Introduction to UNIT 1 INTRODUCTION TO ELECTRO- Electroanalytical ANALYTICAL METHODS Methods

Structure 1.1 Introduction Objectives 1.2 Basic Concepts Electrical Units Basic Laws of Electrochemistry Potential Liquid-Junction Potentials Electrochemical Cells The Cell Potential 1.3 Classification and an Overview of Electroanalytical Methods Potentiometry Amperometry and Conductometry 1.4 Classification and Relationships of Electroanalytical Methods 1.5 Summary 1.6 Terminal Questions 1.7 Answers

1.1 INTRODUCTION This is the first unit of this course. This unit deals with the fundamentals of electrochemistry that are necessary for understanding the principles of electroanalytical methods discussed in this Unit 2 to 9. In this unit we have also classified of electroanalytical methods and briefly introduced of some important electroanalytical methods. More details of these elecroanalytical methods will be discussed in the consecutive units.

Objectives After studying this unit, you will be able to: • name the different units of electrical quantities,

• define the two basic laws of electrochemistry,

• describe the single electrode potential and the potential of a ,

• derive the Nernst expression and give its applications,

• calculate the electrode potentials and cell potentials using Nernst equation,

• describe the basis for classification of the electroanalytical techniques, and

• explain the basis principles and describe the essential conditions of the various electroanalytical techniques.

1.2 BASIC CONCEPTS Before going in detail of different electroanalytical techniques, let’s recapitulate some basic concepts which you have studied in your undergraduate classes.

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Electroanalytical 1.2.1 Electrical Units Methods -I Ampere (A): Ampere is the unit of current. This is so called in honour of the French Physicist and Chemist A.M. Ampere. It is abbreviated as ‘A’. One ampere is equal to the unvarying direct current which when passed through a silver nitrate solution, under certain specified conditions, will deposit silver at the rate of 0.00111800 g s -1.

Ohm (Ω): The unit of electrical resistance is called the Ohm in honour of the German physicist G.S. Ohm. The resistance offered by a uniform column of 106.300 cm long and with a mass of 14.4521 g with a direct current at 0 o C is equal to one Ohm.

Volt (V): The unit of electromotive forces (emf) and potential difference are called the in honour of Italian physicist C.A. Volta. The unit, volt, is derived from the units of current and resistance via Ohm’s law, thus, One volt is equal to the electromotive force which when applied to a conductor whose resistance is one Ohm will produce a current of one ampere.

Coulomb (C): The coulomb is the usual unit to express the quantity of electricity. The name has been given in honour of French physicist C.A. Coulomb. One coulomb corresponds to a constant current of one ampere flowing for one second.

Faraday (F): The quantity of electricity associated with one equivalent of chemical change in an electrochemical process is called the Faraday. One Faraday is equal to 96494 coulombs. It is named in honour of English Scientist M. Faraday.

Siemens (S): This is the unit of electric conductance. S = A/V

1.2.2 Basic Laws of Electrochemistry

Ohm’s Law The mathematical relationship among three fundamental electrical quantities, namely, (1) electromotive force, E (in ), (2) current strength, I (in amperes), and (3) resistance, R (in Ohms), is expressed by Ohm’s law. The law states that the current flowing in a conductor is equal to the potential difference between any two points divided by the resistance between them. That is, I = E/R or E = IR … (1.1)

Faraday’s Law Faraday’s law states that the quantity of current (Coulombs) associated with an transfer process is directly proportional to the number of equivalents of the substance involved in chemical change at the electrode. The number of equivalents are the number of moles divided by the number of taking part in electrons transformation reaction. It is expressed as: Q ∝ number of equivalents or Q= F × number of equivalents … (1.2) or QF= × number of moles/n … (1.3) Note that F could be defined as the quantity of where F is the Faraday constant and is equal to 96494 Coulombs, n is the electricity associated with number of electrons taking part in the electrical transformation reaction, such an Avogadro number of electrons. as considering the general reaction for reduction with n electron transfer:

O + ne R where O is the species being reduced and R is the reduction product.

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1.2.3 Electrode Potential Introduction to Electroanalytical The understanding of electrode potentials is essential in electroanalytical chemistry; Methods therefore, this will be discussed first. Whenever two dissimilar conducting phases are brought into contact an electric potential is developed across the interface. In order to understand this effect let us consider first a metal solution interface, which gives the origin of electrode potential.

