Electrochemistry Basic Concepts

7/30/2019 Electrochemistry Basic Concepts

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1. Introduction

1.1. Basic conceptsThe origins of electrochemistry can be traced back 200 years ago (1791) and is due to Luigi

Galvani who first performed an "electrochemical" experiment while dissecting a frog. Nine years later,

Volta discovered the first electrochemical cell, having salt water between two plates, made of silver

and zinc. In the following years, pioneering work of Nicholson (1800), Davy (1807 1808), Faraday

(1833), Kohlrausch, Hittorf, Arrhenius, Nernst and Leblanc in the XIXth century lead to the

development of electrochemistry as an important branch of science.

We can say that now electrochemistry deals with two major issues: the physical chemistry ofionically conducting solutions or pure substances (such as molten salts) the ionics and the physical

chemistry of electrically charged interfaces the electrodics. The ionics describes mainly ions and

solvents, as well as the interaction between them. The electrodics is concerned with the interface

between an electrode (metal or semiconductor) and an electrolyte and all the phenomena that happen

when such interfaces are brought together. In the following we need to define some basic concepts,

which will be encountered throughout the course.

An electrolyte is a substance, either dissolved in a solution or in a molten salt, that forms

charged species (ions). An electrode consists of a second phase (usually solid, e.g. a metal) which is

immersed in an electrolyte. The electrode charged positively, i.e. having a deficit of electrons, is called

the anode, while the electrode charged negatively, i.e. having an excess of electrons, is called the

cathode. The charged species in solution move towards the electrode having opposite charges and are

called cations (positively charged they move towards the cathode) and anions (negatively charged

they move towards the anode). The terms ion, anion and cation were introduced by Michael Faraday

in 1834.

The process of adding electrons to either an ion or a neutral species is called reduction, while

the reverse process (i.e., removal of electrons) is called oxidation.

1.2. Solvents and ion solvation

For many years, electrochemistry dealt mostly with aqueous solutions, but in time, with the

development of electrochemistry, non-aqueous solvents became important as well. The aluminum

industry for example is entirely based on electrolysis in a molten salt system (fused cryolite). There arethree types of solvents used in electrochemistry, outlined below.


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1. Molecular solvents which consist of molecules. The forces between solvent molecules range from

hydrogen-bond type (water) and other type of "bridges" (oxygen, halogen) these are highly polar

solvents to dipole-dipole interactions (moderately polar liquids, e.g. acetone) and van der Waals

interactions (non-polar liquids, such as hydrocarbons). The latter solvents are dielectrics and do not

conduct appreciably; in some of them the autoionization phenomenon occurs, conducting electricity

to some extent (very little however):

2H2O H3O+ + OH; 2HgBr2 HgBr

+ + HgBr3; 2NO2 NO

+ + NO3;

2. Ionic solvents which consist of ions, and are mostly molten salts. Not all salts yield ions when

fused, some form instead molecular liquids (like HgBr2). Usually, molten salts exist at high

temperatures (at standard pressure, NaCl is liquid between 800 and ca. 1450 oC), but in the past years

"room-temperature" molten salts were discovered, which have low melting points (ethylpiridinium

bromide, -114 oC, tetramethylammonium thiocianate, -50.5 oC). In some cases, mixtures of salts

(called eutectics) have also low melting points, such as the AlCl 3 + KCl + NaCl in the ratio 60:14:26

(mol %) which melts at 94 oC. The ions in these melts can be monoatomic (like Na+ and Cl) or

polyatomic (molten cryolite, Na3AlF6, contains Na+, AlF6

3, AlF4 and F ions).

3. Polymer solvents which contain polymeric chains capable of dissolving salts. These are (almost)

solid electrolytes and they are very important in the manufacturing of solid-state batteries and any

other practical device that needs a solid electrolyte. The most important solvents of this type arepolyethylene oxide (PEO) and polypropylene oxide (PPO). Ions are dissolved by coordination of the

cation by electronegative heteroatoms (such as oxygen), the anions surrounding the polymer chain

which adopts a helical structure (Figure 1).

CH

2

CH

2

O

n

CH

CH

2

O

n

CH3

PEO PPO

O

Li+

O

O

O

O

O

O O

O

Li+

ClO4_

ClO4_

2

2


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Figure 1. Schematic structure of a PEO LiClO4 "complex".

In a fluid medium, most commonly used in electrochemistry, the dissolved ions interact

strongly with the solvent molecules: the higher the dielectric constant of the solvent, the stronger the

interaction. The solvent-solute interaction is called solvation (orhydration, if the solvent is water).

The energy changes accompanying this interaction are very large for ions (~ 400 kJ/mol for single

charged ions), and much smaller for non-polar species (~10 15 kJ/mol). Transport parameters, such

as ionic mobilities and diffusion coefficients, are influenced by the solvation: the ion does not move

alone, as a single entity, but carries some solvent molecules (in some cases quite many of them) with

it.

Figure 2. Schematic of a hydrated cation, showing the different water layers surrounding the

cation.

1.3. Electrolysis, Faraday's law and electrode types.

The electrolysis is an (electro)chemical process which occurs due to the passage of electric

current through an electrolyte by applying a large enough voltage between two electrodes.

According to Faraday's law, the amount of substance transformed during the passage of current

is related to the charge:

m =KQ =

0

)( dttIK =KIt(at constant current)

3

3

Primary hydrationshell

Disorganized

water

Secondaryhydration shell

Normal water


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where Q is the charge passed,Iis the current, tis the electrolysis time and Kis the equivalent of the

substance:

nF

A

nF

MK == or

nF

AK=

where M is the molar mass of the substance (atomic mass, A, if we deal with an element), F is the

Faraday constant (96487 C/mole) and n is the number of transferred electrons.

