of
ions and each contribute its part to the total conductivity, therefore,

  =   +   … (10.12)

where   
 and   are the ionic conductivities at infinite dilution of the cation
and anion, respectively.

The molar conductivity of the ionic species is a measure of the amount of

current carried by ions in question. Comparison of the molar conductivities of
ions is, therefore, more meaningful when related to per unit charge, for
example when   (Na+) is compared with ½  
 (Mg ) rather than   (Mg )
2+ 2+

or in terms of equivalent conductivities. The value of the limiting ionic molar

and equivalent conductivities for some ions in water at 25oC are given in
Table 10.2.

Table 10.2: Limiting ionic molar conductivities and limiting ionic

equivalent conductivities of selected ions in water at 25o C

Catio   /(S cm2   /(S cm

2
Anion   /(S cm2   /(S cm2
n –1 –1 –1 -1
mol ) eq ) mol ) eq )

OH 
+
H 349.8 349.8 198.3 198.3

F
+
Li 38.7 38.7 55.4 55.4

Cl 
+
Na 50.1 50.1 76.3 76.3

Br 
+
K 73.5 73.5 78.1 78.1

I
+2
Be 90.0 45.0 76.8 76.8

NO3 
2+
Mg 106.2 53.1 71.5 71.5
72
Unit 10 Conductometry

SO4 
2+ 2
Ca 119.0 59.5 160.0 80.0

CH3COO 
2+
Ba 127.2 63.6 40.9 40.9

C6H5CO 
3+
Al 183.0 61.0 32.4 32.4

HCO3 
2+
Cu 107.2 53.6 44.5 44.5

CO3 
+ 2
Ag 61.9 61.9 138.6 69.3

Fe(CN)6 
2+ 3
Zn 105.6 52.8 302.7 100.9

Fe(CN)6 
3+ 4
Ce 209.4 69.8 442.0 110.5

Ionic Mobilities and Transport Number

The next question which arises in connection to the values of conductivity

given in Table 10.2, is why should there be a difference between the values of
limiting molar conductivities of similarly charged ions, if these ions are just
acting as carriers of electric charges only?

The answer lies in the fact that different ions have different mobilities in
solution. The mobility of an ion in solution is mainly dependent upon the size of
the hydrated ion. The ionic mobility is defined as the velocity with which an ion
would move under a potential gradient of 1 V m–1 in a solution. It provides a
link between theoretical and measurable quantities. For instance, ionic
mobility, (u) is related to limiting molar ionic conductivity (  ) by the following
equations:

  = z+u+F and   = z–u–F … (10.13)

where z+ and z– are the valency of the ions, u+ and u– represent the ionic
mobilities and F is the Faraday constant. In the above equation, if one of the
two quantities,   or u, is known, the other can be calculated.

To find the values of   

 or   ,we define yet another quantity, called
transport or transference number of an ion indicated by the symbol t+ or t–. It
is defined as the fraction of the total current carried by an ionic species and
can be expressed mathematically as,

t+ =  
 /m and t– =  
 / m … (10.14)

The transport number and the limiting molar conductivity are measurable
quantities. Hence, the molar ionic conductivity value can be calculated from
Eq. 10.14. The limiting molar conductivities of some common ions are given in
Table 10.2. These values are important in predicting the molar conductivity of
electrolytes and course of conductomatric titrations. Finally, once the molar
ionic conductivity value is obtained, we can then make use of Eq. 10.13 to
calculate the ionic mobility. Some typical values of ionic mobility (in infinite
dilute solutions) are listed in Table 10.3. 73
Block 3 Thermal and Electroanalytical Methods

Table 10.3: Limiting ionic mobilities in water at 298 K

Cation 108 u+ / m2 v–1 s–1

H+ 36.24

Li+ 4.01

Na+ 5.19

K+ 7.62

Ag+ 6.42

Anions 108 u– / m2 v–1 s–1

OH– 20.58

Cl– 5.74

Br– 7.92

I– 8.09

NO3– 7.41

It is interesting to look at Table 10.3 in more detail. You will see the Li+ ion,
because of its larger hydration shell, has a lower mobility than the potassium
ion. Similar argument can be applied to the F– & Br– ions. Exceptional
mobilities are observed for the H+ and OH– ions. This is because, in these
case charge is transported through proton jump mechanism along with general
migrations mechanism, consider he case of H+ ion.
H H H H
|1 | |3 |4
 2
H   H  O  H - - - O  H- - - O  H - - - O  H