Development of Electrode Potential Consider a metal M that is placed in a solution containing its M n+. The metal may be looked upon as being composed of metal ions and electrons. Both the phases, the metal and the solution contain metal ions M n+ but the activity of M n+ in the metal will be different from that in the solution and distribution of metal ions takes place in the two phases in order to get the position of equilibrium. We will consider, for two types of metals, one less active, for example copper, and the other more active say zinc by placing them in contact with their salt solutions. i) In case one, when a less active metal, say a piece of copper is placed in a solution of copper sulphate. Some of the copper ions may deposit on the copper metal, accepting electrons from the metal conduction band and leaving the metal with a small positive charge and the solution with a small negative charge. ii) In the second situation with a more active metal it will be the other way around, a few metal ions from the metal surface may pass into the solution phase, giving the metal a small negative charge and the solution a small positive charge. In both the above two cases, the positive and negative charges will be located at the surface of the metal solution phases, called the interface (see Fig. 1.1).

Fig. 1.1: Metal – Metal Interface As a result an electrical double layer is established with a corresponding potential difference between metal and solution, and is called the electrode potential .

Measurement of Electrode Potentials Unfortunately, there is no way of measuring directly the potential difference between an electrode and a solution. However, it can be measured, with respect to an arbitrarily defined . Such a reference electrode was first proposed by Nernst, known as standard hydrogen electrode (SHE) and was given arbitrarily zero potential (at all temperatures). By universal agreement among chemists the standard hydrogen electrode was chosen as the reference electrode.

Thus, the electrode, whose potential is to be measured, is coupled with a standard hydrogen electrode and the electromotive force (emf) of the resulting cell is the

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Electroanalytical electrode potential of the electrode being studied, the experimental conditions being Methods -I such that the liquid-junction potential is negligible. 1.2.4 Liquid-Junction Potentials When two different electrolyte solutions are brought into contact an electrical potential difference arises at the zone of contact. This potential difference is termed liquid- junction potential ( Ej) or diffusion potential. It is caused due to the diffusion of ions from regions of higher to lower concentrations depending on the concentration gradient and the individual mobility of each ion. Various types of liquid-junction

potentials are possible, one simple type of Ej is illustrated below.

Suppose we could prepare a quiet interface between two solutions containing the same electrolyte but at different concentrations, such as 0.1 M HCl and 0.01 M HCl. On making a contact of these two solutions, immediately, both H+ and Cl− ions diffuse from left to right (see Fig. 1.2) due to concentration gradient. However, hydrogen ions move much more rapidly than do chloride ions and is indicated by the longer arrow for H+ in Fig. 1.2. Thus, H+ outruns Cl − and there is a slight tendency for a charge separation with the right side of the junction acquiring a positive charge and the left side a negative charge.

Fig. 1.2: Liquid-Junction Potential The liquid-junction potentials may vary over a considerable range depending on the conditions of the cell. These potentials can be minimized by using a salt bridge containing a concentrated electrolyte solution of cation and anion having comparable mobilities. For example, potassium and chloride ions have comparable mobilities, and salt bridges of saturated aqueous potassium chloride, with agar gel, are widely used to minimize liquid junction potentials.

1.2.5 Electrochemical Cells An electrochemical cell consists of two metallic immersed in either the same electrolyte solution or in two different solutions that are in electrolytic contact. An electrochemical cell can operate to convert chemical energy into electrical energy or vice-versa depending on whether the cell reaction is spontaneous or force to occur in the non-spontaneous direction.

The cell in which the electrode reaction occurs spontaneously when the electrodes are externally connected by a conductor and it serves as a means of converting chemical energy into electrical energy is called the Galvanic cell or voltaic cell . Alternatively, the cell in which the cell reaction is force to occur in the non-spontaneous direction by passing the current through the cell from an external source to affect a chemical transformation is called the e lectrolytic cell . Some confusion is possible if we attempt to discuss both types at once. Therefore, we will confine our attention in this unit to galvanic cells. The discussion of cell will be made elsewhere.

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Galvanic Cells Introduction to Electroanalytical In a galvanic cell, the system comprises of two electrodes (half cells), processes occur Methods whereby the energy associated with chemical reactions is converted into electrical energy. In this way we can obtain a useful system upon which meaningful measurements can be performed. One such cell known as Daniell cell is illustrated in Fig. 1.3.

Fig. 1.3: A Galvanic cell (Daniell cell) The solutions of the two half-cells are connected with a salt bridge, say an inverted U-tube containing a solution of potassium chloride with agar gel. The zinc strip immersed in zinc sulphate constitutes zinc electrode, one half cell, and the copper strip immersed in copper sulphate constitutes copper electrode, the second half cell. The combination of these two half cells will give the complete cell. Such a cell was invented by Luigi Galvani . It was many of such cells developed to supply electrical energy before electrical generators were available.

