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GOVERNMENT OF INDIAATOMIC ENERGY COMMISSION

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BASIC PRINCIPLES OF INORGANIC REDOX REACTIONSIN AQUEOUS SOLUTIONS

by~.rA, S. Ghosh Mazumdar

Chemistry Division

'if.

BHABHA ATOMIC RESEARCH CENTRE

BOMBAY, INDIA .... 'i

K.C. - 5 2 0

o GOVERNMENT OF INDIA'•? ATOMIC ENERGY COMMISSION

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BASIC PRINCIPLES OF INORGANIC REDOX REACTIONSIN AQUEOUS SOLUTIONS

by

A. S. Ghosh MazurndarChemistry Division

BHADHA ATOMIC RESEARCH CENTREBOMBAY, INDIA

1971

T A B L E q F JCONTENTS

Introduction j

Some General Ideas 3

Couples /Half-reactions 4

Oxidation State 5

Free Energy 6

Thermodynamic Activity 7

Hydrogen Reference Couple 9

Non-metallic Electrodes 9

Redox Potential 10

Variation of Potential with Activity 11

Conventions Regarding Sign 12

Potential Diagram 13

Disproportionation 15

Reversibility and Chemical Friction 15

Criter ia of Reversibility 17

Direct Measurement of Potential 17

Hydrogen and Oxygen Over-potential 19

Instability of Water towards H2 and O2 Evoluticn 21

Apparent Inertness of Oxygen in Oxidation Reactions 22

Free Radicals in Aqueous Solutions 23

Hydrated Electron and its Oxidation Potential 24

Relationship of Ionization Potential and Electron 27Affinity with Redox Fotential

Effect of Charge and Size of an Ion in Aqueous Reactions 29

References 31

Appendix: Table of Standard Potential of Redox Couples 32arranged alphabetic illy

BASIC PRINCIPLES OF INORGANIC REDOX REACTIONSIN AQUEOUS SOLUTIONS*

byA. S. Ghosh Mazumdar

INTRODUCTION

Water cannot be considered as an ideal solvent, mainly because of

its dipole character, which gives rise to clustering or polymerisation cf the

molecules leading to some anomalous properties like negative expansion co-

efficient at low temperature and so on. This dipole chaiacter again is respon-

sible for breaking down of the solute molecules into charged portions known as

ions. In other words, those solutes which readily dissolve in water lose their

original identity and often change their character in a very marked way, which

does not lead to a very happy situation for many fundamental investigations.

Finally, the narrow range of temperature within which water remains liquid,

viz. , 100°C, is also a serious limitation in regard to the activation energy

that can be furnished to aqueous reactions, particularly when we now possess

means of attaining almost any temperature we wish. No wonder, therefore,

that in modern technology the do-called high temperature or dry reactions and

non~aqueous reactions are becoming so popular. .

In spite of these limitations, however, the immediate future of water

as a solvent does not appear to be dark at all either in the industry or in the

laboratory. By virtue of its extensive occurrence, it is very difficult to dis-

lodge it from its position of a "universal solvent". Lastly, it would be real

•Summary of a talk given at a seminar arranged by the AnalyticalDivision, BARC, Trombay, on April 9, 1970

-2-

hard for mankind to lose interest in i material which constitutes more than

three fourths of its own biological system.

Inorganic chemistry , whether of aqueous systems or not, is a notorious

example where the vast mass of information concerning hundred and odd ele-

ments and an unlimited number of their compounds seem to be apparently un-

coordinated. Periodic classification is only an effort to coordinate them in

terms of a si igle pattern. Undoubtedly, the concept which is universally con-

sidered as the most fundamental one is that concerning the theory of atoms and

of sub -atomic particles. The atomic structure, energy levels of electrons are,

so to say, the bricks while the theory of probability and statistical laws form

the mortar of the super - structure of this branch of science. This approach,

though full of possibilities, is yet to be fully exploited.

Another very useful approach is that of thermodynamics, which r^ables

us to understand this science not in terms of intangible concepts involving

atomic structure, but in terms of parameters which can be directly measured,

e.g. , weight, volume, energy and so on. In the latter treatment, the finer

details of nuclear or atomic physics are very much sacrificed and only

average values are dealt with. Obviously, the domain of usefulness of these

two treatments may also be entirely different. For example, problems on

chemical equilibria, energy transfer and so on are better understood in terms

of thermodynamics, whereas problems connected with the structure of matter

and similar problems can be profitably investigated only in the light of the

other treatment.

Thermodynamics being neainly concerned with systems in equili-

brium, has another limitation that time does not form a variable in it, and

therefore, it does not directly concern itself with questions regarding the

mechanism of any overall process. Nevertheless, thermodynamics does con-

stitute the bed rock-on which stand all postulates involving kinetics and

mechanism, as we shall illustrate hereinafter. This is so because none of the

individual steps constituting the overall reaction can violate the basic laws of

thermodynamics. The object of the present talk would be to illustrate this

approach to systematisation, with examples of oxidation-radiation reactions

of inorganic ions in aqueous solutions. I would like to acknowledge that the

famous book of W. M. Latimer'*' will be freely used for this purpose.

Some General Ideas

Aqueous reactions are of different types, e.g. , (a) oxidation-reduction,

(b) acid-base, (c) complex-formation. All such reactions take place through

electron transfer, and are also often associated with making and breaking of

covalent bonds. Let us consider, for example, the well known reaction leading

to the formation of water from the elements oxygen and hydrogen.

2 = 2H 2 O. (!)

This o v e r a l l react ion, which is in fact the reduction of oxygen by

hydrogen to w a t e r can be v i sua l i zed to consis t of ve ry simple s teps as shown

below:

2H 2 —•-- ;= 4H (2)

o 2 .__.. 20 (3)

4H . > 4(H+

- 4 -

2(O + e~) > 2O" (5)

2(O" + e - ) > ZO~" (6)

4H+ + 2CV~ - > 2H,O (7)

Another alternative set for steps (6) and (7) would be

2(O" + IT+) - > 2CH (8)

2(OH * e") - ' - 2OH" (9)

Z(H+ + OH') ... , 2H2O (IP)

The steps (2) and (3) involve purely breaking of bonds and no chargt t ransfer ,

while (4), (5), (6) and (9) are examples of pure charge transfer (ionization and

electron capture in these cases), Though steps like (7) and (8) a re depicted

as examples of charge neutralization, yet the bonds formed may be to a large

extent co-valent in character , and therefore they a re somewhat like a mixture

of charge transfer and bond formation.

Couple s/Half-reactions

In lieu c : visualizing in the above fashion an overall reaction to con-

sist of so many elementary steps, some of which moreover may not have any

pract ical importance, chemists prefer to break it down into two steps, as

shown below, while talking about oxidation-reduction reactions:

2H2 = 4H+ + 4e~ (being combination of the steps (2) and (4) . . . (11)

andO2 + 4H+ + 4e~ = 2H2O (being combination of the steps (3),

(S), (6) and (7) . . . (12)

which, on adding up, give the overall reaction (1), 2H2 + O2 = 2H2O.

Each such step demonstrates at least in a formal way (the actual

- 5 -

process may not be exactly identical) as to how the electrons go from the

reducing agent to the oxidizing agent, and is known as a half-reaction or

couple. Every half reaction of a given element will obviously not contain any

species of another element, except of course H+, OH" or e", the former two

species arising out of necessity in aqueous solutions. It should further be

borne in mind that for the sake of simplicity in representation, none of the

above species are explicitly shown as hydrated, though they are known to be

so to various degrees, (e. g. , H in lieu of HjO+). Note that the energy of

the overall reaction is the algebraic sum of the energies of the two half

reactions.

Oxidation State;

In the following examples, sulphur from its elemental state changes

either to H2SO3 or to SO4";

S + 3H2O = H2SO3 + 4H+ + 4e" (13)

S + 4H2O = 8H+ + SO4"" + 6e" (14)

The number of electrons available in the above couples indicates the oxida-

tion number or the oxidation state of sulphur in H2SO3 which is 4, and that

in SO4 which is 6. "Oxidation state" of an element in a simple ion or in

any oxygenated Bpecies is another name of valency commonly used in

chemistry. In examples like H2O + HZSO3 = SO~+ 4H+ + 2e", the number of

electrons, however, represents only the change from one oxidation state to

the other.

- 6 -

Free Energy

Let us again take the example of reaction (1), ZH^ + Oj = 2H2O

When this reaction takes place quantitatively, that is, when 2 gm moled or

36 gms of water are formed from the elements, 136. 634 kilo-calories of

thermal energy is liberated. In thermodynamic language we say AH of •

the reaction is (- • • -•'—=•—-=) - 68. 317 kcal/gm mole. Now the whole amount

of £±H, for any reaction as a matter of fact, cannot be utilized for doing

useful work, i. e. , for driving a chemical reaction or for producing electrical

energy, and so on, since a certain portion of AH gets tied down to the

system, say, for maintaining the temperature (since the specific heats of

the products of reaction may not be the same as those of the reactants). The

amount of useful energy, otherwise known as free energy of a reaction, is

given by the thermodynamic relationship.

A F = A H - T A S (A)

where T stands for absolute temperature, and S for entropy, a thermodynamic

function. For our purpose it would be enough if we can lay our hand on the

known values of entropy given in standard tables readily available' ' . At

room temperature, therefore, the free energy of formation of water.

A F = 68,317 - 298X(16.716-31.211 - 24.501)

= 56, 695 calories

The symbol A F° is used when all gases involved in the reaction are at a

fugacity (thermodynamic pressure) of 1 atmosphere and all dissolved sub»

stances at an activity (thermodynamic concentration) of 1 molal, i. e. , 1

mole per 1000 gme of water.