H H H H
|1 |2 |3 |4
- - - H  O- - - H – O  H - - - O  H - - - O  H


H H H H
|1 |2 |3 |4
– H  O – - - -H – O- - - H – O  H - - - O  H

You can see how hydrogen ion jumps from O1 to O2, O2 to O3, ......., this
result is equivalent to as the migration of charge from left to right. This
conduction mechanism is more like a charge than ion movement. Such
conduction is possible because of the peculiar structure of water and therefore
only found in hydrogen-bonded solvents.

10.2.4 Effect of other Factors on Conductivity

Beside concentration, there are some more factors which affect the
conductivity of the electrolyte solution.
(a) Effect of temperature and pressure: The conductivity of all electrolytes
increases with increasing temperature. The variation of molar
conductivity at infinite dilution with temperature is given by an empirical
equation.
74
Unit 10 Conductometry

  (t) =   (25)[1+ x(t – 25)] … (10.15)

where   (t) and   (25) are the value of molar conductivities at t and
25oC respectively, and x is a constant for each electrolyte. For salts x is
about 0.022 to 0.025 and for acids and bases it is usually 0.016 to 0.019.
It means that molar conductivity increases approximately by 2% for
every one degree rise in temperature. For strong electrolytes, even at
appreciable concentration,
Eq. (10.15) holds well, whereas in case of weak electrolytes, the
variation of  with temperature is not so regular. The rise in conductance
with temperature is due to the decrease in the viscosity of the solution,
increase in the speed of the ions and an increase in the degree of
ionization in cases of weak electrolytes.

The conductivity increases slightly with increase in pressure. The effect

is mainly through changes in the viscosity of the medium, which
decrease by an increase in pressure. Consequently, the molar
conductance of the solution will increase with rise in pressure.

(b) Effect of solvent: In solvents of low dielectric constants, having small

ionizing effect on the electrolytes, the electrostatic forces between
oppositely charged ions would be appreciable and molar conductance
will have small value. However, solvents with high dielectric constants
yield more conducting solutions.

(c) Viscosity of the medium: The dependence of conductance on viscosity of

the medium is given by Walden's rule, according to which the molar
conductance of an electrolyte is inversely proportional to the viscosity of
the medium, i.e.

  0 = constant … (10.16)

where 0 is the molar conductance at infinite dilution and o is coefficient

of viscosity of the solvent. If ions are not solvated, i.e., they have the
same size in all the solvents, then it follows from Walden rule that   0
should be constant and independent of the nature of the solvent. This is
true only for ions like tetra-alkyl ammonium cations, which are not
solvated. Ions where extensive solvation occurs, effective radii of the
ions will not be constant and Walden rule will not be obeyed.

SAQ 4
List the factors which are affecting the conductivity of the solution.

10.3 MEASUREMENT OF ELECTROLYTIC

CONDUCTANCE
The conductance of a solution can be determined by measuring the resistance
offered by solution contained within the two electrodes of a conductivity cell.
75
Block 3 Thermal and Electroanalytical Methods

For measuring resistance, the Wheatstone bridge principle is employed.

Therefore, before taking up the measurement of conductance of solution, let
us study the principle of Wheatstone Bridge.

10.3.1 The Wheatstone Bridge Principle

A Wheatstone bridge (Fig. 10.3) be employed to measure the resistance of an
electronic conductor. It works on the principle of obtaining balance between
two arms with the help of a balance indicator (e.g. a galvanometer) at the
condition of potential being equal.

Let Rx be an unknown resistor, R1 and R2 two standard resistors, R3 an

adjustable resistor and G a galvanometer. The bridge is connected to a
source of power S, a battery, and a tapping key K is placed in the path to
control the connections.

i1 i2
R1 R2

S
B D
G K
_
i1

R3 i2 RX

Fig. 10.3: A DC Wheatstone bridge circuit.

To measure the resistance Rx, the tapping key K is held down momentarily
and the bridge is balanced by adjusting R3 to get no deflection in galvanometer
under these conditions.