(A) (B)

(C) (D)

Figure 3. Common electrode processes. (A) simple electron transfer; (B) metal deposition;

4

4

Cu2+ Cu2+

Cu

Cu

Cu

Cu

Cu

Cu

Cu

ELECTRODE

SolutionCu

e

Fe2+

Fe3+Fe3+

Fe2+

Solution

e

ELECTRODE

Cl2

E

LECTRODE

ClCl

ClCl

ClCl

e

e

Solution

e

PbSO4

H+H+

SO4

2SO4

2

Solution

E

LECTRODE

PbO2


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(C) gas evolution; (D) surface film transformation.

Some examples of common electrode processes are shown in Figure 3.

(E)

(E)

Figure 3. Common electrode processes. (E) anodic dissolution.

2. Ionics

2.1. Ion migration and transference numbers

Although positive and negative ions are discharged in equivalent amounts at the electrodes, the

anions and cations do not necessarily move with the same velocity in an electric field. The total

amount of ions, and hence the corresponding quantity of electricity, carried through the solution is

proportional to the sum of the anion and cation velocities.

Ifu+ is the absolute migration velocity (ormobility) of the cation and u- for the anions (in the

same solution), the total amount of electricity passed will be proportional to the sum u+ + u-. The

amount of electricity carried by each ionic species, Qi, is proportional to its own mobility. The fraction

of current carried by each ionic species is called transference (ortransport) number, and for a 1:1

electrolyte it is given by the simple equation:

+

+

+ += uuu

t and+

+=

uu

u

t ; t+ + t- = 1 (1)

In general, for az+:z- electrolyte, one can write:

5

5

Solution

ELECTRODE

Fe2+ Fe2+

Fe

e


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+++

+++

++

=uczucz

uczt and

+++

++

=uczucz

uczt (2)

Ifz+ =z- = 1 (1:1 electrolyte), then c+ = c- as well, and we recover eq. (1).

Obviously, the faster the ion, the greater its contribution to the total current. If, and only if, the

mobilities of anions and cations are exactly the same, the current will be transported in the same

proportion (50%) by each species. To calculate the transference number one does not need the

absolute mobility of an ion, but only the ratio between the two mobilities. The transference numberis

notconstant with concentration, because the mobilities change with changing the concentration (due to

ionic interactions see ). As a rule, if the transference number is close to 0.5, it changes only slightly

with concentration. Also, if the transference number for the cation is less than 0.5, then it decreases

with increasing concentration , while ift- > 0.5, it increases with increasing concentration.

The mobilities u represent the migration rate of an univalent ion under a potential gradient of 1

V/m and can be calculated through a force balance: the electric force must balance the frictional force

of movement in the fluid medium. The electrical force can be written as:

Fe =zeE (3)

whereEis the electric field (dV/dx)

The frictional force is assumed to be given by Stokes law for spherical particles:

Ff= 6rv (4)

where is the solution viscosity (for dilute solutions it can be taken equal to the solvent's viscosity), r

is the radius of the ion and v is its speed (in m/s). From the balance of the two forces (i.e., equality of

eqs. (3) and (4)) one obtains:

zeE= 6rv, or rze

E

vu

6== (5)

Eq. (5) holds well for large ions, but large deviations are seen for small ions, as Stokes' law is

not appropriate to describe the movement of very small particles. One can define also an effective

hydrodynamic radius if the mobility is known:

i

i

iu

ezr

6= (6)

As with eq. 5, the hydrodynamic radius is close to the real radius (including the solvent

molecules in the solvation shell!) for large ions, but it is usually larger for small ions.

2.2. Measurement of transference numbers

In metallic conductors the current is carried by electrons only, and for such conductors one can

write t- = 1 and t+ = 0. For electrolyte solutions it is often difficult to guess a priori what fraction of the

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current is carried by positive and negative ions. The simplest method for measuring transference

numbers is due to Hittorf, and it is called actually the "Hittorf's method". In general, the number of

equivalents removed from any compartment during the passage of current (or electrolysis) is

proportional to the speed of the ion moving away from it:

+==u

u

anionofspeed

cationofspeed

tcompartmencathodefromlostsEquivalent

tcompartmenanodefromlostsEquivalent(7)

The total number of equivalents lost from both compartments, which is proportional to u+ + u-,

is seen to be equal to the number of equivalents deposited on each electrode; hence:

lossFaradaicelectrodesbothfromlostsEquivalent

tcompartmenanodefromlostsEquivalentt

uu

u===

++

+

+

(8)

and

lossFaradaicelectrodesbothfromlostsEquivalent

tcompartmencathdefromlostsEquivalentt

uu

u===

+

+

(9)

Figure 4. Hittorf's apparatus for determining transference numbers.

The two expressions provide a basis for experimental determination of transference number by

the Hittorf method (1853). A schematic diagram of a Hittorf cell is shown in Figure 4. Stirring is

performed only near the anode and cathode, in order to enhance the mass transfer, while the central

part is not stirred. Consider such a cell which is filled with a e.g. HCl solution and let as assume that

we pass 1 Faraday charge. The current is carried across the cell by the flow ions, and in view of the

definition of the two transference numbers, the passage of 1 Faraday of charge means that t+

equivalents of H+ move towards the cathode and t- equivalents of Cl move towards the anode. The net

flow across the cell's section is t+ + t- = 1 equivalents of ions, which corresponds to 1 Faraday of

charge. Obviously, the number of equivalents in the middle of the cell is not changed by the passage of

current. Let us consider now the changes that occur in the cathode region. The change in equivalent of

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H+ and Cl due to ion migration is given by the transfer across the cross section line. In addition to

migration, there is a removal of 1 equivalent of H+ through the electrode reaction (H+ + e H2).