- 7 -

The free energy of formation of a substance, often called the free

energy of the substance, refers to its formation from its elements. Note

that the free energies of all elements and H+ are taken as zero in their

standard states of unit activity.

Thermodynamic Activity

Before proceeding further let us briefly recapitulate a few elementary

ideas about this topic. If we dilute a solution of 1M of any compound, say,

from 500 ml to a litre with water, then its concentration is changed to half,

i. e. to 0. 5 M. The variation of the thermodynamic activity with dilution does

not, however, always follow such a simple rule of proportionality. The rela-

tionship between activity (a) and molality (M) is in fact given by the relation-

ship a = MV , where V is known as the activity coefficient. It is only at

infinite dilution that Y becomes unity, i. e. , activity equals molality. For

calculations of potentials or free energies in dilute solutions, therefore, one

may use concentrations in lieu o£ activity, but for the highest accuracy it is

necessary to make use of values available in standard tables'3'.

Since it is not possible to measure the activity of one ion independent

of an ion of the opposite sign, the information required is the mean activity

a_+. The activity of a salt which ionizes according to the following equation

A = p+ A+ + p^ A"

is defined as a = a|+ x a?

The geometrical mean of positive and negative ion activities is given by

a+ * (a)1 / p where p = p+ + p_ - • • • (B)

- 8 -

Example:

A12(SO4)3 = 2A13+ + 3(SO4)2"

a = (2M)2 x (3M)3 = M5 x 22 x 33

= (a+) , assuming very low molality (M)

a+ = M(22 x 33) * / 5

If a similar definition is given to mean molality

M± = M(P +P + x P _ P - ) 1 / p . . . . (C)

then mean activity coefficient is defined as

M±

This coefficient may be considered as the thermodynamic degree of disso-

ciation and becomes, as mentioned before, equal to unity at infinite dilution

for all types of salts.

Empirically, it is known that in a mixture of electrolytes, the activity

coefficient of a salt is determined by the average ionic strength, M , of the

positive and negative ions, defined as

M _ Z? M+ + Z2 M . _ 2

2

where Z is the charge on an ion. For instance, the A-i of

of molality M

_ 2Mx 32 + 3Mx 2?

In dilute solutions, the activity coefficients of a given strong electrolyte

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are the same in all .solutions of the same ionic strength. Large deviations

occur at high concentrations.

Hydrogen Reference Couple

There are major difficulties in measuring the absolute value of the

free energy of any individual couplev ' . But since any chemical reaction

involves only the algebraic sum of the energies of two coupleB, th^ absolute

values are unnecessary. For this reason, it is a common convention to

choose free energy of some one couple as an arbitrary zero and use this as

a reference couple for the free energy of all other couples. The reference

couple so chosen is the hydrogen ion-hydrogen gas couple:

2H+ + 2e" = H2, AF° = 0 , (15)

This choice Is consistent with the assumption made earlier that <> F° for

H+ is zero (See reference 5 for a discussion of the implications of this

assumption).

Non-metallic Electrodes

The hydrogen couple is thermodynamically reversible, but the rate

at which equilibrium is reached is generally slow. In presence of a suitable

catalyst, however, the reaction becomes rapid, and then one can make use

of this as a reversible working electrode. The electrode consists of hydrogen

gas in contact with hydrogen ion on a platinized platinum surface, all con-

tained in a suitable receptacle, the platinum serving for electrical connections.

Platinum surface is platinized for the purpose of catalysis. When the

pressure of hydrogen gas is exactly one atmosphere and the activity of

hydrogen ion in solution is 1 molal, this electrode is known as a normal

-IP-

hydrogen electrode. Use of platinum, gold and similar non-attackable metals

is in fact very common in the construction of non-metallic electrodes (or

half cells) e. g. H+/H2, V+++/V++, S2C>8"~/So|~ , e t c .

The potential of the couple, depending upon the relative concentrations of the

oxidizing and reducing species is impressed upon the inert metallic electrode

and can be readily measured directly in the same way as any other metallic

electrode e.g. , Cu/Cu++, Ag/Ag , as we shall see later.

Redox Potential

In lieu of expressing the free energy in thermal units like calories,

it is often convenient to express the same in electrical units while talking of

half reactions which are associated with the transfer of electrons. Following

Faraday's laws of electrolysis, the equivalence between thermal and elec-

trical units is given by

A F(joules) = — E.n. 96,484 (F)

Z\ F(cal) = ~ E . i i . 23,060 (G)

Where E stands for the potential difference (if we are able to set up a cell

with two half reactions taking place in the tv*o electrode compartments)

between the two couples constituting the overall reaction, and n stands for

th number of equivalents (or the number of electrons taking part in the

reaction). Redox potential of a couple may therefore be defined as the free

energy expressed in volts per equivalent taken with reference to hydrogen

couple.

Since the relative driving force of various couples is determined by

the potential values, a table of these values for different couples (see the append!

- 1 1 -

for the more impor tan t ones or any chemistry reference book) is of immense

value to chemis t s . Even with a v e r y elementary knowledge of thermodynamics,

one can make u s e of such a table for answering many of the qualitative

quest ions involved in the interpretat ion of inorganic chemistry. The familiar

"Elec t rochemica l s e r i e s of m e t a l s " in fact consis ts of redox potential values

arranged in a certain order.

Variation of Potential with Activity

Let us consider a thermodynamically reversible reaction:

aA + bB + £-$. cC + dC +

For an appreciable process, under constant temperature and pressure, as

we normally come across in aqueous reactions, the free energy change is

given by the well known Van't Hoff isotherm:

(a c ) c (aD)d

&> F = ^ F + RTln( a A . ) a ( a B ) b

= A F ° + RTlviGL (say) (H&

Where a A e tc . , r epresen t the thermodynamic activit ies of A, B etc.

A F ° depends upon the standard s tate chosen (say 1 molal), but once the

la t te r i s chosen, the former would remain constant. When equilibrium is

attained, i. e . , when no chemical reaction is taking place, A F = O, and

Q=K, the equi l ibr ium const.

Thus A F ° = - R T l n K = -1364.3 log K at 25°C (J)

Moreover, s ince , A F =&F° + RTlnQ,

the re fo re , - E n . 2306P = - E ° n 23060 + RTlnQ

or E = E ° — ° 0 5 9 1 6 log. n Q at room tempera turen ^

-12-

This is commonly referred to as Nernst equation, from which the potential

at any pressure and concentration can be calculated from known E values.

At equilibrium, since. E = O,

E°= ° - ^ 9 1 6 l o S l 0 K (L)

Conventions Regarding Sign

When we say that AH or A F of a. certain reaction is negative, we

imply that the process is exo-energetic and therefore spontaneously possible

at least theoretically. If A F is - v e for O2 + 2H2 = 2H2O, then for the

reverse reaction, 2H2O = O2 + 2H_ A F becomes positive, the numerical

value of A F remaining unaltered. In the case of potential values of com-

pleted reactions, on the other hand, a + ve value would indicate an exo-

energetic process, as would be seen from the relationship (F) or (G).

In the case of a couple, when we quote a value for potential, some

confusion might arise regarding its sign unless we write down the couple

explicitly. For example

O2 + 4H+ + 4e~ = 2H2O, E° = +1. 229 v

2H2O = O2 + 4H+ + 4e", E° = -1 . 229 v

In potential tables, compiled by European authors, the values refer to couples

written with electrons on the left side of the equation, while opposite is the

case with the American authors. In the European system, a stronger oxidi-

zing agent will have more positive value, while in American system a

stronger reducing agent will have more positive value.

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Potential Diagram.

When an element exists in Beveral oxidation states, it is sometimes

convenient to summarize the values of potentials relating the various states

in the form of a diagram, which is helpful for correlating the chemistry of the

element. An example of such a diagram is given

Oxygen potential diagram in acid solutions

1M H+

+ 1.229

-0. 13 +1.5 + P. 72 +2.82

OH + H2O 2H2O

+ P. 67 +1.77

The numerical values stand for the E° values relating the oxidation

states, e. g.

i HO2, E° = - P . 13 v

H2O2 f 2H+ + 2e" = 2H2O, E° = + 1. 77 v

As -written at the top of the diagram, these potential values refer to QB J =

1M in the solution. If values at some other pH are required, then the

same may be calculated using the Nernst equation. From such diagrams, one

can at a glance have an idea of the salient chemical properties of the element,

and of its compounds. For example, the above diagram immediately shows

that H7O, can act both as a reducing agent (itself getting oxidized to Ov) and

as an oxidizing agent (itself getting reduced to H2O). The numerical values

-14-

moreover show that coupler having potentials less positive than + 0. 67 v

(in the European convention) cannot be reduced by H2O2 and therefore should

be oxidized, while those more positive than + 1.77 v should, for similar

reasons, be reduced by H2G2 '

Sn4+H

H 2 O 2

Sn4+H

Similarly

- 2e" =

+ 2H+ -

L T T f*\

Sn2 + ,

f 2e" = 't

+ 2K+ =

E° =

! H 2 O l

Sn2+

+ 0

E°

+ 2H

. 15

- +

[2O,

1.