In the bridge the total current is divided into two paths: i1 through R1 and R3,
and i2 through R2 and Rx. Under the balancing conditions, the potential at
points B and D must be the same, i.e. the ohmic voltage drop through the
resistors R1 and R2 must be the same. Hence, the potential at B (EB) must be
equal to potential at D (ED).

EB = ED … (10.17)

Or i1 R1 = i2R2 … (10.18)

Similarly, i1 R3 = i2 Rx … (10.19)

Dividing (10.18) by (10.19) we get,

R1 R 2

R3 R x

R2R3
and Rx  … (10.20)
R1
76
Unit 10 Conductometry

Thus, we can calculate Rx as R1, R2 and R3 are all known. Conductance G,

being the reciprocal of resistance will be,
R1
G … (10.21)
R 2 R3

Alternatively, the conductometric cell can be incorporated into operational

amplifier control circuit, as shown in Fig. 10.4. The amplifier balances the
potential of two inputs. The current from the input potential, Ei, is balanced by
the current from amplifier output which passes through a feedback resistor
(Rf). The output potential, E0 is in terms of resistance:

E0 = Ei (Rf/Rx + 1)

Where Rx is the resistance of conductometric cell.

With respect to the solution conductance, G, above equation becomes

E0 = Ei(RfG + 1)

Rf

_
D
E0
+
Rx
Ei

Fig. 10.4: An operational amplifier control circuit for conductometric

measurement. Rx is the solution resistance and Rf is the feedback
resistance

10.3.2 Measurement of Conductance of a Solution

The Principle of the Wheatstone bridge discussed above can be used to
measure the conductance of solutions. However, the following considerations
must also be kept in mind:

(i) Since a direct current would polarize the electrodes in the conductivity
cell by electrolyzing the solution; to avoid polarization an alternating
current (ac) source of power must be used in place of a dc source
(battery) usually ac voltages of 3-6 volts with frequency of 50 Hz or
1000 Hz used across points A and C of Fig. 10.5.

(ii) A suitable conductivity cell (with electrodes dipped in the solution) is

located between points C and D. Thus Rx represents the resistance of
the conductivity cell.

(iii) Since, the cell also acts like a small capacitor (Cx), and to balance its
capacitive resistance a variable capacitor, CB, must be inserted into the
bridge.

(iv) The balance indictor (BI) may be an ac galvanometer, but some other
devices may also be used:

 An earphone can act as a balance indicator if the frequency of the ac

source is in audio-range. 77
Block 3 Thermal and Electroanalytical Methods

 A magic eye, which gives a green fluorescence as a result of

electrons striking a phosphor coating inside the glass tube, is used in
several commercial instruments.
 For much precise conductance measurements a cathode ray
oscilloscope is used as the balance indicator.
A

R1 R2

ac
B BI D

Conductivity cell
R3

RX
CB
CX
C

Fig. 10.5: A conductivity bridge circuit.

(v) Conductance (G=1/Rx) can be read directly on commercially available

instruments as a panel mounted meter. Now several digital instruments
are also available, such instruments give the conductance directly as the
numerical value.

Conductometer

From above discussion we can conclude that conductance is reciprocal of

resistance and the resistance of a cell can be measured by placing it in an arm
of a Wheatstone bridge. The inverse of the resistance gives the conductance
and can be directly read on a conductivity measuring instrument, known as
“Conductometer”.

A typical conductometer, consists of an ac source, a Wheatstone bridge

circuit, a null detector or direct reading display and a conductivity cell.

To avoid the effects of polarization, i.e. the change in composition of the

measuring cell, alternating current (ac) is used. The instrument has an
arrangement to convert the supply of 50 Hz to higher frequency, say 1000 Hz.
For measuring low conductance solutions, the lower frequency is preferable
and for high conductive solutions higher frequencies are preferably used.

Several inexpensive conductometers are commercially available. The

instruments come as a line-operated unit with and without digital readout.
Fig. 10.6 gives the view of a typical conductometer, which can be operated as
with given instructions.

Read
.4 .8 1.2 Cal.
0 1.6
2.0 Sensitiv ity

mS range
selector

Conductometer

Fig. 10.6: Conductometer.