The net change in the cathode compartment is:

change in equivalents ofH+

= electrode reaction + migration = 1 + t+ = t+ 1 = t- (10)change in equivalents ofCl = electrode reaction + migration = 0 t- = t- (11)

The passage of 1 Faraday results thus in the removal of t- equivalents of HCl from the cathode

compartment. In a similar manner, the change in the anode compartment is:

change in equivalents ofH+ = electrode reaction + migration = 0 t+ = = t+ (12)

change in equivalents ofCl = electrode reaction + migration = 1 + t- = t- 1 = -t+ (13)

Figure 5. Schematic of the Hittorf's cell showing the changes that occur in each compartment.

The net effect at the anode is the loss oft+ equivalents of HCl; the faradaic loss of material can

be easily measured using a coulometer. Thus, the experimental procedure for measuring the

transference numbers consists in filling the Hittorf cell with the desired solution (e.g., HCl) previously

measuring accurately its concentration. Then electrolysis is performed and the charge passed is

accurately measured. The anode and cathode compartments are drained and analyzed to give the

concentration after passing the current. The concentration change is related to the number of

equivalents lost during electrolysis. If the charge passed is not too large and if no mixing occurs in the

central compartment, then it is found that the concentration in the central compartment is unchanged.

The changes in concentration in the anodic and cathodic compartments will give the transference

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1 Faraday

+

Cl Cl2

H+ + e H2

t+

H+t+

H+

t- Cl

t- Cl


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numbers for the anions and cations; Table 1 shows some measured values for various electrolytes at

different concentrations.

Table 1. Transference numbers of cations at various concentrations in water solution.

c (mol/L)

Electrolyte 0 0.01 0.02 0.05 0.1 0.2

HCl 0.8209 0.8251 0.8266 0.8292 0.8314 0.8337

CH3COONa 0.5507 0.5537 0.5550 0.5573 0.5594 0.5610

CH3COOK 0.6427 0.6498 0.6523 0.6569 0.6609 --

KNO3 0.5072 0.5084 0.5087 0.5093 0.5103 0.5120

NH4Cl 0.4909 0.4907 0.4906 0.4905 0.4907 0.4911

KCl 0.4906 0.4902 0.4901 0.4899 0.4898 0.4894

KI 0.4892 0.4884 0.4883 0.4882 0.4883 0.4887

KBr 0.4849 0.4833 0.4832 0.4831 0.4833 0.4841

AgNO3 0.4643 0.4648 0.4652 0.4664 0.4682 --

NaCl 0.3963 0.3918 0.3902 0.3876 0.3854 0.3821

LiCl 0.3364 0.3289 0.3261 0.3211 0.3168 0.3112

CaCl2 0.4380 0.4264 0.4220 0.4140 0.4060 0.3953

1/2Na2SO4 0.3860 0.3848 0.3836 0.3829 0.3828 0.3828

1/2K2SO4 0.4790 0.4829 0.4848 0.4870 0.4890 0.4910

1/3LaCl3 0.4770 0.4625 0.4576 0.4482 0.4375 0.4233

1/4K4Fe(CN)6 -- 0.515 0.555 0.604 0.647 --

1/3K3Fe(CN)6 -- -- -- 0.475 0.491 --

2.3. Electrical conductivity of ionic solutions

Ionic solutions, just like metallic conductors, obey the Ohm's law (provided that the applied

voltage is not too large and no electrode reaction takes place), which relates the applied voltage to the

current flowing through the electrolyte solution:

R

VI = (14)

where Vis the applied voltage. The resistance of any uniform conductor is proportional to its length, l,

and inversely proportional to its cross section area,A, so that:

A

lR = (15)

The proportionality factor, , is called the specific resistance (or resistivity); in

electrochemistry the inverse of the specific resistance, = 1/, is more often used, and it is called

specific conductance, its units being -1cm-1, or Scm-1. In the same way, one can define the

conductance of the electrolyte solution, as the inverse of the resistance:

lA

R=1 (16)

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which is measured in -1 (also called Siemens, S, ormho, as the word "mho" is just the reverse of

"ohm").

Practical measurement of conductance require a cell with known values of interelectrode

distance (l) and electrode area (A), and therefore, since these values are constant for the same cell, theirratio is a constant called cell's constant. Thus, when measuring the conductance of a solution, we can

write that:

RA

l 1= = (cell constant)

R

1(17)

The cell constant is either known from the manufacturer, or it can be determined (as a

calibration procedure) by measuring the conductance of a standard solution for which the conductance

is known very accurately (e.g. a solution of KCl 0.02 M at 25 oC, having = 2.76810-3-1cm-1).

As the conductance of an electrolytic solution depends on the concentration (because the

number of charged species carrying the current usually increases as the concentration increases), it is

convenient to define a conductivity, called equivalent conductivity, which measures the conductivity

relative to the same equivalent concentration, thus allowing to compare different salts:

zc

=

1000eq (18)

where c is the molar concentration and z is the total(absolute) charge of positive and negative ions.

The factor 1000 is the transformation factor for the concentration (which in chemistry is usually

measured in mole per liter, while the equivalent conductivity is measured in Scm2mol-1). The molar

conductivity has been more often used in the past years (in an effort to stop using the normal, or

equivalent, concentration, which is often a source of confusion), defined as:

c

1000c

= or

c

=c (19)

(in the last relationship, one should remember that the concentration must be given in molecm-3 !).