E

77

1.62 v (16)

S2O82" + 2e" = 2SO4

2", E° = +2. 01 v

H2°2 ~ °2 + 2H+ + 2e"' E ° = "°- 67 v

H2O2 + S2Og2- = 2SO4

2 -+O2 + 2H+, E°=+1.34 v ' (17)

The positive valueB of the potentials indicate that the reactions as written

can take place spontaneously. As regards the couples lying in between 0. 67 v

and 1.77 v, there could arise three possibilities: (a) the stronger oxidizing

agents like MnO4"~ (E° for MnO4~~/Mn++ = 1. 51 v) would be reduced, while

(b) the reducing agents like Fe++ (E° for Fe3 + /FeZ + = <\ 77 v) would be mainly

oxidized; (c) the intermediate couples on the other hand would provoke cata-

lytic dicomposition of H2O2, as in the following case:

Br2 + H2O2 = 2H+ + 2Br" + O2> E° = + 0. 39 V

H2O2 + 2Br" + 2H4" = Br2 + 2H2O, E° = + 0. 70 V

So that the net result is

2H2O2 = O2 + 2H2O, AI'° = -50. 44 K cal

(E° = +1.1V) (18)

More than one type can also proceed simultaneously under certain

circumstances.

-15-

Dlsproportionation

The reaction (18) of hydrogen peroxide discussed just now can be

considered as an example of disproportionation, where one molecule is

oxidized at the same time aB another in reduced.

2H2O2 = O2 + 2H2O, A F° = -50. 44 K cal.

There are, however, many known reactions where disproportionation takes

place without any catalyst. For example, in the caBe of uranium

UO2+ = UO2

++ + eT E° = - 0. 06 V

+ + + e~= U4+ + 2HO, E° = 0. 58 V

giving 2UO2+ + 4H+ = UO2++ + U4+ + 2H2O, E° = + 0. 52 V (19)

Thus, in a solution of 1MH pentavalent uranium is unstable towards diB-

proportionation, two molecules of U(V) giving one of U(IV) and another of

U(VI). This reaction is, however, hydrogen ion dependent, Thus at

pH=3, when the potential changes to —0. 19 V, U(V) become stable.

Reversibility and Chemical Friction

In all the discussions above, the equations of thermodynamics, which

are applicable only to systems in equilibrium or reversible processes, have

been taken for granted. There are, however, many dynamic processes,

which may not be reversible and where additional complications arise due to

what can be described as chemical friction, similar to mechanical friction.

The magnitude of friction in either case depends upon the speed and can be

ignored in statics or in systems in equilibrium. For instance, the reaction (1),

2H2 + O2 = 2H2O is expected to take place readily in view of the negative

free energy to the extent of 56. 7 K cal/mole. Contrary to this expectation,

.16-

dry hydrogen and oxygen, in actual practice, do not react to any detectable

extent with each other at room temperature, in the absence of a catalyst. Or

even if they react, the rate is extremely slow. The chemical friction in this

i

case is, therefore, very high, and the system behaves for all practical i

purposes almost like ar irreversible one. Hence, in such cases, the

thermodynamic reasoning adopted earlier does not apply in the strict sense.

Nevertheless it should be noted that £1 F° value would represent in such cases

also the maximum energy which one would obtain if the reaction could be made

to take place by some means or other.

Similarly, potentials for many couples given in tables which may not

be reversible, cannot be used in equilibrium (thermodynamic) reasoning.

However, these values do indicate the minimum energy which must be fur-

nished to accomplish oxidation or reduction, and they often give considerable

information regarding the possible reaction mechanisms and the cause of

slowness of reactions, as we shall illustrate a little later.

AB a general guiding principle, it may be stated that reactions involving

making and breaking of bonds are sluggish and are therefore more irreversible

than these involving only charge transfer. Thus with uranium for example,

U + + e" = U + couple behaves as a reversible one since it involves only charge

transfer, while the U(V)/U(IV) couple does not, since it involves making and

breaking of bond:

UO2+ + 4H+ + e" = U4+ + ZH2O

The water oxygen couple for the same reason does not behave as a purely

reversible one. (See oxygen overpotential)

-17-

It may be mentioned, in this connection that for many completed

oxidation-re«l'Jction reac tions, particularly when they are irreversible, the

number of equivalents of electricity is sometimes ambiguous, since direct

potentiomettlc measurements are just not possible in such cases. In these

cases (e.g. 2H2O2 = 2H2O + O2) one might prefer to express the free energy

In terms of calories in lieu of electrical units.

Criteria of Reversibility

The notion of electrochemical reversibility in fact implies several

practical criteria* ' : rapidity in attaining the equilibrium potential, constancy

and reproducibility of the measured values, potential values being independent

of the nature of the inert electrode, low chemical polarization, correct

variation of the measured potential with thermodynamic activity. All these

conditions do not have necessarily the same importance, the last one (repro-

ducibility being understood) is probably the most important, while the first

one the least. It, therefore, follows that a system which dies not show perfect

reversibility, need not be considered as absolutely irreversible. There exiBts

the possibility of arising various degrees of irreversibility.

Direct Measurement of Potential

The potential values can not only be calculated from thermal energy

data, but can also be measured directly in electrolytic cells, as has been done

for a fairly large number of reactions. A cell consists of two electrode re-

actions, which must be reversible and reasonably rapid as explained just now.

In the construction of the cell, moreover, the reducing and oxidizing agentB

(the reactants at the two electrodes) must not be allowed to come into direct

contact with each other.

-18-

UBually, a potential develops at the junction of the two electrolytes.

For simple Baits, the junction potential can be calculated. For convenience,

however, a bridge of concentrated potassium chloride is often used to bring

down the liquid junction potential to a few rnilll-volts.

Let us consider the reaction, 2AgCl + H2 = 2Ag + 2H+ + 2C1*

consisting of two half reactions H2 = 21l+ + 2e"\ and AgCl + e" = Ag + Cl~.

In this case a cell may be constructed, using as one electrode metallic silver

coated or in contact with silver chloride, and as the other electrode hydrogen

gas, in contact with hydrogen ion on a platinum surface. The electrolyte

throughout the cell may be hydrochloric acid and uniform in concentration

except for the slight solubility of silver chloride. Moreover, since the reduc-

ing agent (H, in this caBe) should be the strongest reducing agent at the anode,

and the oxidizing agent (AgCl in this case) the strongest oxidizing agent at the

cathode, air should be excluded as otherwise oxygen would be a stronger

oxidizing agent than silver chloride.

The measurement of the electromotive force of such cells is carried

out by the well-known null method, under conditions when no current is flowing

(that is under equilibrium) as otherwise complications due to chemical fric-

tion mentioned earlier might arise. One common method of measurement is

schematically shown, in Fig. 1.

From a measured E. M. F. value, and knowing the concentration and

pressure of the reagents, and also the respective V values from tables,

one can calculate E° with the help of Nernst equation.

-19-

Hydrogen and Oxygen Over-potential

AB mentioned earlier, hydrogen couple is reversible, but the rate at

which equilibrium is reached is slow. Because of this sluggishness, more

energy than theoretically predicted Is required for rapid evolution of hydrogen

gas from acid solutions. For example, in an actual electrolysis of a normal

solution of an acid, cathodic liberation of hydrogen gas is experimentally

possible only when the potential applied is appreciably higher than the reversible

value, viz. , 0. 0 volt. This excess voltage depends upon experimental condi-

tions and is higher, higher the current, that is, the speed of the reaction. It

also depends upon the nature of the metallic electrode, being very high with Hg,

Cd, Zn, Pb etc. , and being the lowest with platinum black. The platinum black

is, therefore, the most suitable material for the construction of a reversible

working hydrogen electrode as mentioned before. The reaction of acids with

metallic zinc may be cited as another example of the slowness of hydrogen ion

as an oxidizing agent: Zn + 2H+ = Zn++ + H2, E° = 0. 763 V. Inspite of the

potential being in favour by 0- ?6 volt of the oxidation of metallic zinc to zinc

ion, there is no appreciable evolution of hydrogen with pure zinc in dilute

acida If there is another metal say Pt of lower overpotential in contact with

zinc metal, then hydrogen gas starts evolving on the former metal and zinc

starts dissolving. Hydrogen overpotential at different acidities, current den-

sities or on different electrode materials can be measured by measuring the

excess potential required to be applied at a cathode, over the reversible or

theoretical potential, for the liberation of hydrogen gas in an actual electro-

lytic reduction of hydrogen ion.

Key

Fig. 1. E. M. F. measurement by null method.S is a source of knovn E.M.F. say of S volts. C is the cell whose potentialis to be measured. It is connected in opposition to S. AB is a standardresistance wire of known length. G is a galvanometer.

In the experiment, the position of F Is adjusted such that no current flowsthrough G. Under these conditions the potential drop across PB due to Sbecomes equal to that of C,

EMF of C -- S xPBAB VOlt-*

-20-

The explanation of the slowness of hydrogen reactions is to be found in

the reaction mechanism. For changing hydrogen gas to hydrogen ion, the

first step should logically be the dissociation of a hydrogen molecule

I Ho -—> H AF° = + 48.57 kcal

H —> H+ + e"

|H2 —> H++ e , A F.° = O

Irreversibility, in the system, would then be understandable In view of this

first step being that of bond breaking. Moreover, since the A F° for the

overall reaction is zero, fchat for H —^H+ + e" has necessarily to be equal

to - 48. 57 k cal. E° for hydrogen atom - hydrogen ion couple then becomes

2.10 volts. In the same way, if we/ analyse the reverse process namely the

reduction of hydrogen ion,- the 'first step should logically be the formation of

hydrogen atom

H+ + e "-T> H, E° = - 2. 10 volt.