When the circuit is closed, the cell operates spontaneously. The copper has a higher positive potential than the zinc, and electrons flow from zinc to copper in the outer circuit through the wire. The flow of electrons is called an . Conventionally, the flow of current is considered in a direction opposite to that of electrons, based on the consideration of potential, such that from a region of more Reduction occurs at the positive potential to a less positive (or more negative) potential. cathode. Oxidation occurs at the . The cell reactions are the oxidation and reduction products. At copper electrode, copper ions are reduced where electrons are consumed, and this is known as cathode . At zinc electrode, electrons must be supplied which is done by the oxidation of zinc and this electrode is called the anode .

It is reasonable to write the cell reactions in a logical manner following a convention such that the anode (negative electrode) is always on the left and the cathode (positive electrode) is on the right. The logic in writing in this way is that the chemical reaction taking place in the cell follows the way that occurs in it. In a more general way it is to say that the left hand electrode of the cell, as written, corresponds to the oxidation reaction i.e. reaction of supply of electrons to the external circuit; and the right hand electrode corresponds to the reduction, i.e. reaction for accepting electrons from the external circuit. The given cell is illustrated below:

2+ 2+ Left Zn Zn (a 2+ ) Cu (a ) Cu Right Zn Cu 2+ where, a single vertical bar indicates a metal solution interface and two vertical parallel bars indicate a liquid-junction and separate the two half cells. The two half cell reactions are:

2+ Zn (s)  Zn (aq) + 2e … (1.4)

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Electroanalytical 2+ Methods -I and Cu (aq) + 2e  Cu (s) … (1.5)

The net cell reaction can be considered as the sum of the two half reactions (1.4 & 1.5) and is,

2+ 2+ Zn + Cu  Zn + Cu … (1.6) The emf of a galvanic cell is the deference between the potentials of the two electrodes and the potential difference at the zone of contact of the two electrolyte solutions. The latter is usually termed the liquid junction potential. Thus, when there is no liquid- junction potential, the emf of the cell is, the potential difference between the two electrodes.

Ecell = Eright − Eleft … (1.7)

or Ecell = (Ecathode ) − (Eanode ) …(1.8)

where Eright is the potential of the right electrode and Eleft that of the left electrode. By the convention, all electrode potentials are reduction potential, therefore the negative sign in Eq. 1.8 is compensating for the electrode reaction occurring in the reverse

direction. Using the same convention, Ecell for the above discussed Daniell cell may be written as E = E − E ...(1.9) cell Cu 2+ / Cu Zn 2+ / Zn [Note :- The cell emf is always positive. The cell is, therefore, written in such a way

that Ecell is positive.]

SAQ 1 Fill in the blanks:

a) The reference electrode whose potential has been arbitrarily given a zero value at all temperatures is …………….. . b) A galvanic cell operates to convert ………… energy into ………….. energy and the cell reaction is ………………. . c) Cell diagram for the Daniell cell is ………………………………………………

SAQ 2 Write down the cell reaction for the galvanic cell represented below:

Pt Fe 3+ Fe, 2+ Cu 2+ Cu

………………………………………………………………………………………….. …………………………………………………………………………………………

1.2.6 The Nernst Equation The electrode potential of a couple varies with the concentrations of the reduced and oxidized forms of the couple. A quantitative relation between equilibrium potential and activities of the involved substances was given by W. Nernst in 1889. The relationship is called the Nernst equation.

Derivation of the Nernst Equation :

The first law of thermodynamics may be stated as:

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∆u = q + w … (1.10) Introduction to Electroanalytical where ∆ u is the change in the internal energy of the system and w the work done on Methods the system consider a reversible process taking place in a system at constant temperature and pressure in which both mechanical work (– P∆V ) and electrical work

(welec ) are done, i.e.

w = −P∆V + welec … (1.11) We know that for a reversible process at constant temperature the entropy change is q ∆S = that ,is q = T∆S … (1.12) T Substituting from Eqs. (1.11) and (1.12) into Eq. (1.10), we get

(∆u)T .P = T∆S − P∆V + wele … (1.13) Also, at constant pressure, the change in enthalpy ( ∆H ) of the system is given by,

(∆H ) P = (∆u) P + P∆V … (1.14) and at constant temperature, the change in Gibbs free energy ( ∆G ) is given by

(∆G) P.T = (∆H)T − T∆ S … (1.15) From Eqs. (1.14, and 1.15), we get

(∆G)T.P = (∆u)T, P + P∆V − T∆ S … (1.16) and now from Eqs. (1.13 and 1.16), we get