We should also mention that all the quantities defined above for solutions can be used formolten salts too, which are also ionic conductors. Selected values for are shown in Table 2.

The large differences in conductivity between electronic and ionic conductors should be noted

and is due to the different conduction mechanism: in electronic conductors charge is carried by

electrons, which are small and consequently very fast charge carriers, while in ionic conductors,

charge is carried by mobile ions, which are massive and have therefore much smaller mobilities.

The conductivity depends on the concentration of ions and their mobility: more ions means

more charge, i.e., larger conductivity, while faster ones means more charge can move in a given time;

we can relate to the ion mobility by the following relationship:

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=i

iii cFuz2

(20)

Table 2. Electric conductivities for various conductors and electrolyte solutions.

Electronic conductors , -1cm-1

Cu 5.6105

Al 3.5105

Pt 1.0105

Pb 4.5104

Ti 1.8104

Hg 1.0104

Graphite 2.5102

Aqueous solutions , -1cm-1

0.1 mole/L 1 mole/L 10 mole/LNaCl 0.011 0.086 0.247

KOH 0.025 0.223 0.447

H2SO4 0.048 0.246 0.604

CH3COOH 0.0004 0.0013 0.0005

LiClO4 solutions , -1cm-1

Water 0.073 (1 M)

Propylene carbonate 0.005 (0.66 M)

Dimethylformamide 0.022 (1.16 M)

As the conductivity is expected to depend linearly with concentration, it would appear that

the molar conductivity does not depend on concentration. This is not true however; for weak

electrolytes, which are not totally dissociated when dissolved, this is obvious, as the concentration of

free ions depends on the total concentration in a non-linear manner. For strong electrolytes, like NaCl,

it is less obvious, but similar effects occur due to interaction between ions at relatively large

concentrations. Only for totally non-interacting ions would the molar conductivity be constant with

concentration, but this is only an ideal situation; real electrolyte solutions approach this behavior only

in the limit of extremely dilute solutions.For weak electrolytes it is easy to obtain a dependence of the molar conductivity on the

concentration. Let us consider for example a weak acid, HA, dissolved in water and write down the

equilibrium:

HA + H2O H3O+ + A

initial: c 0 0

equilibrium: (1 )c c c

where is the dissociation degree (0 < 1). The equilibrium constant (assuming that the water

concentration is very large and almost constant) is:

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=1

2cK (20)

Figure 6. Dependence of the molar conductivity on the square root of concentration for a strong

(HCl) and a weak (CH3COOH) electrolyte.

Figure 7. Plot showing the validity of Ostwald's law for CH3COOH.

Thus, for weak electrolytes the conductivity depends on the concentration because the ion

concentration is only c, with depending on concentration according to eq. (20). At the limit of very

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low concentrations (c 0) the dissociation degree is one ( 1); we can define a limiting molar

conductivity, 0, corresponding to c 0, and we can write:

c = 0 or0

c

= (21)

(note that from eq. 21, the molar conductivity for weak electrolytes decreases as the concentration

increases, but the totalconductivity, , usually increases. In many cases has a maximum at some

concentration, after which it starts to decrease, as an increase in the totalconcentration, c, will actually

lead to a much largerdecrease in c see Figure 6)

Using eq. 21 we can write eq. 20 as follows:

K=K + 2c orK

c+=

11

or

K

c

0

c

c

0 1

+=

(22)

from where, dividing by 0, we obtain:

K

c2

0

c

0c )(

11

+

=

(23)

which is known as the law of dilution (orOstwald's law). A plot of 1/c vs. cc will give a straight

line (Figure 7) with an intercept of 1/0 and a slope of 1/(02K), allowing thus to determine both the

limiting molar conductivity, 0, and the acidity constant,K.

For strong electrolytes the theoretical treatment giving the conductivity dependence on

concentration is quite complicated and involves elaborate computations. Ionic interactions and the

"electrophoretic effect" are considered, in order to give a complex dependence on the concentration.

The electrophoretic effect (which occurs also during the electrophoretic motion of charged colloidal

particles in an electric field whence its name) is due to the simultaneous movement of ions and their

ionic atmosphere: while the central ion moves in one direction, the counterions surrounding it move in

the opposite direction. All ions, including the central one, carry some solvent along (their solvation

shell), the net result being a slow down of the central ion. Thus, the molar conductivity decreases as

the concentration increases. In the limit of zero concentration, where ions are far apart and do not

interact with each other, the movement of cations and anions are totally independent: the presence of

cations does not influence in any way the movement of anions (and vice-versa). As a result, in this

region the molar conductivity of any strong electrolyte can be described as the sum of contributions

from its individual ions (the law of the independent migration of ions):

c =++ +-- (24)

wherei are the numbers of cations and anions per formula unit (+ =- = 1 for NaCl and CuSO4 while

+ = 1 and- = 2 for MgCl2). This simple result allows one to calculate to calculate the limiting molar

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conductivities of any strong electrolyte. In this concentration range, it was found empirically (by

Kohlrausch) that the conductivity of strong electrolytes varies with the square root of the

concentration:

c = 0 Kc1/2 (25)

which is known as the Kohlrausch's law; the theoretical description leading to the same equation was

made later by Onsager.