The high negative value of the potential would evidently act as a potential

barrier, the union of two hydrogen atoms (exoenergetic) of course supplying

the energy for the net reaction 2H+ + 2e*"—f H2. Though the potential barrier

is high, yet as is well known in wave mechanics, there exists a finite probabi-

lity of leakage through the barrier, hence hydrogen ion discharge can take

place at a finite rate even when the potential applied is lesB than the above

value. Calculations are available for the dependance of over voltage on

current density and temperature.

Apart from the above, there may be other factors affecting the over-

voltage. For example, formation of a hydride surface by the action of hydrogen

-21-

atom on the electrode metal could take place, e.g.

M + H+ + e" —> HM

HM + H+ + e" > M + Hz

The variation of hydrogen over-voltages will then depend upon the energy of

formation of surface hydrides. This explains at least partially why the over-

voltagee are low on metals which are known to diBBolve hydrogen to form

hydrideB.

Oxygen over-potential has similarly been explained by the presence of

rate determining steps like, either

OH" = OH + e~, E° = -2.0 V

or H O = OH + H+ + e", E° = -2. 8 VCM

followed by

2OH = H2O2, AF° = -48.7 kcal.

and H2O2 = H2O + \ C2, AF° = -5P. 44 k cal

or by 2OH = H2O + C, A F° = -10. 8 k cal.

and O = | O2 , A F° = -54. 99 k cal.

In addition to this mechanism, the electrode material could as well be con-

verted to an oxide or hydroxide layer, affecting oxygen over-potential, which

in addition depends upon the current density or the rate of evolution as in

the case of hydrogen overpotential.

Instability of Water towards H? and O? Evolution

It is obvious that a strong oxidizing agent (theoretically, more positive

than the water oxygen couple) would be able to oxidize water to O2- Similarly

a strong reducing agent should be able to reduce water to H2. Thus, there

are certain limits within which oxidizing and reducing agents can remain

•table in water. For example,

y++ = y+++ + e - , E ° = 0. 255

H+ + e" = | H 2 , E° ^O

giving V + + + H+ = V+ + + + | H 2 , E° = + 0. 255. The positive potential value

indicates that the reaction, as written, proceeds in a solution containing

1 MH+. In other words, V+ + would be unstable in water giving out H_ gas,

in the same way as a reactive metal like zinc reacts in acid solutions. Now

the E value for the H+/H2 couple varies with H+ ion concentration according

to the relation, E = 0-0^5916 log i~ 2^ . Hence, at pH 14, ELHJ

becomes - 0. 828 volt'at pH 7, -0. 414V and so on. It can thus be calculated

that at pH = 5, the potential of the completed reaction becomes negative

(-0. 04V). Hsuce V + + becomes stable at this pH.

In the same way O2 evolution takes place with persulphate, for

instance

S2O8= + H2O = 2SO4 + 2H++| O2> E° = + 0. 78 V

Note that this reaction is also pH dependent.

In figure 2, the area between the full line represents the region of

theoretical stability of oxidizing and reducing agents in water solutions of

different pH. Because of the over-voltages for the evolution of H2 and Og»

which are on the average of the order of 0. 5 V, this area i s extended in

general to that bounded by the dotted lines.

Apparent Inertness of Oxygen in Oxidation Reactions

There are several cases, where O2 appears to be inerc inspite of

its high energy. For example, ferrous ion should be readily oxidized by

air in acid solutions:

E (Volts)-1-2

- 0 - 8 - -0-828V

+0 401 V

+16

1014M

Fig,2 Region of stability of oxidizing andreducing agent in aqueous solutions.

-23-

2Fe + + + £ 6 2 + 2H+ = ZFe + + + + H.,0, E° = + 0. 46 V.

But in actual practice the oxidation is so slow that volumetric titrations with //jferrous ~

sulphate are carried out without any precaution to exclude air. To explain

this, it is postulated that O^ in lieu of being reduced to H2O is reduced only

to H2O2 (such a postulate is not unreasonable since formation of H?O2 does

not involve breaking of the bond of an oxygen molecule). The overall reaction

then becomes

Fe++ + | O 2 + H+ = Fe"1"1"1" + \ H2O2, E° = - 0. 09 V

giving a slightly negative value for the potential. The slowness then becomes

unde r standable.

Free Radicals in Aqueous Solutions

Since water consists of both hydrogen and oxygen , all the species

formed by these two elements might become important in one condition or

other. The species formed by the gradual reduction of O2 to H2O are

depicted below:

: o : b * . - ^ > ; b V o ; + H A H : O : O : H +H> H &H +H .

H *•• L

(oxygen ) (perhydroxyl) (hydrogen- (water and (water)peroxide) hydroxyl)

Thus, besides H , O , H+ and OH" the species that have to be reckoned with

under one condition or other are HO2, H2O and OH. The potentials relating

these species have been described earlier. H2O2 is a well known stable

molecular species, while HO2 and OH are highly reactive unstable radicals.

-24-

A radical should have at least one unpaired electron and theorefore be

oaramagnetic. The highly reactive O2 molecule is a biradical since it has

two unpaired electrons. Free radicals, atomic O and H are readily formed

by the action of ionizing radiations on water:

H2OH2O

H+ + OH

e" + H-O —f e^q («aq - hydrated electron)

e"aq + «*" -? H

H + O? —> HO-j and so OEU

Excited water molecules, H2O , which are also obtained in photo-chemical

reaction readily give H and OH;

H2O* — ^ H + OH.

Free radicals are also formed in several thermal reactions, the well known

example being that of Fenton's reagent:

Fe2* + H2O2 = Fe 3 + + OH" + OH

Fe3+ + HO2" = Fe 2 + + HO2

Hydrated Electron; and its Oxidation Potential

While talking about half-reactions or couples, we have freely taken

the name of electrons as taking part in such reactions. But beyond using

them for writing on paper, many working chemists generally feel uncon-

cerned about them in an actual experiment, one reason probably being that

they are too short-lived. Moreover, the free energy of electrons does not

enter in the calculations, and in any case completed reactions are free from then

-25-

ChemiBts have nevertheless succeeded in increasing the life-time

of an electron by aolvating it. The blue solution that one obtains by dissolving

metallic sodium in liquid ammonia does in fact contain ammoniated electroni.

Solvated electrons can now be handled in the laboratory just like any other

reagent.

The recent discovery of hydrated electrons, whose life-time 1B much

less than that of ammoniated electrons, being of the order of milli-seconds,

has been possible mainly through the efforts of radiation chemists^'*

Hydrated electron has been identified and its properties studied mostly by

absorption spectro-photometry, by virtue of its high optical absorption in the

red region of the spectrum, the molar extinction coefficient being 10, 600 M

cm"1 at 5780A0 and 18, 500 M"1 cm"1 at 7200 A°, the peak of the absorption

band. For the study of short-lived transients like hydrated electrons, the

recently developed technique of fast reaction kinetics is suitable. In this

technique the O. D. can be conveniently seen on the screen of an oscillescope

(by making use of suitable electronic circuits) instead of in a meter as in a

conventional spectrophotometer. From photographs of the oscilloscope

screen showing the O. D. decaying with time, taken under different conditions,

several spectroscopic and kinetic properties can be evaluated.

For obvious reasons, Tiydrated electrons should be considered as

the most important species in so far as aqueous chemistry is concerned. It

is the simplest, most primary and highly reactive species taking part in

reactions, probably to a much large extent than we can imagine now.

When hydrated electrons represented by the symbol e"aq act as a

-26-

yeducing agent, the reaction with the oxidizing agent H+ (with A F° = O) would be

\ H2

Because of its short life-time it is difficult to measure directly its free energy

or potential. Hence an indirect approach as explained below is adopted.

In absence of any other impurity, hydrated electrons react with water:

eaq+ H2P = H + OH" .(20)

the rate constant k* being 16 M" sec ' while the rate constant of the

reverse reaction k r is 2. 3 x 107 M"1 sec"1. Thus, the equilibrium constant,

kK20 = L . = 7. Ox 10-7

k rTherefore, A F° =-1364. 3 log 7 x 10* = +8.40 Kcal/mole.

Combining this value with other known ones, one can complete the following

cycle:

A F (Kcal/mole)

H(aq) = H, v - 4.5 (from hydration of H)

H, » = \ K2 -48. 5 (from dissociation of H2)

H+ + OH* = H2O -19. 3 (from K = 1. 0 x 10+14)

e a q + H 2 ° = H(aq) + O H " • + 8.-4

one gets, e^ q + H+ = £H • " 6 3 -9

The free energy of -63. 9 Kcal/mole corresponds to a standard

potential of 2. 77 volt. The hydrated electron is therefore a more powerful

reducing agent than atomic hydrogen (E° = 2. 1 v)9 and its position lies just

below sodium and just above lanthanum, in so far as its reducing power is

concerned.

-"2-7-

R elation ship of Ioniaation Potential and Electron Affinity withRedox Potentials:

Redox potentials can be calculated from known ionization potential or

electron affinity values. But, since the latter always refer to monoatomic

gaseous state, one has to take into consideration the energy of other Btepa

for going from the standaf d state of the element to that of an aquated ion.