(∆G) P.T = T∆S − P∆V + wele + P∆V −T∆ S

That is, (∆G) P.T = wele … (1.17) Now considering a galvanic cell which has two terminals across which a potential difference is E, when a charge Q is moved through the external circuit, the work done is By convention the work done on the system is positive and by the system welc = EQ … (1.18) is negative. We know that, Q = nF … (1.19) where F is the Faraday constant equal to 96490 C, and is the charge on one mole of electrons, and n is the number of moles of electrons involved in the cell reaction. Thus, the work done by the system on the resistance is

welc = − nFE … (1.20) Combining with Eq. 1.17, we get that the free energy changes, or work done is – nFE. Hence, ∆ G = – nFE … (1.21) Considering a chemical reaction such as:

aA + bB pP + rR … (1.22) The change in free energy is given by the equation a p a r ∆ G = ∆ Go + RT ln P R … (1.23) a b aA aB

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Electroanalytical where R is the gas constant, T is the temperature on Kelvin scale and ∆ Go is the Gibbs Methods -I free energy change when all the reactants and products are in their standard state. For

standard conditions, Eq. 1.21 may be written as ∆ Go = – nFEo … (1.24) where Eo is the standard redox potential. Using Eqs. 1.21 and 1.24 to substitute for ∆ G and ∆ Go gives a p a r – nFE = – nFEo + RT ln P R …(1.25) a b aA aB After dividing both the side by – nF , RT a p a r Activity of a species is E = Eo – ln P R … (1.26) related to the concentration a b nF aA aB by a = γc Alternatively it can be written as reactant/product which require a change of sign in where γ is the activity before the ln terms, coefficient. It approaches a b unity as the concentration RT a a E = Eo + ln A B … (1.27) of an electrolyte nF a p a r approaches zero. Thus, we P R can assume at low 3.2 RT a a a b concentration it is equal to or E = Eo + A B …(1.28) log p r the concentration. nF aP aR The term ‘ln’ refer to natural logarithm (i.e. to the base). In practice, it is more convenient to use logarithm to base 10 (written as log). Equation (1.28) is the expression for Nernst equation for the chemical reaction 1.22.

Substituting the numerical values of R and F and making the approximation that activities and concentration are equal, at 25oC we get following form of Nernst equation: .0 0591 [A]a [B]b E = Eo + log … (1.29) n ]P[ p [R]r This is the form in which we commonly use the Nernst equation. To further understand Nernst equation, now we will take up few examples. Considering first a simple electrode, that is for a half-cell with metal-cation equilibrium

n+ n+ M + ne  M … (1.30) o .0 0591 [M ] E = E + log at 25 oC, the Nernst equation can be written as n []M .0 0591 []M = 1 E = Eo + log [Mn+ ] … (1.31) n E = Eo + .0 0591 log [Mn+ ] as the [M] is unity. Remember that the activity/concentration of a pure substance and an electron is unity and therefore they do not appear in the equation.

For a more general form of the redox reaction

xO + mW  yR + zZ … (1.32) where O is the oxidized species which is being reduced, R is the reduction product, W and Z some other species and x, m, y & z are the stoichiometric coefficients of the respective species, the Nernst equation for this reaction at 25 oC is

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.0 0591 [O]x [W]m Introduction to o Electroanalytical E = E + log y z … (1.33) n [R] ]Z[ Methods For the Galvanic cell (Eq. 1.6), at 25 oC, Nernst equation can be written as,

2+ o .0 0591 [Cu ] Ecell = E cell + log … (1.34) 2 Zn[ 2+ ] It can be applied for evaluating the emf of the cell.

Now consider following reaction:

− + 2+ MnO 4 + 8H + e5 = Mn + 4H 2O ….(1.35)

The Nernst equation for this half cell is

2+ o .0 0591 [Mn ] E − 2+ = E − 2+ − log ….(1.36) MnO 4 /, Mn MnO 4 /, Mn − + 8 5 [MnO 4 [] H ]

1.2.7 Cell Potential The potential difference between the two electrodes (half-cells) connected properly to form a galvanic cell, under conditions when no current flows through the system, is called the emf of the cell or cell potential . It is expressed in units of volts.

However, under the conditions when an appreciable current flows through the cell, the methods of measurement of cell emf result the voltage values lower than the cell potential this is because the passage of current allows the appropriate reactions to occur, hence changing the concentrations of solution species and lowering the potential difference between the two electrodes. Also Ohmic drops due to the flow of current through internal resistance of the cell may lower the voltage and providing the measured potential which is less than the potential expected under conditions of no current flow.