As the measurement of conductivity for a salt yields the totalconductivity, c, the individual

contributions from anions and cations, orionic conductivities (eq. 24) are obtained from transference

numbers measurements:

+

++ +

=t and

+

+

=t (26)

The measurement of electrolyte conductivity was initiated (and extensively performed

afterwards) by Kohlrausch and his coworkers, between 1860 and 1880. They used a Wheatstone bridge

(which is still used as principle for measuring conductivities even in modern electronic devices). As

d.c. voltages may often cause electrode reactions (thus introducing large errors), a.c. voltage is usually

employed when measuring conductivities, as it allows better accuracy. Thus, an a.c. voltage, having a

frequency of about 1 2 kHz, is applied in an a.c. bridge arrangement and the adjustable capacitance is

changed until the bridge is balanced and the impedance of the cell (from which the resistance can be

easily extracted) is determined.

Water is by and large a unique solvent for electrolytes, as it has several, quite important

features:

(a) water molecules are able to bond with its neighbors through hydrogen bonds, leading to a

highly structured solvent;

(b) it self-ionizes to a small extent, containing thus a small concentration of H+ and OH ions; it

can act as both a proton donor and proton acceptor;

(c) water is a small molecule, having a substantial dipole (this is why water is a verypolar

solvent, with a high dielectric constant), interacting strongly with charged species and thus being able

to solvate most ions; this is actually why most of the salts are dissociated in ions when dissolved in

water. Non-aqueous solvents are not able to solvate ions to the same extent as water (even when their

dielectric constant is higher, such as for dimethylformamide, they are much larger molecules and

therefore interact much less with ions), and incomplete ionization (orion pairing)commonly occurs

in such solvents.

(d) it is found virtually everywhere on earth, and it is the most common and cheapest solvent

available.

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When comparing solvents for ionic substances, two factors should be considered first:

(a) the ability of the solvent to interact with ions, which is related to its dielectric constant and

the size of the solvent molecule. Solvents with high dielectric constant and small molecules will

solvate ions better and will provide larger conductivities. The ion-solvent interaction is however very

important also, and in some cases, even solvents with very low dielectric constant (such as ethers) may

give reasonable conductivities when very specific ions are dissolved. For example, ions (I) and (II)

give reasonably high conductivities in solvents like tetrahydrofuran (THF) and tert-butyl methyl ether

(both having low dielectric constants), electrochemistry being thus accessible in such solvents.

O

B

CF3

CF3

4

B

F

F F

F F4

THF I II

(b) the solvent's viscosity, as it determines the ionic mobility. For example, propylene

carbonate has a high dielectric constant, and thus would be expected to give high conductivity

solutions, but as it is a rather viscous solvent, its solutions have quite low conductivities.

From a practical point of view, aqueous solutions are always preferred, whenever possible, as

they have better conductivities (and thus will lead to lower ohmic losses), while pure water is readily

available at only a fraction of the price needed for other solvents. For many applications though, water

electrochemistry is not possible and one must use other solvents, including molten salts (e.g., for

aluminum and silicon electrodeposition).

2.4. Practical applications of conductivity measurements

Determination of solubility by conductance measurements

Ifs is the solubility (in mole/L) of a sparingly soluble salt and is the specific conductivity of

this saturated solution, then:

s

= 1000

c (27)

The salt being only sparingly soluble, the saturated solution will be so dilute, that c will not

differ appreciably from the limiting value at infinite dilution, 0, hence:

s

= 1000

0 0

1000

=s

(28)

The specific conductivity, , can be determined experimentally, while 0 may be derived from

ion conductivities; thus, it is possible to calculate the solubility of the salt from eq. (28). This method

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can be used only if the solute undergoes simple dissociation into ions of known conductivity.

Conductivity titrations

When a solution of a strong acid, e.g. HCl, is gradually neutralized by a strong base, e.g.,

NaOH, the protons of the former are replaced by metal ions (Na+), which have a much lower

conductivity. The conductivity will therefore decrease steadily as the base is added. When

neutralization is complete, further addition of the base does not remove any more ions, but instead will

bring more ions, and thus the conductivity will start to increase. The conductivity change with

equivalents of base added has thus a minimum at the equivalent point (orend point), when the acid is

neutralized. In practice, the neutralization point is determined from the intersection of the two straight

lines that give the conductivity in the regions with excess of acid and excess of base ( Figure 8).

If the acid is moderately weak or very weak, the conductivity curve shows a different shape,

depending on the relative strength of the acid. If the acid is moderately weak (such as CH 3COOH), the

salt formed during the neutralization usually dissociates better than the free acid, and after a small

decrease, an increase is observed again. After the neutralization, the conductivity increases again, but

with a different slope. If the acid is very weak (such as boric acid or phenol), the conductivity

increases steadily, but again with a different slope after neutralization. In this case it is better to titrate

the very weak acid with a weak base, for which, due to its low conductivity, a (almost) constant

conductivity is reached after neutralization.

Figure 8. Conductivity titration curve for the neutralization of a strong acid with a strong base.

Conductivity titrations are rarely used nowadays, but the principle is used for ion

chromatography detectors, widely used as they allow an easy conversion of the concentration into an

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electric signal; conductivity measurements are also quite sensitive to low amount of ionic substances.

Precipitation titrations

When a NaCl solution is added slowly to an AgNO 3 one (or viceversa), AgCl, a sparingly

soluble salt, is formed. AgCl, being sparingly soluble will have a very small (almost negligible)

contribution to the total conductivity. As a result, the conductivity will remain almost constant until the

neutralization point is reached, after which increases sharply as the total ionic concentration increases.

2. Electrodics

Electrodics is a fundamental part of electrochemistry, and it deals with electrodes and

electrochemical reactions. Before the advent of various materials for electrodes, the electrode was

viewed as a metal in contact with an electrolyte, with current flowing at the interface

electrode/electrolyte. As now there are many non-metallic electrodes, we shall define an electrode as a

system comprised of an electronic conductor (metal, semiconductor, graphite or conducting organic

materials such as conducting polymers) and an electrolyte (not necessary liquid!) in contact with it.