This would generally involve terms for sublimation or dissociation energy

of the element and also the hydration energy of the gaseous ion. Let us take

the example of metals which are. solids in their standard states:

Naj , + e" = Na(s)(aq)

+ + e" =' Ag(s)(aq)

These couples can be broken down into the following steps of known energy:

& H°(Kcal) A H°(Kcal)Sublimation energy

Na(s) -> Na(g), + 26 Ag(s)-?. Ag(g), + 67

Ionization energy

Ma(g) - , . Na+(g) + e \ +118 Ag(g) —> Ag+ +e", +174

Hydration energy

Na+(g) —» Na+(aq), -95 Ag+(g)-* Ag+(aq), -111

Adding+ A- e~ +49 j Ag(s)-^Ag (aq)+e , +130

The sign of the energy values clearly shows that silver is nobler

than sodium. Factors, then, which tend to make a metal noble in aqueous

are (1) high iouization potential; (2) high sublimation energy,

-28-

which is associated with high boiling point, and (3) low energy of hydration

which is associated with large size of ion, (4 E, the energy liberated in

case of electrostatic attraction of two ions of radii r is given by

e2 !A E = — — — (1 — —) where e is the charge and D the dielec-

( r ^ ^ Dtrie constant of the solvent). In the case of silver, its noble character

arises as much from the high value of factor(2) as from factor(l),

Na + Ag+ —f Na+ + Ag, A H° = -81 Kcal

Because the entropy change for the reaction is very small, the free energy

o

is approximately equal to the heat of the reaction, E = 3. 5 volts, in agree

ment with the measured reaction potential.

In the same way, relative oxidising power of non-metallic couple*

can be assessed:Dissociation energy

or sublimation energy

\ F2(g) ->

Electron affinity

F(g) + e" —^

Hydration energy

F"(g) — ^

(Kcal/mole)

F(g) 32; | l2(s) -

F"(g) -92; I(g) + e l

F"(aq)-223 I"(g) - ^

> Kg)

^ I"(g)

I-(aq)

AH°

(Kcal/mole)

26

-75

-72

|F 2 (g ) + e* —> F"(aq), -183jil2(s) + e - ^ r a q , -121

It is not difficult to calculate the potential values after making

necessary correction for the entropies. These values clearly show that

-29-

fluorine is a better oxidizing agent, in part because of the higher electron

affinity, but principally because of the greater energy of hydration of the

smaller fluoride ion. In general, a large electron affinity, large energy of

hydration, and a small energy of formation of the mono-atomic gas atom

from the standard state will favour a high oxidizing potential for elements

for negative ions.

Effect of Charge and Size of an Ion in AqueouB Reactions

Higher the positive charge of an ion and smaller the size, higher

will be its electrophilic character, as can be judged from a consideration

of the basic principles of electrostatics. Since chemical reactions are not

purely electrostatic in origin, but may get mixed up with bonds of covalent

character, the above simple coulombic picture does not always remain

valid. Nevertheless, the coulombic picture is often helpful in understanding

at least qualitatively several chemical trends. For example, in the case of

acids we may state in a general way that the ionization of hydrogen acids

increases (1) with increasing size of the negative ion, and (2) with decre-

asing charge on the negative ion. Thus, HI is a stronger acid than HF and

H2S is stronger than H2O because of the effect of the size. Here the non-

metals belong to the same family, and the weakening of the bond due to in-

creased size of the non-metal more than compensates for any increase in

covalent character and therefore gives correspondingly increased acidity.

HF is stronger than H2O because of the effect of the charge, even though

size decreases in the horizontal series, since size changes here are small

- J O -

and without appreciable effect. It also follows that if the negative element-

forms hydrogen compounds of different oxidation states, the smaller the

negative number of the oxidation states, the stronger will be the acid. Thus,

H Oo i s a stronger acid than H^O and N-H^ is less basic than NH,.

In the same way the tendency to complex formation by metal ions

can also be understood. For example, lanthanides do not readily form

complexes, because of the large size of these ions, in general. But in thia

group, due to the lanthanide contraction, gradual enhancement in the com-

plex formation is noticed as one goes from lower to higher atomic weights.

Ce(lV), because of its higher charge, has much stronger complexing pro-

perties than Ce (III). The chemistry of the transition metal complexes

provide several examples of this type, when the liigher oxidation state (where

of course the charge is also higher) is stabilized more than the lower one

through the use of a suitable complexing agent (e.g. H3PO4 for Fe+++). For

quantitative measure of the relative stabilities, however, one has to look

for the respective equilibrium constants or stability constants. Since the

presence of a complexing agent affects the ratio of the concentrations of

the free ions of the two oxidation states, the observed redox potential would

also be similarly affected, as can be predicted by formula K (Nernet

equation). From the measured potential values, it might therefore be

possible to estimate the stability consent of the complex in favourable

circumstances.

-31-

ACKNOWLEDGEMENT

While writing this report Dr. R. G. Dhaneshwar of the Analytical

Division and his colleagues have extended their ungrudging help and made

Several constructive suggestions, for which I would like to record my

appreciation. I am also thankful to the Head, Chemistry Division, for hia

kind interest in this write-up.

REFERENCES

1. W. M. Latimer; "Oxidation potentials", 2nd Ed., Prentice Hall (1959)

2. See for example, B. E. Conway, "Electrochemical data", p. 25,Elsevier (1952); Circular of the Natl. Bur. Stnds. 500, "Selectedvalues of chemical thermodynamic properties", (Feb. I, 1952)

3. See for example, H. S. Karned and B. B. Owen; "The physicalChemistry of Electrolytic Solutions", Appx. A, Reinhold (1958).See also Appx. II of ref. 1 for the activity of strong electrolytes

4. See pages 22 and 23 of ref. 1 and the bibliography mentioned therein

5. For a discussion on the "Conventions Defining ThermodynamicProperties of Aqueous Ions and other Chemical Species" seeR. M. Noyes, J. Chem. Ed. 40, 2(1963)

6. See for example, M. Haissinsky; J. Chi. Phys. 43_, 224(1948)

7. For a review see E. J. Hart; "Hydrated electrons", Survey andProgress in Chemistry 5, 129(1969)

8. The Table has been compiled from data given in ref. 1 and M. Pourbaix,"Atlas of electrochemical equilibria in aqueous solutions",Pergamon (1966)

-32-APPENDIX

Table of standard potentials (expressed in voltB, as reductionaffinity for unit charge) of rcdox couples arranged alphabetically (8)

Ac + 3e~

Ag+ + e"

Ag2+ + e"

Ag Ac + e"

Ag Br + e"

Ag BrO -r e"

Ag2 C204 + 2e"

Ag Cl + e"

Ag CN f e"

Ag (CN)2" + e"

Ag CO3 + 2e"

Ag 2Cr 04+2e-

Ag4 Fe (CN)6+4e~

Ag I + e"

Ag IO3 + e"

Ag2 M0O4 + 2e"

Ag N02 + e"

Ag2 O(s) + 2H20+2e"

Ag2 O(s) + 2H++2e"

Ag2 03(s) + H20+2e'

2Ag 0(s) + 2H20+2e"

Ag 0 CN + e"

= Ac (s)

= Ag (s)

= Ag+ (4M HC104)

= Ag (s) + Ac"

= Ag (s) + Br"

= Ag (s) + BrO3"

= 2Ag (s) + C2042"

= Ag (B) + Cl-

= Ag (s) + CN"

= Ag (s) + 2CN"

= 2Ag (a) + C03Z"

= 2Ag (s) + CH>42"

= 4Ag (s) f Fe(CN)64-

= Ag (B) + r

= Ag (s) + IO3

= 2Ag (B) + Mo04Z"

= Ag (s) + N02"

= 2Ag (s) + 20H"

= 2Ag (s) + H20

= 2Ag 0(s) + 20H"

= Ag2 O(s) + 2QH"

= Ag (s) + OCN"

Ca - 2.6

0.799

1.980

P. 643

P. 095

0.55

0.472

0.222

-0.017

-0. 31

P. 477

0.446

0.194

-0.151

0.35

0.49

0.564

0.344

1.173

0.74

0.57

0.41

A g 2 s (9) + 2e~

Ag S C N + e"

Ag2 S04 + 2e"

Al3++3e"

H2 A103"+H20+3e"

Al F 63 " + 3e-

Am3 + + 3e"

Am4 + + e"

Am 02+ + + e"

Am 02++ 4H+ + e*

As (s) + 3H+ + 3e"

As 2 03(s) + 6H++6e"

HAs 02(aq) + 3H++3e"

As 02" + 2H20 + 3e"

H 3 AsO4+2H++ 2e"

As 043~ + 2H20 +2e~

Au+ + e" =

Au3+ + 2e"

Au3+ + 3e"

Au Br2" + e"

Au Br4" + 3e"

Au Cl4" + 3e"

-33-

= 2Ag (s^ ; S2"

= Ag (s) + SCN'

= 2Ag (s) + SO42"

= Al(s)

= 40H" + Al (s)

= Al(s) + 6F"

= Am (s)

= Am3+(1MHC104)

= AmO2+ (1 M HCIO4)

= Am4++ 2H20 (1 M HC104)

= AsH3

= 2As (s) + 3H20

= As (s) + 2H2G

= As (s) + 4 OH"

= H As 02 + ?H20

= 40H" + As(i2"

= Au (s)

= Au+

= Au (s)

= Au (s) + 2Br"

= Au (s) + 4Br*

= Au (s) + 4C1"

-0.69

0.089

0.653

-1.66

-2. 35

-2.07

-2.32

2.44

1.60

1.261

-0.608

0.234

0.248

0.68

0.559

-0.67

1.692

1.401

1.498

0.963

0.87

1.00

Au (OH) + 3H+ + 3e~3

Au (CNS)4"+ 3e"

H, BO," + H O + 3e"

H3 B0 3 + 3H"1" + 3e"

B F 4 " + 3e~

Ba 2 + + 2e"

Ba(0H)2. 8H20+2e"