Since no method of measurement of potential is possible for a no current flow through the cell it is apparent that what we measure is the emf (or voltage) of the cell at an insignificant current flow as a close approximate of the cell potential. Therefore, the cell potential is measured by a null point method with a potentiometer which involves balancing the cell output emf against an identical and measured externally applied voltage under an insignificant current (practically no current) flow through the cell.

The cell potential of a system can also be calculated on a theoretical basis using the Nernst equation . These calculations can be done in two ways. In one way, we calculate the potentials of the individual electrode using the Nernst equation that is each half-cell (electrode) involves a separate reaction which is considered in isolation. The higher value of reduction potential that is more positive value (or less negative) of the potential of the electrode indicates that it will act as cathode and will be written on the right side, whereas the less positive value (or more negative) that is lower value of potential indicates that it will act as anode and will be written on the left side. Now, Standard electrode the cell potential is the difference between the two electrode potentials (neglecting the potentials of some liquid-junction potentials) such as: common half-cell reactions are given Ecell = Eright – Eleft … (1.37) Appendix A at the end of O In the other way, we calculate Ecell in a consolidated manner by first calculating E cell this unit. from the values of standard potentials of the individual electrodes: 0 o o E cell = E right – E left … (1.38)

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Electroanalytical Methods -I and then we apply the Nernst equation for the cell reaction to calculate Ecell (Equation 1.33). In both the ways the two half-cell reactions are to be written essentially in order to determine n, the number of electrons involved in the cell reaction. To further understand this, consider following examples

Example 1.1: A cell is set up as follows:

Zn Zn 2+ (a = 5 ×10 3- ) Cu 2+ (a = 2 ×10 2- ) Cu

o o The standard potentials are: E Cu 2+ / Cu = .0 337 V and E Zn 2+ / Zn = − .0 763 V

a) Calculate the cell potential.

b) Indicate the polarity of the electrodes and the direction of the spontaneous reaction.

a) The cell diagram specifies that the overall cell process involves the oxidation of Zn to Zn 2+ and the reduction of Cu 2+ to Cu metal.

The electrode reactions written as reductions are:

2+ o Zn + 2e  Zn .... (i) ; E = – 0.763 V 2+ o Cu + 2e  Cu .... (ii); E = + 0.337 V

The individual electrode potentials can be calculate by Nernst equation as:

o .0 0591 E = E 2+ + log a 2+ Cu 2+ / Cu Cu / Cu 2 Cu … (1.39) .0 0591 = .0 337 + log 2( ×10 −2 ) 2 = 0.337 – 0.050 = 0.287 V

o .0 0591 E = E 2+ + log a 2+ … (1.40) Zn 2+ / Zn Zn / Zn 2 Zn

.0 0591 E = - 0.763 + log (5 ×10 -3 ) Zn 2+ / Zn 2 = – 0.763 – 0.068 = – 0.831 V

It is apparent that the copper half-cell has a higher reduction potential, hence it will act as cathode. Obviously the zinc half-cell works as the anode. So that the interlinked half-cells will result in the reactions 2+ Cu + 2e  Cu, and 2+ Zn – 2e  Zn and an overall cell reaction will be

2+ 2+ Zn + Cu  Zn + Cu … (1.41) The voltage between the electrodes is established as: E E E E E cell = right − left = cu 2+ / Cu − Zn 2+ / Zn

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Introduction to Electroanalytical E = E 2+ − E 2+ cell Cu / Cu zn zn/ Methods

or Ecell = 0.287 – (– 0.831) = 1.118 V

Alternatively, the cell potential can be calculated from the expression a o .0 0591 Cu 2+ E = E cell + log cell 2 a Zn 2+

−2 o o .0 0591 2×10 =(E 2+ − E 2+ ) + log Cu / Cu Zn / Zn 2 5×10 −3 .0 0591 = {0.337 – (– 0.763)} + log 4 2 = 1.100 + 0.018 = 1.118 V b) The cell reaction, as written in Eq. 1.38, tends to occur spontaneously as having positive potential.

From Eqs. 1.38 and 1.39 it is clear that the copper electrode will be the positive terminal and the zinc electrode will work as the negative terminal of the cell.

SAQ 3 Calculate the emf of the cell in which the reaction is

+ 2+ Mg + 2Ag  Mg + 2Ag and where [Mg 2+ ]= 1.0 M [; Ag + ] = 1×10 −4 M,

o E Mg 2+ / Mg = − .2 363 V

o E Ag + / Ag = + .0 799 V

…………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………... …………………………………………………………………………………………...