A more sophisticated, and somewhat more rigorous, definition identifies an electrode as a system

consisting of two or more electronically and ionically conducting phases, switched in series, between

which charge carriers (electrons and ions) can be exchanged, one of the terminal phases being an

electronic conductor (e.g. metal) and the other an ionic conductor (e.g. electrolyte). The electrode can

be schematically denoted by these two terminal phases, e.g., Cu/CuSO4 solution.

2.1. Electrode potentials

When two phases, either of them containing charged species, a (electric) potential difference is

established between the bulk of these phases. According to electrostatics, the electric potential at a

point in space is defined by the work required to move a unit electric charge from infinity to that point.

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(Galvani potential

(Volta potential

(surfacepotential


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Figure 9. Fundamental electrode potentials used in electrochemistry.

In electrochemistry, there are several types of electrode potentials in use, in order to better

understand and define its behavior.

The Galvani potential (or inner potential), , is the work required to move a unit charge

from infinity into the given phase.

The Volta potential (orouter potential), , is the electric potential of an electrical charged

body which is defined as the work required to move a unit (electric) chargejustoutside the phase. The

term "just outside" is somewhat vague, but it can be viewed as a distance of about a thousand

nanometers outside the surface. The distance is chosen as to make the Volta potential notto have any

influence from the surface.

The surface potential, , is the work required to pass the charge across the surface layer. Th

main contribution to this potential arises from the electric double layer, which is always formed at the

interface between two phases containing charged species.

It is obvious that the sum between the Volta and surface potential must give the Galvani

potential:

= + (29)

The Volta potential, and the difference of such potentials between two electrodes, is directly

measurable and thus accessible to experimental data. By contrast, the Galvani potential cannot be

measured and thus it is inaccessible through experiments. However, Galvani potentials are vey

important in electrochemistry, since the "true" electrode potential is the difference between the Galvani

potentials of the electrode phase and the electrolyte phase. As the Volta potential can be measured, one

can say that the surface potential is also important, as one can obtain the Galvani potential from it.

Even though the Galvani potential cannot be measured, it can be estimated theoretically with a

margin of about 0.2 V: the error is quite large for most practical applications, but the estimates are

still useful in comparing various systems.

2.2. The electrochemical potential

The work associated with the transfer of charged species (electrons, ions) is composed of two

parts:

(a) First, the chemical environment of the particle is changed, regardless of the electric

potential difference at the phase boundary. The corresponding work (referred to 1 mole of component)

represents the chemical potential, i of the species in the given medium;

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(b) On the other hand, regardless of the change in the chemical environment of the particle, the

transfer across the potential difference is accompanied by electrical work.

The total quantity, combining the two above quantities, is the electrochemical potential, i~ ,

which is the total work associated with the transfer of 1 mole of the i-th component (having the chargez), from infinity into the given phase (Butler in 1926 and Guggenheim in 1930):

+= Fziii ~

(30)

The electrochemical potential, i~ , can be defined also as:

jnpTin

G

,,

i

~

~

= (31)

where G~

contains an electric component (namely, zF; actually it includes the sum for all

components).The electrochemical potential is thus a work (i.e., an energy), not an electric potential, and it

should be stressed out that the electric potential and the electrochemical potential, although related to

each other, are fundamentally different quantities.

In order to understand better the physical significance of the electrochemical potential, let us

consider a simple example: a Zn electrode immersed in a ZnCl2 aqueous solution and let us focus on

the Zn2+ ions in both metallic zinc and in solution. In the metal phase, the Zn 2+ ions are fixed in the

metal lattice, with electrons freely moving throughout the lattice. In solution, the Zn2+ ions are

hydrated, thus interacting with the water (more generally, with the solvent), while also interacting with

the Cl- ions. The energy state of the Zn2+ ions at any location clearly depends on the chemical

environment (solvent and counterions), which is manifested through short-range interaction forces. In

addition to this energy, there is also an energy required simply to move the +2 charge (disregarding

any chemical effects) to different locations, which may have different electric potentials. This energy

is clearly dependent on the electric potential at that specific location, hence it depends on the

electrical properties ofboth the environment and the ion (its charge).

2.3. More about electrode potentials

As we have already seen, the term "electrode potential" is a complex quantity, and it's meaning

is not so obvious only from its name. We can think of the electrode potential as the potential difference

between the electrode's surface and the region in the solution adjacent to the electrode.

All the practical methods of measuring the electrode potential involve the completion of an

electric circuit and, therefore, require a second electrode-solution interface. Thus, these measurements

always give the difference between potential differences at the two interfaces.

As the electrode potential is such a complex quantity, and their absolute values being

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experimentally inaccessible, electrode potentials are therefore expressed as the measured potential

difference between the electrode of interest and an arbitrarily selected standard. The electrode that

serves as the standard for potential is the Pt electrode at which an equilibrium between protons and

hydrogen is established (the activity of the protons in solution is chosen to be 1 mole/L):

H+ + e 1/2H2

This electrode is called the normal hydrogen electrode (orNHE) and serves as the reference

point for potential measurements in electrochemistry. The NHE consists of a platinized-Pt electrode (to

ensure a fast reaction and thus attaining the equilibrium fast) immersed in a solution with proton

activity equal to unity, saturated with hydrogen gas at unit fugacity (close to 1 atm pressure). By

definition, as this electrode serves as standard, its potential is 0 V at all temperatures. The sign of the

electrode potential is always the observed sign of the polarity when coupled with a NHE. Thus, the

term anodic of NHE denotes an electrode whose potential is positive. More recently, it was proposed

that the platinized-Pt type NHE should be replaced by a palladium electrode saturated with palladium

hydride (PdH0.3), which proves to be more stable, its potential being +50 mV vs. NHE.