Ba 02 (hydr. s) + 2H++2e"

B e 2 + + 2e"

B e 2 0 32 " + 3H20 + 4e~

Bi (Cl)4" + 3e "

B i 2 0 3 (hydr. s)+3H20+6e*

B12O4 (s) !- 4H+ + 2e"

BiO/ + 2H++ 3e"

BiO Cl + 2H+ + 3e"

Bk 4 + + e "

B r 2 (aq) + 2e"

B r 2 (1) + 2e"

H BrO+ H+ + e"

H BrO + H + + 2e"

Br Q" + H20 + 2 e '

BrO3* + 6H+ + 5e"

-34-

- Au (s) + 3H20

= Au (s) + 4CNS*

= B (s) + 40H"

= B (s) + 3H20

= B (s) + 4 F "

= Ba (s)

= Ba (s) + 8H20> + 20H"

= BaO (hydr. a) + ZH20

= Be (a)

= 2Be (s) + 60H"

= Bi (B) + 4 Cl"

= 2Bi (s) + 60H"

- 2H20 + 2BiO+

= Bi (a) + H2O

= Bi (s) 4r:Cl~ + H20

- B* ; 3 '

= 2Br"

= 2Br"

= iB'2'ff) + H2°

= Br" + H20

= Br" + 20H"

= |Br 2 + 3H20

1.45

0.66

-1.790

-0. 869

-1.04

-2.9P5

-2.97

1.626

-1.847

-2.627

0.168

-0.46

1.593

0.320

0. 16

1.6

1.087

1.065

1. 579

1.331

0.76

1.491

BrO3" + 6H+ + 6e -

BrO3" + 3H20 + 6e*

(CN)2 + 2H+ + 2e"

2HCN0 + 2H+ + 2e*

CNO" 4 H2O + 2e"

(CNS)2 + 2e"

C6 H 4 °2 + 2 H + + 2 e "

C02(g) + 2H+ + 2e"

HCOOH (aq) + 2H+ + 2e~.

HCHO(aq) + 2H+ + 2e~

CH30H (aq) + 2H+ + 2e"

2C02 (g) + 2H+ + 2e"

H 2 C 2 ° 4 ^ + 6 H + + 6 e "

CH3C0OH (aq) + 2H+ + 2e"

CH CHO(aq) + 2H+ + 2e~

C2H50H(aq) + 2H+ + 2e"

Ca 2 + + 2e"

Ca(0H)2 + 2 e -

CaO2(s) + 4H+ + 2e"

Calomel electrode

Calomel electrode

Calomel electrode

Cb 0(s) + 2H+ + 2e '

-35-

= Br" + 3Hz0

= Br" + 60H"

s 2HCN(aq,)

* (CN)2 + 2H2O

= CN" + 20H"

= 2CNS"

= C 6 H 4 ( 0 H ) 2

= HCOOH (aq.)

= H , a + HCHO (aq)

= CH3ftH (aq)

= ii2a + CH 4 (g)

= H2C2°4 ( a q )

= 2H-.0 + CH, COOH (aq)

" = H20 + CH3 CHO (aq)

= C2H50H (aq)

= H20 + CzH6(g)

•= Ca (s)

= Ca (s) + 2(QH)~

= Ca+ + + 2H20

NKC1 (in air)

0.1 N KC1 (in air)

Satd KC1

= Cb (s) + H 20

1.423

0.61

0.37

0.33

-0.97

0.77

0.6994

-0.196

0.056

0.19

0.586

-0.49

0.31

-0.118

0.192

0.46

-2.866

-3.03

2.224

0.2825

0. 3354

0.2415

-0.733

- 3 6 -

Cb 0 (B) + 2H+ + 2e"2

Cb205{s) + 2H++2e"

Cb 0(S04)2"+2H++5e"

Cb 0(B) t H.,0

2CbO2(s) + H20

H-,0 + 2!

Cd (s)

Cd (s) +

Cd (s) +

Cd (s) +

Cd(s) +

Cd(s) +

Ce (B)

Ce 3 + + :

Ce 3 + (1

3042"+ Cb(

20H'

s2-

4CN"

co32"

4NH3

H 2 0

M H 2 S04)

Cd2++2e-

Cd(0H)2 + 2e~

Cd S + 2e"

Cd(CN)42"+2e"

Cd C0 3 + 2e"

Cd (NH3)42++2e*

Ce 3 + + 3e*

Ce(OH)3++H++e"

Ce 4 + + e"

Cl2(g) + 2e" = 2C1-

HC10 + H++e" = | C 1 9 + H?O

HC10 + H+ + 2e° = Cl" + H2O

C10" + H20 + 2e" = q i " + 20H"

cio2 + e~ = nio2"

C102 + H+ + e" = HC102

HC102 + 2H+ + 2e" = HCIO + H2O

± | C 1 2 + 2H20

CIO" + 2OH"

C102 +

HC102

C 1 0 2 " •»

C103" 4

f 3H+ -

-H 2 0 4

• 2 H + 4

V 3e

2e

• e "

-0.

-0.

-0.

-0

-0

-1

- 1 .

-0

-0

-2

-1

1

1.

1.

1.

0.

1.

1.

1.

1,

0.

1.

.625

. 289

. 63

.403

.809

. 2 4

. 0 9

. 7 4

.61

.483

.715

. 44

358

594

494

89

160

277

645

628

66

152

CIO3* + 3H+ + 2e"

CIO3 + H20 + 2e"

G104" + 2H+ + 2e~

C104~ + H20 + 2e"

Co2 + 2e

Co 3 + + e"

Co 3 + + e-

Co(0H)2 + 2e '

Co(OH)o + e"

-37-

HC10, + H,P

C1O?" + 2OH~

ClO3" + H20

C1Q3- + 20H"

C6(s)

Co 2 +

Co 2 + (3M HNO3)

Co(s) + 20H"

Co(0H)2 + OH"

1.214

0.33

1.189

0.36

-0.277

1.808

1.842

-0.73

-0,17

V-#3f T £&

C r 2 0 72 " + 14H+ + 6e"

CrO 42" + 4H20 + 3e"

' - + 4H+ + 3e"

i<T + 8H++3e"

Cr(0H)3+ 3 e '

2H z0+ 3e"

Cs + + e"

Cu+ + e"

Cr (s)

C r 2 +

2Cr3 ++ 7H20

Cr(OH)3 (hydr. ) + 5OH"

Cr3+-

Cr(s) + 30H"

Cr(s) + 4OH'

Cs(s)

Cu(s)

-0.

-0.

1.

-0.

0.

1.

-1.

-1.

-2.

b.

0.

913

407

333

13

945

477

3

2

923

52

153

V 2e

CuZ+ + 2CN~ + e"

Cu2 + f Cl" + e"

Cu 2 + + I" + e"

Cu2 + + Br" + e"

CuT + e"

Cu20(s) + H20 + 2e"

C u B r •+• e~

CuCl + e"

D+ + e-

Dy3 +3e~

E r 3 + + 3e"

Eu 3 + + e

F 2 + 2 e "

2H+ + 2e

F20 + 4H+ + 4e"

F 20 + 2H+ + 4e

Fe2 +

2e"

F e 3 + + 3e"

F e 3 + + e"

FeC0 3 + 2e~

Fe(CN)63" + e"

FeO42~+8H+ + 3e"

Cu(s)

Cu(CN)2"

CuCl

Cul

CuBr

Cu J- I"

2Cu(s) + 2 OH"

Cu + Br~

Cu 4- Cl-

Dy (s)

Er (s)

Eu2 +

2F"

2HF

2HF + H2O

2F" + H20

Fe(s)

Fe(8)

Fe2+

Fe(s)

Fe(CN)6

Fe 3 +

2 -

4 "

Ca

0.

1.

0.

0.

0.

-0.

-0.

0.

0.

-0.

-2.

-u-o.

2.

3.

2.

2.

-0.

-0.

0.

0̂.

0.

1.

337

12

538

86

640

185

358

033

137

0034

353

296

429

866

053

246

153

440

037

771

756

36

700

Fe(OH)3 + e" ' = Fe(0H)2 + OH" _O. 56

Fe(OH)2 + 2e~ = Fe(s) + 20H" -0 . 877

Fe (Phenanthroline)33 + + e" = Fe (ph) ?