78
Unit 10 Conductometry

Cells

Various types of cells have been designed and are in use for the
measurement of conductance of a solution. These are made of Pyrex glass
fitted with electrodes of platinum or gold. To overcome the imperfections in the
current and the other effects at the electrodes, these are coated with a layer of
finely divided platinum black. This is achieved by electrolyzing a 3% solution of
chloroplatinic acid containing a little of lead acetate. The distance between the
electrodes is determined by the conductance of the solution to be measured.
For highly conducting solution, the electrodes are widely spaced whereas for
low conducting solutions the electrodes are mounted near each other. A cell
suitable for conductometric titration is depicted in Fig. 10.7 (a, b and c); the
electrodes are firmly fixed in the Perspex lid which is provided with opening for
the stirrer and the jet of the burette. A magnetic stirrer can be used in place of
mechanical stirrer.

For most purposes a special cell is not required and good results are obtained
by clamping a commercially available dip cell [shown diagramatically in
Fig. 10.7 (b)] inside a beaker which is placed on a magnetic stirrer. With this
arrangement, the dipping cell should be lifted clear of the solution after each
addition from the burette to ensure that the liquid between the electrodes
becomes thoroughly mixed. Since absolute conductivity values are not
required it is not necessary to know the cell constant.

For spot checking on a process stream or tank, a dip-type of conductivity cell

is used. In some titrations an open beaker with fixed electrodes is sufficient.
However, for fairly dilute solutions an open beaker would not be satisfactory
because atmospheric CO2 may alter the conductance.

Fig. 10.7: Typical designs of conductivity cells.

Procedure for Direct Measurement of Conductivity

1. Plug the instrument to an ac supply.

2. Put the frequency selector switch to required frequency (say 1000 Hz).

3. Set the mode selector on CAL and set the range selector on the desired
setting e.g., 2, 20 or 200. These figures refer to the full scale meter value 79
Block 3 Thermal and Electroanalytical Methods

in milli Siemens (mS). With the help of sensitivity knob keep the pointer
roughly midway between the lowest and highest sensitivity say at 1
position.

4. Connect the conductivity cell electrodes to the appropriate terminals of

the instrument. Clean the conductivity cell with distilled water
(Conductivity water).

5. Take the standard KCl solution (say 0.1M) in a clean beaker. Introduce
a stirring rod (to be used for magnetic stirring) in the solution and put the
solution beaker on a magnetic stirrer plate.

6. Insert the conductivity cell in the solution. Ensure that the platinum plate
electrodes are completely immersed in the solution and they do not
touch the stirring rod or the sides or the bottom of the beaker.

7. Switch on the instrument and allow it to warm up for 2-5 minutes.

8. Measure the conductance, Gs, of the standard KCl solution by putting

meter switch to READ position.

9. Remove the KCl solution from the beaker, wash the conductivity cell
properly with distilled water. Take the unknown solution in the beaker
and measure its conductance, Gu, in the manner as for standard KCl
solution.

10. Calculate the cell constant, from the conductance and conductivity
values of the standard,
Conductivi ty (specific conductanc e)
K cell 
Observed conductanc e of the standard

S
K cell cm 1  cm 1
GS

11. Calculate the conductivity (specific conductance) of the unknown solution

= cell constant × observed conductance
 u  K cell Gu

12. For titration work, the value of cell constant, Kcell is not required to be
calculated, since the cell constant will remain unchanged during the
course of any given titration.

Notes:

(i) When the range selector is switched to a new position, it is essential to

check the calibration again. Set the meter again to read one with the
sensitivity control, if any deviation is observed.

(ii) The conductivity cell, when not in use, should be kept in distilled water to
prevent drying the platinum electrodes.

(iii) In case of fouling the conductivity cell electrode plates, clean them by
keeping in dilute K2Cr2O7 containing H2SO4 solution (i.e. dilute chromic
acid) for 24 hours and then washing with running water followed by
rinsing with distilled water.
80
Unit 10 Conductometry

SAQ 5
At 298 K, the resistance of 2.00  102 M KCl is 195.96  and that of 2.50  10-
3
M K2SO4 is 775.19 . The conductivity () of 2.00  102 M KCl at 298 K is
0.2768 S m1. Calculate molar conductivity of K2SO4 solution.

10.4 APPLICATIONS OF CONDUCTOMETRY

The high sensitivity of the conductometric measurements makes it an
important analytical tool for environmental analysis and certain other
applications. A continuous or spot check measurement of conductance is
employed, usually, with a dip electrode cell and meter. In certain cases
continuous recording of conductance is also employed. Since conductance
depends on ionic concentrations, the purity of steam distillate, demineralized
water, and the ionic contents of raw water can be checked with measuring
conductance directly. Metal industries, electroplating baths and rinse baths
are monitored by conductance methods.