To demonstrate the relation between the difference

2.4. The Nernst equationThe electromotive force of a cell reaction has also a thermodynamical interpretation. The link

between the electromotive force and the free enthalpy is:

G = nFE (32)

with G < 0 forE> 0. If all substances are at unity activities, then:

G0 = nFE0 (33)

whereE0 is the standard electrode potential.

Now, from a thermodynamic point of view, the free enthalpy change for a chemical reaction

can be expressed as (van't Hoff isotherm):

G = G0 +RTln(Q) (34)

in which Q indicates the ratio of activities of products to those of reactants (Q is also called the

activity quotient). If we substitute forG and G0, we obtain:

nFE= nFE0 +RTln(Q) (35)

which can be rearranged to give:

QnF

RTEE ln0 = (36)

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the well-known Nernst equation.

Thus, for a simple reversible oxidation-reduction process:

Ox + ne Red

where Ox and Red represent the oxidized and reduced forms, respectively, of a given species, onecan write:

R

O0 lna

a

nF

RTEE += (37)

where aO and aR are the surface (i.e. near the electrode) activities of Ox and Red species. E0 is the

value of the electrode potential when the surface activities are equal to one. From a practical point a

view, the use of standard electrode potential is somewhat restricted, as the knowledge about activities

in solution is quite limited. For this reason, E. H. Swift advocated the use of formal potentials,

denoted byE0', to replace the standard potential in practice. If one writes the activities as ai = ici, then:

R

O0

R

O

R

O0 ln'ln

ln

c

c

nF

RTE

c

c

nF

RT

nF

RTEE +=++= (38)

The formal potential,E0' is experimentally accessible, but it depends on the concentration of

Ox and Red, contrary toE0, as it contains the ratio of activity coefficients.

2.5. The thermodynamics of interfaces

Let us suppose that we have an interface of surface area A separating two phases and

(Figure 10). The region between the solid lines represents the interfacial zone. To the right we have

pure phase , while to the right we have pure phase . The intermolecular forces are short-range

forces, so the interfacial zone extends only over a few hundred angstroms. As this region is very

narrow, we can regard the perturbation of the properties of the pure phases and within this region

as properties of a surface, orinterfacial properties.

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A B

A' B'

Interfacial zone

Dividing surface

Pure Pure


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Figure 10. Schematic diagram of an interfacial region separating two phases, and . The

phases and can be any phases.

Let us now compare the real interfacial zone with an imaginary reference interfacial zone. In

the reference zone, we shall define a dividing surface, shown with a dotted line in Figure 10. The

position of the dividing surface is arbitrary and does not influence in any way the final results; it is

convenient though to consider that it coincides with the actual interfacial surface. With respect to this

reference, we shall consider that phase lies to the left from the dividing surface, while phase lies to

the right. The reason for defining the reference system is that the properties of the interface are

governed by excesses and deficiencies in the concentrations of components, i.e., we are concerned with

differences between quantities of various species in the actual interfacial region, with respect to the

quantities we would expect if the existence of the interface did not perturb the pure phases. These

differences are called surface excess quantities. For example, the surface excess in the number of

moles of any species, such as ions or electrons, would be:

R

i

S

iinnn =

(39)

where

in is the excess quantity and

S

in and

R

in are the numbers of moles of species i in the

interfacial region for the actual system and the reference system, respectively. Surface excess

quantities can be defined forany extensive variable.

One of these variables is the electrochemical free enthalpy. For the reference system the

electrochemical free energy depends on the usual variables: temperature, pressure and the molar

concentrations ofallcomponents, i.e., ),,(~~

RiRR npTGG = . The surface area has no impact on RG~

because the interface does not perturb the phases and . Therefore, there is no energy of interaction.

On the other hand, we know from experience that real systems have a tendency to minimize (or

maximize) the interfacial area; hence the free enthalpy of the actual system, SG~

, must depend on the

area. Thus, ),,,(~~ S

i

SS nApTGG = . If we write the total differentials:

+

+

=i

R

iR

i

RRRR dn

n

Gdp

p

GdT

T

GGd

~~~~

(40)

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+

+

+

=i

S

iS

i

SSSSS

dnn

GdA

A

Gdp

p

GdT

T

GGd

~~~~~

(41)

If we deal with experiments at constant temperature and pressure, we can drop the first two

terms in each expression. The partial derivatives (R

G

~/

Rin ) are the electrochemical potentials, i

~.

Since the system is considered at equilibrium, the electrochemical potential is constant throughout the

system forany given species. Since the electrochemical potential is the same in all regions, i.e. in the

pure phases and , it must be the same in the interfacial region:

=

=S

i

S

R

i

R

in

G

n

G~~

~ (42)

We can also define the partial derivative ( SG~

/A), namely as the surface tension, . The

surface tension is a measure of the energy required to produce a unit area of new surface, e.g. by

dividing the system more finely. Doing this requires that atoms or molecules previously in the bulk of

their phases be brought to the new interface. They have fewer binding interactions with neighbors in

their original phase, but may have new ones with neighbors in the opposite phase. Thus, the surface

tension depends on the identity ofboth phases, and .

Now we can write the differential excess free enthalpy as:

+==i

R

i

S

ii

RS nnddAGdGdGd )(~~~~

(43)

and from (39) we have:

+=i

ii dndAGd

~~

(44)

Eq. (44) tells us that the interfacial free enthalpy can be described (at constant pressure and

temperature) by the variablesA and ni, all of which are extensive.