2 + 1. 14

FeS + 2e" = Fe(s) + S2" -0.97

Fe_S, + 2e" = 2FeS + S2" -0.67

FeO42" + 2H20 + 3e" = FeO2" + 40H" 0.9

Ga 3 + + 3e" = Ga(s) -0 . 529

H2 GaO3" + H20,+3e" = Ga(s) + 40H" Ca -1.22

H Ge03"+ZH20+4e" = Ge(s) + 50H" -1 .0

H2 GeO3(aq) + 4 H + + 4e" = Ge(s) + 3H20 -0.182

GeO2(s) + 4H+ + 4e" = Ge(s) + 2H20 -0.202

-2.397

0. 0000

-2.251

-0. 828

-2.93

1.776

3d J T + 3e"

2H+ + 2e~

| H 2 + e"

2H20 + 2e~

H20 + e"

H 20 2 + 2H+ + 2e~

H+ + e-

H02 + H+ + e"

HfO2++2H+44e"

HfO, (s) + 4H+ + 4e"

HfO (0H),+H,0+le-

Hf4+ r 4=-

Gd

= H 2

= H"

H2 + 20H"

= H(g) + OH-

= 2 H 2°= H(g)

= H 2 0 2

= Hf (s) + H20

H£(s) + 2H20

H£(s) + 40H

= Hf(s)

1.5

-1.724

-1.685

-2.50

-1.70

»40-

Hg2++ 2e~

2Hg2+ + 2e"

| H g 22 + + e"

Hg2 (CH3 C0 2 ) 2+2e- =

Hg B r 42 " + 2e" =

Hg2 B r 2 + 2e" =

Hg2 Cl 2 + 2e"

Hg2 HP0 4 + H+ + 2e" =

Hg2 I 2 + 2e" =

Hg I 42 " + 2e"

Hg 0(r) + H2O + 2e* =

Hg2 S04+2e"

Ho 3 + + 3e"

I 2 + 2e -

I 3 " + 2e" =

H 3 I 0 62 " + 2e"

H5 I0 6 + H+*2c-

HI.0 + H+ + e"

HID + H+ + 2e" =

10" + H20 + 2e"

IG3" + 6H+ + 5e"

IO3- + 6H+ + 6e"

IO3- + 4H+ + 4e"

Hg(l)

Hg22+

Hg (1)

2Hg (1) + 2CH3CO2"

Hg (1) + 4Br"

2Hg (1) + 2Br"

2Hg (1) + 2C1"

2Hg (1) + H 2 P 0 4 "

2Hg (1) + 21"

Hg (1) + 41"

Hg (1) +20H"

2Hg (1) + S 0 42 "

Ho

21"

31"

I0 3" + 30H"

I0 3 " + 3H20

i h + H20

I" + HZO

2OH" + I"

\ 12 + 3H2O

I" + 3H20

10" + 2H20

0.854

0/920

0.788

0.511

0.21

0.1397

0.2676

0.638

-0.0405

-0 .04

0.098

0.6151

-2.319

0.621

0.536

Ga 0.7

Ca 1.6

1.354

0.987

0.49

1.178

1.085

0.972

I0 3 " + 3H 0 + 6e* = I" + 6QH"

I C 1 2 " + e

ln 2 + + e"

ln 3 + + e '

In + 3e"

In(0H)3 + 3e*

Ir Cl62"+4e"

Ir Cl62~+e"

Ir 02(s)+4H+ + 4e"

Ir203(s)+3H20+6e-

ln2+

In(s)

In(s) + 3QH"

Ir + 6C1"

I rC l 6

Ir(s) H

2Ir(s)

3 -

h 2H 2 0

+ .6 OH"

l r 3 ++

K+ +

La 3 +

3e"

e

+ 3e

= K(s)

« La(s)

La(0H)3 + 3e" = La(s) + 3OH"

L i + + e ' = Li (B)

Lu3 ++3e" = Lu(s)

Lu (0H)3 + 3e* = Lu(s) + 3OH"

Mg2++2e"

2e" = Mg(s) + 2OH

2e" = Mh(s)

MnJX + e1•34. , , 2+1-5+ + e~ = Mn

0.

1 .

- 0 .

rO.

- 0 .

- 1 .

0.

1.

0.

0.

1 .

•)

^ t-* 1

- 2 .

-2 .

-3

-2

-2

-2

-2

-1

1

26

06

400

489

342

0

835

017

926

1

156

,924

.522

.90

.045

.255

.72

.363

.69

.179

.509

-42 -

4H+ + 2e = Mn2+ + 2H20

4H+ + 3e

8H+ + 5e

MnO4" + e'

MnO4" +

MQO4" +

MhOA" + 2H,0 + 3e"

Ma(0H)2+ 2e"

Mn(0H)3 + e"

MnCO3 + 2e'

H2Mo4(aq) +

Mo34" + 3e*

Mo042"+4H20+6e

3N2+2H++2e"

N2 + 5H++ 4e"

N2H5++3H++2e"

NH30H++2H++2e'

N03"+3H++2e*

N03"+4H++3e*

N204+2H++2e"

N204+4H++4e"

N03"+H20+2e"

MnO2(s) •

Mn2+ + 4H20

MnO2(s) + 40H"

Mn(s) + 20H"

Mn(0M)2 + Ok"

Mn(s) + C0 32"

Mo(s) + 4H20

Mo(s)

MO(B) + 80H"

2HN,

N 2 H 5 +

2NH4+

H20 +

H20 +

NH4+

HN02

NO + 2H20

2 H 2 0 H hN2°4

2HN02

2H20 + 2N0

2 OH" + N02*

H2a+NO

1.228

0.564

1.692

i.507

0.588

-1.55

0.1

-1.48

0.0

-0,200

-1.05

-3.1

-0.23

1.275

1.35

0.934

0.937

0.803

1.065

1.035

0.01

1.004

-45-

2HN0 +4H++4e' H 2 N 2 0 2

2HN02+4H++4e"

H2N2O2 + 6H++4e"

H 2 N 2 0 2 + 2H++2e" =

2 N 0 + 2 H + + 2e" =

2N0+2H++2e"

2NH OH + 2e"

Na+ + e" =

Nb - see under Cb

Nd3+ + 3e~

Ni2 ++2e"

Ni(0H)2+2e-

Ni 02(s) + 4H+ + 2e" =

Np3 + + 3e"

Np4+-l-e-

NpO2+ + 4H+ + e"

NpO2++ + e"

N20 + 3H20

2NH30H+

N 2 + 2 H 2 0

H 2 N2 °2

N20 + H2Q

N 2 H 4 + 2 OH"

Na(s)

Nd(s)

Ni(s)

Ni(s) + 20H"

Ni 2 + + 2H20

Np(s) (1 M HC104)

Np 3 + (1 M HC104)

Np4++2H20 (l U

NpO2+ (1 M HC10.

0 2 + 4H+(lP"7M)+4e" =

02 +4H++4e =

02+2H20+4e"

02+2H++2e"

02+H2Of2e"

2H20

40H"

H 2 0 2

HP2"+0H"

0.86

1.297

0.387

2.65

0.71

1.591

0.73

-2.714

-2.431

-0.250

-0.72

1.593

-1.83

0.152

0.739

1.137

0.815

1.228

0.401

0.682

-0.076

X T 1

n -j *

HP.

H O<

°3

[>2 + 2H+ f2e"

, + H+ + e"

.,"+ H 7 0 + Zfc"

+ 2H + 2e"

+ H2P + 2e"

0(g)+2H+-i-2e~

on

OH

H 2

HO

°2

+ e"

+ H+ + • "

O2 + H+ + e"

2" + H 2 ° + e"

+ e"

-44-

2H20 1.776

H ?O, 1.5

3 OH" 0.88

0 2 + H20 2. 076

0 2 + 20H" 1.24

H 2 0 2.421

OK" 2. 0

H ?0 2 .8

OH + H20 0.72

OH + 20H" -0 .24

0 2 " -0 .56

Os 0 4 ( B ) + 8H++8e" = Qs(s) + 4H20 0.85

HOs 0 5* + 4H20+8e" = Os (s) +90H" 0.02

P(s. white) + 3H+ + 3e" = PH3 (g) -0 . 063

= PH3(g,) + 30H" -0 .89

= P(s) + 20H" -2.05

= P(s) + 2H20 -0.508

= H3 PO2 + H20 -0.499

H P0 32 -+2H 2 0+2e- = H 2 P 0 2 " + 30H" -1.57

H 3 P0 4 +2H + +2e" = H3 P 0 3 + H ? 0 -0.276

P 0 43 " + 2H20 +2e" = H PQ 3

2 " + 30H" - 1 . 12

H4 P 2 0 6 + 2H+ + 2e" = 2H,, P 0 3 0. 38

P + 3H

Hj P0 2

H3PO2

H 3 P0 3

20+ 3e"

* + e"

+ H+ +

+ 2H++

1

e"

2e

- 4 5 -

Pa 0 + + 4H1 + 5e"

Pa

PbCl2 + 2e

Pa(s) + ZH.O(inF" soln.)

PaIV (in halide soln)

Pb(s)

Pb(s) + 2C1"

Pb Br 2 + 2e

Pb I2 + 2e~

Pb S + 2e"

Pb S04 + 2e"

HPbO ~ + H.,0 + 2e~2 ^

PbO (s) + 4H+ + 2e"

PbO (s) + H-,G+ 2e"2 *

FbOfeM • S 0 4 * - + « + « ,

Pd2+ + 2e"

Pd(0H)?+2e"

PdCl42"+2e"

Pd B r 42 " + 2e"

P d C l 62 " + 2e"

Pm3 + + 3e"

Po 2 + +2e"

Po 032"+6H++4e"

Pb(s) + 2Br

Pb(s) + 21"

Pb(fl) + S 2 '

= Pb(s) + S042"

= Pb(s) + 30H"

Pb 2 + + 2H20

PbO(s) + 20H"

;" = PbS04 + 2H2

= Pd (8)

Pd(s) + 2 OH"

Pd(e) + 4C1"

Pd(s) + 4Br~

PdCl42" + 2C1

Pm(s)

= Po(s)

Po(s)+3H20

Ca

Ca

-1 o

-0.1

_p . 1 2 6

-0.268

-0.280

-0. 365

_0. 98

-0. 3563

-0.54

1.449

0.248

1.685

0.987

0. 07

0.62

0.6

1.288

-2.423

Po0 3 (s)

° - 7 4 8

-46-

Pr3 + + 3e" = Pr(s)'

Pr ©2(s) + 4H+ + e"

Pt 2 + 4- 2e"

Pt Cl 42 * + 2e~

Pt C l 62 " + 2e"

Pt (0H)2 + 2e~

Pt S + 2H+4-2e"

Pt B r 42 " + 2e"

Pu 4 + 4- e-

Pu 02++4H++e-

= Pr3+

= Ft(s)

= Pt(s)

= PtCl

= Pt(s)

= Pt(.)