Perhaps the most common application of direct condutometry has been for
estimating the purity of distilled water. Kohlrausch with a painstaking work
after 42 successive distillations of water in vacuo obtained a conductivity water
with specific conductance,  = 4.3 × 10‾8 S cm‾1 at 180C. Traces of an ionic
impurity will increase the conductance appreciably. Ordinary distilled water in
equilibrium with the carbon dioxide of the air has a conductivity of about
7.0 ×10–7 S cm–1. The sea water has much higher value of conductivity and
the conductometric measurements are widely used to check the salinity of
water in oceanography.

Measuring conductance of soil helps in finding the moisture content of soils at

various places with portable instruments. All soils contain varying amount of
water soluble salts upto 0.1% or even more. These salts are usually present
as sulphate, chloride, carbonate or bicarbonate of sodium, potassium, calcium
and magnesium and contribute to the conductance of the soil. The soil may
be classed as saline and non-saline depending on the nature and quantity of
the salts present. Conductivity of a saturated extract with water of saline soil
at 250C has a conductivity greater than 4 mS cm1.

Based upon the relative change in the conductance/resistance of a solution

with the addition of another electrolyte, methods have been developed for the
titration of a strong acid with a strong base, weak acid versus strong base or a
weak base and a mixture of a strong acid and weak acid versus a strong base.
Other types of titrations which can be performed conductometrically include
displacement titrations: a salt of a weak acid (sodium acetate) versus a strong
acid like HCl or a salt of weak base ( ammonium chloride) versus sodium
hydroxide; precipitation titrations: silver nitrate versus KCl; complexometric
titrations: mercuric nitrate versus KCN or EDTA versus metallic ions and
oxidation – reduction (redox ) titrations like the titration of Fe(II) versus KMnO4.

Conductometric methods based upon precipitation or complex formation

reactions are not as useful as those involving neutralization processes. 81
Block 3 Thermal and Electroanalytical Methods

Conductance changes during these titrations are seldom as large as those

observed with acid-base reactions because no other reagent approaches the
great ionic conductance of either hydronium or hydroxide ion. The main
advantage to the conductometric end point is its applicability to very dilute
solutions and to systems that involve relatively incomplete reactions. For
example, while neither a potentiometric nor indicator method can be used for
the neutralization titration of phenol(Ka= 10-10) a conductometric end point can
be successfully applied.

Direct measurement of conductivity is potentially a very sensitive procedure for

the determination of various parameters like the degree of dissociation of a
weak electrolyte and its dissociation constant, ionic product of water, solubility
and solubility product and hydrolysis constant of a salt. We have already
discussed these parameters in the earlier semester course. Now we will take
up the principle of conducometric titrations.

Conductometric Titrations

The principle of conductometric 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.

The main advantages to the conductometric 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
conductometric endpoint can be successfully applied.

Some Typical Conductometric Titration Curves:

1. 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 large conductivity of OH- ions (Fig. 10.8).

Fig. 10.8: Conductometric titration of a strong acid (HCl) vs. a strong base
82 (NaOH)
Unit 10 Conductometry

2. Weak Acid with a Strong Base, e.g. acetic acid 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 (Fig. 10.9).

Fig. 10.9: Conductometric titration of a weak acid (acetic acid) vs. a

strong base (NaOH)

3. Strong Acid with a Weak Base, e.g. sulphuric acid with dilute
ammonia: 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 (Fig. 10.10).

Fig. 1010.: Conductometric titration of a strong acid (H2SO4) vs. a weak

base (NH4OH)

4. Weak Acid with a Weak Base: The nature of curve before the
equivalence point is similar to the curve obtained by titrating weak acid
against strong base. After the equivalence point, conductance virtually
remains same as the weak base which is being added is feebly ionized
and, therefore, is not much conducting (Fig. 10.11).
83
Block 3 Thermal and Electroanalytical Methods

Fig. 10.11: Conductometric titration of a weak acid (acetic acid) vs. a

weak base (NH4OH)

5. Precipitation Titration: A reaction may be made the basis of a

conductometric precipitation titration provided the reaction product is
sparingly soluble . The solubility of the precipitate 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 equivalence
point should be given by AB and not the observed AC. The addition of
excess of the reagent 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 (Fig. 10.12).