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Basic Principles of the Kinetics of Electrode Processes

Electrode Processes as Heterogeneous Chemical Reactions

Electrode processes are heterogeneous chemical reactions, which occur at the interface of an

electrode (not necessarily metallic) and an electrolyte, accompanied by the transfer of electric charge

through this interface. The simplest electrode reaction involves an inert electrode (surface), two

electroactive species, O and R, completely stable and soluble in the chosen solvent and an excess of

inert, electroinactive, electrolyte:

O + ne R

O is an oxidized species while R is its reduced form. In general, even this simple

electrochemical process consists in fact of several steps, such as:

(a) electron transfer at the electrode surface;

(b) mass transfer (e.g., of O from the bulk solution to the electrode surface);

(c) chemical reactions preceding or following the electron transfer. Such chemical reactions

may be either homogeneous reactions, such as protonation (e.g., the dissociation of a weak acid) and

dimerization (when the species formed by electron transfer undergoes chemical change to form a more

stable product, e.g., 2H H2), or heterogeneous ones, as is the case with the catalytic decomposition

on the electrode surface;

(d) other surface processes, such as adsorption, desorption or phase formation. Adsorption

plays an important role in electrocatalytic reactions (e.g. the evolution of H2 on Pt electrode), as the

adsorption of reaction intermediates provides alternative lower energy pathways. Also, adsorption of

species which are not directly involved in the electron transfer process is sometimes used to modify the

net electrode reaction (e.g. additives used in electroplating and corrosion inhibition). The electrode

process may involve the formation of a new phase, e.g. the electrodeposition of metals in plating,

refining and winning (the electro crystallization step) or bubble formation when the product is a gas; a

transformation of one solid phase to another can also occur, for example the reaction:

PbO2 + 4K+ 30 ~ + 2 e PbSO4 + 2H2O

The formation of a new phase is itself a multistep process, requiring both nucleation and

subsequent growth; crystal growth may involve both surface diffusion and 3-D lattice growth.

According to Figura, the overall electrode process will consist of the following consecutive

steps:

1. - Mass transfer from the bulk of the solution to the layer in contact with the electrode to replace the

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ions or molecules. This takes place partly by ion migration, partly by diffusion (the replacement of

neutral molecules occurs by diffusion, only). Convection due to spontaneous or external mixing may

also contribute to the mass transfer.

2. The localization of ions or molecules in the region of the electrochemical double layer, dehydration

(in general, desolvation) and chemical reactions (possible in several steps) leading to intermediates

formation.

3. Adsorption of the intermediates.

4. Electron transfer, i.e., neutralization or formation of ions, or alteration of the ionic charge by

electron gain or loss. This is actually the electrochemical step.

5. The removal of primary products by desorption or product incorporation into the crystalline lattice

of the electrode (electrocrystallization, diffusion into the bulk of amalgam electrode, etc.)

6. Secondary conversion of the primary products in a reaction.

7. The departure of the products from the surface of electrode by mass transport. Diffusion is always

involved in this final step (convection as well when the solution is stirred).

From the above discussion it follows that the simplest electrode process involves three steps

only: mass transfer of the reactant, the heterogeneous electron transfer and a final step of mass transfer

of the product or electrocrystallization, etc.). A representative reaction of this sort is the reduction of

an aromatic hydrocarbon in an aprotic solvent, e.g.:

9,10-DPA + e- 9,10-DPA (dimethyl formamide as solvent)

9,10-DPA = 9,10-diphenylanthracene =

The electrode process is a special kind of heterogeneous reaction. The typical feature of

electrode processes, as opposed to other chemical reactions,is, the dependence of the activation energy

for the electron transfer step on the potential difference between electrode and solution. It follows that

in an electrochemical process, changing the potential implies changing the activation energy.

Moreover, as the potential can be easily adjusted, it means that we have an easy way of changing the

activation energy in a controllable manner, which is a great advantage. The second important feature

is that the rate of electrode processes is influenced by the structure of double layer at the metal/solution

interface.

Obviously, since the steps of general mechanism presented in the above figure are consecutive,

the rate of the overall process will be controlled by the "slowest step".

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Note that heterogeneous reactions at the electrode are described differently than homogeneous

reactions in chemistry: the reaction rate v has dimensions of moles-1cm-2, as this is asurface reaction

and not a bulk one (for which the reaction rate is expressed in moless-1cm-3). It is assumed that

electrode reactions are first-order processes, so v = kc. The heterogeneous rate constant, kmust be

measured in cm2/s if the concentrations are expressed in mole/cm3. The rate constant kis dependent on

the electric field close to the surface, and hence on the applied electrode potential.

Note also that the concentrations entering rate expressions are always surface concentrations,

CO(0,t) and CR(0,t), where t is time. Their values may differ from those in the solution bulk, CO(,t)

and CR(,t), and in many cases this difference is significant.

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ELECTRODE

mass transfer

mass transfer

chemical reaction

and/or desolvation

chemical reaction

and/or solvation

adsorption

or desorption

desorption

or adsorption

electron

transfer

electron

transfer


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IONICS

Migration

Transference numbers

The drift speed

Electrical conductivity of solutions

Debye-Huckel

ELECTRODICS

Electrode potentials

The electrochemical potential

Potentials and Thermodynamics of cells

Electrode potential the Nernst equation

The electrical double layer

Electrode kinetics basic principles

Electrode kinetics BV and microscopic treatment

Adsorption phenomena

Various special chapters and applications.

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Documents

Electrochemistry Basic Concepts