1.3 CLASSIFICATION AND AN OVERVIEW 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 there techniques may be divided into two types on the basis of the procedures adopted for the analytical determination:

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Electroanalytical 1. methods in which little or no chemical transformation occurs and the Methods -I measurement of an electrical quantity gives a direct measure of 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 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, , etc. On the basis of above consideration the various electonalytical methods are classified and discussed briefly as below.

1.3.1 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 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 = (E ind − Eref ) + Ej …. (1.42)

where

Ecell is emf of galvanic cell,

Eind = half-cell potential of the indicator electrode,

Eref = half-cell potential of the reference electrode,

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

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Concentration of the solution is determined by a single measurement of cell Introduction to potential applying the Nernst Equation or from the calibration curve drawn for Electroanalytical Methods Ecell vs. logarithm of concentration of the species of interest, from the potentials measured for a series of solutions of known concentrations.

It is important that the indicator electrode should respond selectively to the species of analytical significance and this practical requirement has stimulated the development of many types of indicator electrodes. A common type of indicator electrode for potentiometric measurements consists of a metal in contact with a solution containing its ion. Such an electrode responds to the redox potential of a solution as established by the metal ion/metal redox couple. An inert metal, such as platinum, immersed in a solution containing an appropriate redox couple for example, Fe 3+ and Fe 2+ , can also be used to form an indicator electrode.

Several electrodes with good selectivity for specifications are based on the development of potential across a membrane. Electrodes of this type are referred to as ion-selective electrodes .

The glass electrode commonly used for pH measurement is an ion selective membrane electrode. The excellent selectivity and wide pH range of the conventional glass electrode makes the pH determination of the solution as an important analytical application of the direct potentiometry. The instrument used for this purpose is known as pH-meter which measures the potential of a glass electrode with respect to the external reference electrode and displays the output on a meter scale calibrated to read directly in pH (or with a digital pH read out) the potential of the glass electrode changes by 59 mV per unit change in pH. This will be discussed in further detail in Unit 3. b) 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. Let us consider a redox titration represented by,

R1 + O2  O 1 + R2 … (1.43) where R and O stand for the reduced and oxidized species respectively, the potential of such a system depends upon the ratio of [O]/ [R] (see the discussion in the Nernst Equation). If the above reaction (1.43) is stoichiometric we can plot the cell potential against the volume of titrant. Since the potential of the reference electrode remains constant, the variations of the potential of the indicator electrode are followed during titration and the end point is determined from the resulting titration curve. The indicator electrode should be such that it responds to a component (that is, the reactant or the titrant or the product) used in the titration. The amount of the reactant is calculated from the volume of titrant required to reach the equivalence point. The equivalence point is detected by an abrupt change in potential and can be determined by any of the following three procedures: i) tangential methods ii) first derivative methods iii) second derivative methods Further details of these methods will be discussed in Units 2&3.

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Electroanalytical 1.3.2 Voltammetry Methods -I 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 current potential characteristics are studied commonly, with the arrangement (Fig.1.4) in which the voltage applied to the cell C is adjusted by means of potentiometer P and the current through the cell is read on a galvano meter G.

Fig. 1.4: Circuit diagram for current-potential characteristics 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.

1.3.3 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 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) and 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.1.5) in a simple manner in which the voltage applied to the cell C is adjusted by

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means of a potentiometer P and the current through the cell is read on a galvanometer Introduction to G. Electroanalytical Methods

Fig. 1.5: 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 ionic species is reached. At this point the following reaction takes place,

n+ M + 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. 1.6).

Fig. 1.6: I-E curve for M n+ (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 ).

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Electroanalytical The factors affecting the diffusion current were examined by D. Ilkovic and he gave Methods -I the following equation which is known as the Ilkovic equation. 2/3 1/6 I d = 708 nm D ½ t c … (1.44)

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 M n+ in the solution and 708 is the combination of constants and conversion factors involved in changing in units taken into account.

Equation 1.43 gives a direct relation between Id and hence can be applied for quantitative measurements, we can write from equation 1.44,

Id ∝ c or Id = Kc … (1.45) where K can be evaluated by noting the current with a standard solution of the substance of interest.

The curve shown in Fig.1.6 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. Further details on polarography are given in Unit 8.

SAQ 4 Distinguish between voltammetry and polarography.

………………………………………………………………………………………...… ………………………………………………………………………………………...… ………………………………………………………………………………………...… 1.3.4 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 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. Modifications have been made by the use of an amperometric indicators. On plotting the data for current vs volume of titrant, we get straight lines having different slopes. The equivalence point is obtained by extrapolation of the linear segments to their intersection. The microelectrode (that

is, the indicator electrode) may be a i) dme or ii) a solid state platinum electrode or iii) a rotating platinum electrode or

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iv) an electrode of any other inert material Introduction to Electroanalytical One can dispense with a reference electrode by the use of twin microelectrode Methods procedure called biamperometry or earlier known as dead-stop end point titration. Further details of this technique will be discussed in Unit 8 of this course.