Fig. 10.12: Precipitation titration. Conductometric titration of (NH4)2 SO4

vs. barium acetate

A slow rate of precipitation, particularly with micro-crystalline precipitate,

prolongs the time of titration. Seeding or the addition of ethanol (concentration
up to 30-40 %) may have favourable effect.

If the precipitate has pronounced adsorptive properties, the composition of the

precipitate will not be constant, and appreciable errors may result. Occlusion
may take place with micro crystalline precipitates.

84
Unit 10 Conductometry

In spite of the obvious limitations of the method, still a large number of

precipitation titrations have been carried out; thus silver nitrate, lead nitrate,
barium acetate or barium chloride, uranyl acetate, lithium sulphate and lithium
oxalate have been utilized in precipitation reactions.

10.5 SUMMARY
In this unit, various parameters like resistance (R), conductance (G), resistivity
(), conductivity(K), equivalent conductivity(eq), molar conductivity(m), molar
conductivity at infinite solution(o) and cell constant have been defined in
detail along with their units for measurements. The relationships among these
parameters have also been worked out.Various factors affecting the
conductance of solution are also given. At the end detail procedure for the
measurement of conductance is given.

10.6 TERMINAL QUESTIONS

1. What are electrolytes? How are they classified?

2. Define molar conductivity and equivalent conductivity of an electrolyte.

How are they related to each other?

3. Write expression for a cell constant and conductivity of an electrolyte.

4. What are the various factors affecting the conductance of solution?

5. Explain the necessity of maintaining a constant temperature in

conductometric measurements.

6. The conductivity of 0.1 M HCl is 0.0394 -1 cm-1. What is the molar
conductivity of the solution?

7. The resistance of 0.1 M solution of a salt occupying a volume between two

platinum electrodes 1.80 cm apart and 5.4 cm2 in area was found to be 32
ohms. Calculate the molar conductivity of the solution.

8. A certain conductance cell was filled with 0.0100 M solution of KCl, whose
conductivity is 0.001409 -1 cm-1 (S cm-1) at 25oC, it had a resistance of
161.8 , and when filled with 0.0050 M NaOH, it had a resistance of
190 . Calculate the cell constant, conductivity and molar conductivity of
NaOH solution.

9. A conductivity cell shows a resistance of 3950  at 25oC when filled with

the experimental solution and 4864  at the same temperature when
filled with 0.02 M KCl solution. If the conductivity of the solution is 2.767
x 10-3 S cm-1, calculate the conductivity of the experimental solution.

10. The resistance of a conductivity cell was 702 ohms when filled with 0.1 M
KCl when filled with 0.1 M KCl solution (K = 0.14807 ohm-1 m-1) and 6920
ohm when filled with 0.01M acetic acid solution. Calculate the cell constant
and molar conductance for the acid solution.
85
Block 3 Thermal and Electroanalytical Methods

10.7 ANSWERS
Self-Assessment Questions

1. (i) K =KCl /Gobs. or = KCl × Robs.

= 1.41 × 10–3 Ω−1 cm−1  150  = 0.2115 cm1

(ii)  = KGobs. = K/Robs. = 0.2115 cm−1/51.5  = 4.11  10–3 Ω−1 cm−1

(S cm−1)

2. (a) conductivity: S m−1 or Ω−1 m−1

(b) Equivalent conductivity: Ω−1 cm−1 eq−1

(c) Cell constant : m–1 or cm–1

(d) Molar conductivity: S m2 mol−1 or S cm2 mol−1

3. KCl = sol.  water

(7.44-0.06)  10–3 = 7.38  10–3 S m−1

7.38×10-3 S m-1
m = K/c = -4 3 -1
= 1.476  10–2 S m2 mol−1
5.0 × 10 ×10 molm

4. Concentration ionic Mobility, temperature and pressure, nature of

solvent, viscosity of medium.

5. Consider following equation:

Kcell =   R

= 0.2768 S m-1  195.96 

= 54.24 m1.