= Pt(s)

= Pu3+

= Pu4+

+ 2H70

4- 4C1"

4 2 " + 2C1-

+ 20K"

+ H2S

+ 4Br"

(1 MH C1O4)

Rb+ + e"

Re 3 + 4- 3e

Re 3 + + 4e

ReO4"4-4H

ReO2(s) +

ReO4"4-4H

Re O4" + i

Re 02 + H

-

-

2H"

2 o-2H2

7°

e~

wi- 7e"

0 4- 3e

f 4e"

PuO2++4-4H++2e" = Pu4 ++2H20 (1 M HC1)

Pu 3 + 4- 3e" = Pu(s)

Pu(OH)3 + 3e" = Pu(s) 4- 3OH"

2e" = Ra(e)

Rb (s)

Re (s)

Re"

ReO2(s) +

Re(s) 4- 2H 0

Re(s) + 80H"

ReO2 + 40H"

Re(s) 4 40H"

- 2 .

2.

1.

0.

0.

0.

- 0 .

0.

p.

1.

0.

1.

- 2 .

- 2 .

-2 ,

-2 .

Ca 0

Ca 0

0

0

- 0

- 0

- 0

462

761

188

73

68

15

30

58

982

172

913

052

,031

.42

.916

.925

.300

.125

.510

.252

.584

.594

.576

Rh P 4Z " + 8H++3e"

Rh3 + + e"

RhZ+ + e"

Rh+ + e"

Rh 02(s) + 4H++e"

Rh2 03(s) + 3H20+6e"

RhCl63-+3e"

Ru C1 3 (B) + 3e~

RuO2 (s) + 4H++4e~

Ru 02(s) + 2H20+4e"

Ru 0 4" + e"

Ru 0 (s) + e"

Ru Cl Z '+3e~b

S + 2H++2e"

S + 2e"

4H2S03+4H+-i-6e"

H2S03+4H++4e"

-47-

Rh 3 f + 4Ii,0

= Rh2 J

= Rh+

Rh(B)

Rh 3 + + ?.H20

= 2Rh(s) + 60H'

Rh(s) + 6C1"

= Ru(s) + 3C1"

= Ru(s) + 2H70

= Ru(s) + 40H"

= R u O 4 "

Ru 0 4 "

= RU(B) + 5C1"

= H2S

= s2-

= S4062"+6H20

= S + 3H 0

2H2S03+H++2e" = HS 2 0 4 " + 2H20

S042"+4H++2e" = H 0 + H SO

S042"+H20 + 2e" = S 0 3

2 " + 20H'

SgO62"+4H++2e" a 2 H 2 S 0 3

2H2SQ3 + 2H++4e- = S ^ 2 " + 3H20

2.

1.

P.

P.

1.

P.

P.

P.

P.

-P.

P.

P.

Ca P.

P.

-P.

P.

P.

-P.

P.

- P .

P.

P.

261

198

6PP

6PP

881

P4

44

68

79

P4

59

95

4

142

476

5P9

449

P56

17

93

,564

.40

- 4 8 -

S4°6 +

, 2 V - ,

2S0 32 "+

2S0 42 "+

2e

- 2e"

3H20

4H++2e~

Sb(B) + 3H++3e

sb2 o3 +

SbO++2H

sbo2- +

sb2o5(s)

Sb205(s)

6lT +

++3e"

2H20 +

+ 4H''

+ 6H+

-

6e -

3e"

+4e~

+ 4e"

s2o42"

S 2°3 2 "

S 2°6 2 '

H 3 Sb

3H20 +

Sb(s) +

Sb(s) +

t 40H"

t 60H"

+ 2H20

2Sb(s)

H 2 0

40H"

Sb203(s) +.2H20

2SbO+ ̂ h 3H2O

Sb, 0 (s) + 2H++2eL 5

SbO2"+20H" (1OM)

Sb2 04(s) + H20

Sc3 + + 3e-

Se(s) + 2 e '

Se(s) + 2H++2e*

Ho SeO, + 4H+ •}- 4e"

SeO32- + 3H20 + 4e"

SeO42"+4H++2e"

S e 0 42 - , H 2 0 + 2e"

Se, Cio+2e~ =

SiO2(Quartz)+4H++4e" =

SiO32+3H 0+4e-

Sc(>)

Se 2"

H 2 Se (aq)

Se(a) + 3H20

Se(s) + 60H"

H2Se03 + H?0

SeO32"+2QH"

2Se(B) + 2C1"

Si(s) + 2H20

Si(s) + 6 OH'

0.

2.

- 1 .

- 0 .

- 0 .

- 0 .

0.

0.

- 0 .

0.

p,

-0 .

0,

-2

- 0

-0

0

-0

1

0

1

- 0

-1

08

01

12

58

22

510

152

212

66

,671

,581

.589

.479

.077

.924

.369

.741

.366

.151

. 05

. 1

.857

. 7 0

-49-

Si(s) + 4H +4e" =

Si F 62 ~ + 4e"

Sm + 2e" =

Srn 03(s) + 6H+ + 2e~ =

Sm3 + + e"

Sn2+ + 2e"

Sn4+ + 2e"

H Sn 0 * + H,P + 2e"2 £•

Sn(0H)62"+2e-

Sn 02(s)+4H++2e"

SnF 62 " + 4e~

Sr 2 + + 2e~

Sr 02(B)+4H++2e"

Sr(OH).. 8H90+2e*

Ta 2 O5(s) + 10H++10e" =

T b 3 + + 3e~

Tc2 ++2e*

Tc 0 (s) + 4H++2e"

Tc Q "+4H++3e"4

Te(a)+2e"

Te(s) 4 2H+ + 2e"

T.6 02(s) + 4H++4e"

Si H4(g)

Si(s) + 6F"

Sm(s)

2Sm2 + + 3H20

Sm 2 +

Sn(e)

Sn2+

Sn(s) + 30H"

HSnO2"+3QH"+H

Sn2++2H 0

Sn(s) + 6F"

Sr(s)

S r 2 + + 2H 0

Sr(s)+8H20+20H

2Ta (s) + 5H20

Tb(s)

Tc(s)

T c 2 + + 2H?0

TcO (s) + 2H2O

T e 2 "

H 2 Te(g)

Te(s) + 2H20

-1.2

-3.121

0.230

-1. 000

-0.136

0. 151

-0. 91

-0. 93

-0.077

-0.25

-2.888

2. 333

-2.99

-0.750

-2.391

0. 400

0. 144

0.738

-1. 14

-0 717

0.521

-50-

Te 00 H + 3HT + 4e" =

TeO32" + 3H^0 + 4e"

TeO. " + H20 + 2e" =

H6 Te 06(s)+2H++2e" =

T e4 + +4e-

Th4+ + 4e-

ThO2(s) + 4H++4e"

Th(OH). + 4e"

Ti2++2e"

Ti3 + + 6-

Ti 0 (s)+4H++2e"

Te(s) + 2H20

Te(s) + 60H"

TeO3 * + 20H

TeO2(s) + 4H-

Te(s)

Th(s)

Th(s) + 2H20

Th(s) + 40H"

Ti(.)

T i 2+

Ti2 + f 2H20

(rutile)

Ti 0++ + 2H++e" = H20 + Ti3+

TiO, (hydrated)+4H++4e- = Ti(s) + 2Ho0

Ti F62~ + 4e" = 6F" + Ti(s)

Tl + e" = T1(B)

Tl + 2e- Tl

Tl(OH) (s) + e" = Tl(s) + OH"

Tl Cl + e" = Tl + Cl*

T l l + e " = Tl + I"

Tl Br + e" = Tl + Br"

Tm *'' + 3e" = Tm(s)

Na2U04+4H2(H2e" = U(0H)4 +.2Na++40H"

0.

-0.

0.

1.

0.

- 1 .

- 1 .

- 2 .

- 1 .

Ca -0.

- 0 .

Ca 0.

- 0 .

- 1 .

-0,

1

-0

-0

-0

- 0

-2

-1

551

57

4

020

568

899

789

48

630

37

502

10

86

19

.336

.252

.345

.557

.753

.658

.278

.61

- 5 1 -

U 3 ++ 3 e " -

U4 + + e-

U02+ + 4H+ + e"

U0 22 + + e"

U0-> + 2H-0 + 4e"

V2++ 2e"

3+V + e

- U(s)

= u3+(i

= u 4 + +

uo 2+

-- U(s) +

= V(8)

= v 2 +

M H

2H 0

40H"

cio4)

(1MI

+ (Or V(0H)4+)+2H++e" = V02 + + H20

V (0H)4++4H++5e" - V(s)+4H20

V0 4 " + 4H++e" = V(0H)4+

W02(&) + 4H++4e~ = W(s) + 2H20

W205(s) +2H++2e - = 2W02(s) + H ^

2W0,(s)+2H++2e" = W2(Us)+H 0

W042"+4H20+6e- = W(s) + 80H"

Y 3 + + 3e" = Y(s)

Yb2 + + 2e~ = Yb(s)

Yb3 + + e- = Yb 2 +

Zn2 ++2e" = Zn(s)

Zn 02"+2H20+2e" = Zn(s) + 40H'

Zn S + 2e* = Zn(s) + S

Zn(CN) 42 "+2e- = Zn(s) + 4 CN

" = Z

Zr(s)

Zr 0 , (s . anhydr .)+ 4H++4e" = Zr(s) + 2H20dt

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