1.3.5 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 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 (). 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.

Practically the metallic deposits should be smooth and strongly adherent so that the process of washing, drying and weighing can be performed without mechanic loss of the deposit. The deposits are affected in the physical characteristics by temperature, current density and the presence of complexing agents. Many electrogravimetric deposits based on the use of complexing agents have been found to form smoother and more adherent films. Cyanide and ammonia complexes provide the best deposits. Further detail of this technique will be discussed in Unit 5 of this course.

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 the substance being determined may react in solution with another substance 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,

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Electroanalytical O + ne → R Methods -I 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 n = … (1.46) A 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 6.022×10 23 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 (1.46) 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 idt as shown in Fig. 1.7.

t Area = Q = ∫0 idt

Fig. 1.7: 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 ) 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.

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In these titrations, the titrant is generated at one of the electrodes. The reaction Introduction to may take place directly on the same electrode or on the other electrode. To Electroanalytical remove the interferences, when may occur, the reagent is separated from the Methods 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.

Coulometric methods will be discussed in further detail in Unit 5 of this course.

SAQ 5 Differentiate between potentiostatic coulometry and amperostatic coulometry.

………………………………………………………………………………………...… ………………………………………………………………………………………...… ………………………………………………………………………………………...…

SAQ 6

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

………………………………………………………………………………………...… ………………………………………………………………………………………...… ………………………………………………………………………………………...…

1.3.6 Conductometry Methods which involve the charge transport by the ions in solution (migration) are termed conductometric methods. Under these conditions the resistance of the cell depends upon the velocities of the ions and on the number of migrating ions. It is observed that the conductance of all cells, which is the reciprocal of the resistance of the cell, is approximately proportional to the concentration of the electrolyte. The principle advantage of this technique is its simplicity and relatively good sensitivity, however the selectivity is poor since the conductance of a cell depends on the concentration of all the ionic species in solution.

The principle of the Wheatstone bridge 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 electrode in the conductivity cell by electrolyzing the solution therefore, to avoid polarization an alternating current usually ac voltages of 3-6 volts with frequency of 50-1000 Hz are used. ii) A suitable conductivity cell (with two plating electrodes dipped in the solution) is placed in one end of the bridge in place of an unknown resistor. iii) Since the cell also acts like a small capacitor therefore to balance its capacitive reactance a variable capacitor must be inserted into the bridge. In the above discussion you have seen that the conductance is an additive property of ions in a solution. This principle is the essential basis for conductometric titrations, in which the change in conductance is related to concentration changes of the ionic species involved in the titration curve, varies from one type of titration to another.

In conventional conductometric methods, an ac frequency of 50-1000 cps is used. This procedure can be modified by using high frequencies (frequencies several mega cycles

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Electroanalytical per seconds) and the methods are called high frequency methods. In these methods the Methods -I electrodes are not in the intimate contact of the solution but are separated from the solution by the walls of the containing vessel or some other dielectric (insulating) material. The cell as a whole is now a composite of capacitors and resistor. The response of the cell will depend on (i) the frequency employed, (ii) conductance, (iii) capacitance, (iv) dielectric constant, and (v) the cell geometry. The behaviour of this type of cell is relatively complex, but titration curves with singularity at the end point are also obtained.

1.4 CLASSIFICATION AND 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 very few aspects but often the differences are important and require a good 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. 1.8. 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. 1.8: 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

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Introduction to 1.5 SUMMARY Electroanalytical Methods • An electroanalytical technique is based on the measurement of one or more electrical quantities and their magnitudes could be correlated with the nature, concentration or total amount of the analyte. In most of the cases, the name of the technique is based on electrical quantity measured or the unit of the measured electrical quantity. At least one technique, polarography is named on the basis of a particular type of electrode (dme) used.

• The understanding of electrode potential is of fundamental importance. It is measured with respect to an arbitrarily defined reference electrode, the standard hydrogen electrode whose potential was given zero volts at all temperatures.

• An electrochemical cell can operate to convert chemical energy into electrical energy or vice-versa depending on whether the cell reaction is spontaneous or forced to occur in the non-spontaneous direction. A galvanic cell having two appropriate half-cells operates spontaneously. The emf of a galvanic cell is the difference between the potentials of the two electrodes and the liquid-junction potentials. A quantitative relation between equilibrium potential and activities of the involved substances was given by Nernst. The relationship is called the Nernst equation.