Conductivity of K2SO4 solution can be given by,

K cell 54.24 m 1
=  = 0.06997 S m1.
R 775.19 

Concentration of K2SO4 in mol m3 unit:

c = 1000  2.50  103 mol m3

= 2.50 mol m3

Molar conductivity of K2SO4 can be expressed as

 0.06997
Λm   Sm 2mol 1
c 2.50

= 0.028 S m2 mol1
86
Unit 10 Conductometry

Terminal Questions
1. The ionic compounds which forming ions in solution and conduct electric
current are called electrolyte e.g. MaCl, KCl etc. They can be classified
strong and weak electrolyte on the basis of their degree of ionisation.

2. Molar conductivity: It is the conductivity for Unit molar concentration of a

dissolved electrolyte.

  1000 
Λm   S m 2 mol 1  S cm 2 mol 1 κ
c M1000 M

Equivalent Conductivity: It is the conductivity of 1 g equivalent of an

electrolyte when present in V cm3 of solution

Λeq  V

If c is the concentration of the solution in g equivalent per dm3, then

1000 
Λeq 
c

Its unit is S cm2 eq–1

Relationship

Molar Conductanc e (S cm 2 mol 1 )

Λeq 
η

where η = molecular mass/equivalent mass

3. Cell constant: The quality (l/A) is called the cell constant.

Conductivity = observed conductance × cell.

4. To overcame the imperfection in the current and the other effects at the
electrode.

5. Detail procedure is given in sub section 10.2.4.

6. Because conductivity of all electrolytes increases with increasing

temperature.

7. m = K/c, therefore,

m = 0.0394 ( -1 cm-1)/ 0.1 M =0.0394 (-1 cm-1)/0.1  103 mol cm3

= 394 -1 cm2 mol-1

8. Cell constant = l/A, 1.8/5.4 = 1/3 cm-1

Observed conductance = 1/32 -1

K = Cell constant  conductance=1/3  1/32 = 1/96 -1cm-1

m = K/c = 1/96 (-1 cm-1)  1/0.1 M

=1/96 (-1 cm-1)  1/0.1  103 (mole cm-3) =104.16 -1 cm2 mol-1
87
Block 3 Thermal and Electroanalytical Methods

9. Cell constant = K R = 0.001409 -1 cm-1 161.8  = 0.228 cm-1

κ NaOH = Cell constant/R = 0.228 cm-1/190  = 1.2  10-3 -1 cm-1

m = K/c = 1.2  10-3 -1 cm-1/ 0.0050  103 mol cm-3 = 240 -1 cm2
mol–1

10. Cell constant = KR = 2.767  10-3 (S cm-1 )  4864 ()

Conductivity of the experimental solution = K= Cell constant/R

= 2.767  10-3  4864 (cm-1)/3950() = 3.407  10-3 S cm-1

11. Cell constant = KR = (0.14807 702) (ohm-1 m-1) (ohm) =103.94 m-1
= 1.039 cm-1

Conductivity of acetic acid K = (1/R) (l/A)

= (1 / 6920 ) (1.039) cm-1

= 1.501  10-4 -1 cm-1

= 1.501  10-2 -1 m-1

Concentration = 0.01 M = 0.01 mol dm3 = 0.01  103 mol m-3

m = K/c = 1.50110-2 -1 m-1/ 0.01103 mol m-3

= 1.501  10-3 mol-1 -1 m2

8.11 FURTHER READING

1. H.H.Willard , L.L.Merrit Jr., J.A. Dean , F.A.Settle Jr., Instrumental
Method of Analysis, Wadsworth Publishing Company , USA, 1988.

2. M.E. Brown, Introduction to Thermal Analysis, Kluwer Academic

Publisher , London, 2001.

3. W.W. Wandlandt , Thermal Analysis, Wiley , New York , 1986.

4. H.Gunzzler and A.Williams , Hand Book of Analytical Techniques, Wiley

–VCH , Weinheim , Vol -2, 2001.

5. G.W.Ewing , Analytical Instrumentation Handbook, Marcel Dekker Inc,

New York, 2005.

6. R.A. Meyer, Encyclopedia of Analytical Chemistry, John Wiley & Sons

Ltd , Vol 15, 2000.

7. Skoog, Douglas A., F. James Holler and Timothy Nieman. Principles of

Instrumental Analysis. Seventh Edition, 2018.

8. Dean, John A, The Analytical Chemistry Handbook. New York. McGraw

Hill, Inc. 204.

88