• The various electroanalytical techniques are classified on the basis of the particular electrical variable or variables measured by keeping the other variables constant and the mode of mass transport. On the basis of these considerations the electroanalytical techniques are classified as: potentiometry, voltammetry polarography, amperometry, conductometry, coulometry, and electrogravimetry.

1.6 TERMINAL QUESTIONS

-1 1. A platinum electrode is immersed in a solution which is 10 M in KMnO 4 and -4 o 5×10 M in MnSO 4. Calculate the electrode potential at 25 C for pH zero o - 2+ (E MnO 4/Mn =1.51V).

2. What will be the value of Ecell when silver and copper electrodes with unit activities in contact, given that E0 Cu 2+ /Cu = + 0.337 V and E0 Ag /Ag= + 0.799 V

3. A constant current of 2 A was passed for 6 min. containing CuSO 4 solution. Calculate the grams of each product that was formed on each electrode assuming no other redox reactions.

4. Give a difference between: i) oxidation and oxidizing agent ii) reduction and reducing agent iii) a galvanic cell and an electrolytic cell iv) the and the cathode of a galvanic cell

1.7 ANSWERS Self Assessment Questions 1. a) Standard hydrogen electrode b) Chemical; electrical; spontaneous

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Electroanalytical Methods -I 2+ 2+ 2+ 2+ Zn Zn (a Zn ) Cu (aCu ) Cu c) 2. To get net cell reaction number of electrons must be balanced in both half-cell reactions. So you have to multiply half cell reaction (i) by two and then add both half-cell reactions Half-cell reaction for left hand electrode (oxidation): 2+ 3+ 2×(Fe  Fe + e ) … (i)

Half-cell reaction for right hand electrode (reduction): 2+ Cu + 2e  Cu … (ii)

Cell reaction: 2Fe 2+ + Cu 2+ 2Fe 3+ + Cu

3. Cell diagram is, (on the basis of E 0 values)

Mg Mg 2+ 1.0( M) Ag + 1( ×10 −4 M) Ag

Electrode reactions are 2+ Mg  Mg +2 e (oxidation) + 2×(Ag + e  Ag) (reduction)

+ 2+ Overall reaction is Mg + 2Ag  Mg + 2Ag

Nernst equation may be written as

+ 2 o .0 0591 [Ag ] Ecell = E cell log 2 [Mg 2+ ]

−4 2  o o  .0 0591 1[ ×10 ] = E + −E 2+ + log  Ag / Ag Mg / Mg  2 1×10 1

.0 591 =[].0 799 −(− .2 363 ) + log 10 −7 2 = .3 162 − .0 207 = .2 955 V

4. 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.

5. 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.

6. According to Faraday’s law

nA=Q/n F where Q + It

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Half-reaction for silver deposition Introduction to Electroanalytical Ag + + e Ag (s) Methods

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

Terminal Questions 1. At pH= 0, the half cell-reaction is

− + 2+ MnO 4 + 8H +5e  Mn + 4H 2O

Write Nernst equation, to calculate, the electrode potential

8 .0 059 [MnO − [] H+ ] E = Eo + log 4 5 [Mn 2+ ]

.0 0591 10 −1 × 18 = 1.51 + log 5 5×10 −4 =1.51+ 0.0591/5 log 2×10 2 =1.51+ 0.0268 =1.537 V

2. Cell diagram may be written as:

Cu Cu 2+ a( = )1 Ag + a( = )1 Ag

At unit activities of reactants and products 0 Ecell = E cell 0 o 2+ = E Ag+ / Ag – E Cu /Cu = 0.799 –0.337 V = 0.462 V.

3. The quantity of current, Q=I×t=2×6×60=720 C

At cathode Cu 2+ +2e Cu

Thus, 1 mol of copper is equivalent to 2 mol of electrons. According to

Faraday’s law nA = Q/n F

-3 nCu = 3.731×10 mol Cu

Mass of Cu = 63.5 × 3.731×10 -3 =0.2369 g.

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Electroanalytical Similarly at anode 2H O O (g) + 4e + 4H + Methods -I 2 2

Mass of O 2 = 0.0597g.

4) i) Oxidation is the process whereby a substance looses electrons, a oxidizing agent is a substance that acquires electrons in an redox reaction. ii) Reduction is the process whereby a substance acquires electron; a reducing agent is a supplier of electrons. iii) Galvanic cell: An electrochemical cell that provides electrical energy during its operation. Electrolytic cell: An electrochemical cell that requires an external source of energy to drive the cell reaction. iv) The anode of a cell is the electrode at which oxidation occurs. The cathode is the electrode at which reduction occurs.

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