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Cell potentials and the electromotive series

 

It has long been known that some metals are more "active" than others in

the sense that a more active metal can "displace" a less active one from a

 solution of its salt . The classic example is the one we have alreadymentioned on the preceding page:

Zn(s) + C!+  Zn!+ + C(s) 

#ere $inc is more active becase it can displace %precipitate& copper from soltion. If yo immerse a piece of

metallic $inc in a soltion of copper slfate' the srface of the $inc (ickly becomes covered with a black coating

of finely)divided copper' and the ble color of the hydrated copper%II& ion diminishes.

*imilar comparisons of other metals made it possible to arrange them in the order of their increasing electron)donating %redcing& power. This se(ence became known as the electromotive or  activity series of the metals.

The most active %most strongly redcing& metals appear on top' and least active metals appear on the bottom. more active metal %sch as Zn& will donate electrons to the cation of a less active metal %C!+' for example.&

 ,otice the special role of hydrogen here- althogh #! does not have the physical properties of a metal' it is capable

of being "displaced" %a rather archaic term seldom sed in modern chemistry& from # ! or #+)containing %acidic&

displace #! from water'

steam' or acids

Li ! /i%s& + ! #!% & ! /i#%a(& + #!%g&

K  ! 0%s& + ! #!% & ! 0#%a(& + #!%g&

Ca Ca%s& + ! #!% & Ca%#&!%s& + #!%g&

 ,a ! ,a%s& + ! #!% & ! ,a#%a(& + #!%g&

displace #! from steam

or acids

Mg  1g%s& + ! #!(g) 1g%#&!%s& + #!%g&

Al  ! l%s& + 2 #!%g& ! l%#&3%s& + 3 #!%g&Mn  1n%s& + ! #!%g& 1n%#&!%s& + #!%g&

Zn  Zn%s& + ! #!%g& Zn%#&!%s& + #!%g&

Fe  4e%s& + ! #!%g& 4e%#&!%s& + #!%g&

displace #! from acids

only

Ni  ,i%s& + ! #+%a(& ,i!+%a(& + #!%g&

Sn  *n%s& + ! #+%a(& *n!+%a(& + #!%g&

Pb  5b(s) + ! #+(aq) 5b!+(aq) + #!(g) 

H2 

can6t displace #! 

Cu 

Ag 

Pt 

Au

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soltions. ,ote that the "active" metals are all "attacked by acids"- what this really means is that they are capable

of donating electrons to #+.

The activity series has long been sed to predict the direction of oxidation)redction reactions- see here for a

nicely)done table with explanatory material. Consider' for example' the oxidation of C by metallic $inc that we

have mentioned previosly. The fact that $inc is near the top of the activity series means that this metal has a

strong tendency to lose electrons. 7y the same token' the tendency of Zn to accept electrons is relatively small.

Copper' on the other hand' is a poorer electron donor' and ths its oxidi$ed form' C' is a fairly good electron

acceptor. 8e wold therefore expect the reaction

Zn(s) + C!+  Zn!+ + C(s)

to proceed in the direction indicated' rather than in the reverse direction. n old)fashioned way of expressing this

is to say that "$inc will displace copper from soltion".

The above table is of limited practical se becase it does not take into accont the concentrations of the dissolved

species. In order to treat these reactions (antitatively' it is convenient to consider the oxidation and redction

steps separately.

Standard hal!cell potentials

8hen a net reaction proceeds in an electrochemical cell' oxidation occrs at one electrode %the anode& and

redction takes place at the other electrode %the cathode.& 8e can think of the cell as consisting of two half)cells

 9oined together by an external circit throgh which electrons flow and an internal pathway that allows ions to

migrate between them so as to preserve electro netrality.

"eduction potentials

ach half)cell has associated with it an electrode)soltion potential difference whose magnitde depends on the

nature of the particular electrode reaction and on the concentrations of the dissolved electro active species. The

sign of this potential difference depends on the direction %oxidation or redction& in which the electrode reaction

 proceeds. In order express them in a niform way- we adopt the convention that half)cell potentials are always

defined for the redction direction. Ths the half)cell potential for the Zn;Zn!+ electrode %or couple as it is

sometimes called& always refers to the redction reaction

Zn!+ + !e –   Zn%s&

In the cell Zn(s) < Zn!+(aq) << C!+(aq) < C(s) the $inc appears on the left side' indicating that it is being oxidi$ed'

not redced. 4or this reason' the potential difference contribted by the left half)cell has the opposite sign to its

conventional half)cell potential. 1ore generally' we can define the cell potential or cell 14 as

 E cell  = >V  = E right  ? E left  %@&

in which "right" and "left" refer to the cell notation convention %"redction on the right"& and not' of corse' to the

 physical orientation of a real cell in the laboratory. If we expand the above expression we see that the cell potential

 E cell  = V Cu ? V  solution + V  solution ? V  Zn

is 9st the difference between the two half)cell potentials E right  and E left .

"eerence hal!cells

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The fact that individal half)cell potentials are not directly measrable does not prevent s from defining and

working with them. lthogh we cannot determine the absolte vale of a half)cell potential' we can still measre

its vale in relation to the potentials of other half cells. In particlar' if we adopt a reference half)cell whose

 potential is arbitrarily defined as $ero' and measre the potentials of varios other electrode systems against this

reference cell' we are in effect measring the half)cell potentials on a scale that is relative to the potential of the

reference cell.

The reference cell that has niversally been adopted for this prpose is the hydrogen half-cell 

5t < A #!(g) < #+(aq) << ...

in which hydrogen gas is allowed to bbble over a platinm electrode having a specially treated srface which

cataly$es the reaction

A #!(g)  #+ + e – 

8hen this electrode is operated nder standard conditions of @ atm #! pressre' !BC' and p# = D' it becomes the

 standard hydrogen electrode' sometimes abbreviated *#.

In order to measre the relative potential of some other electrode cople 1

!+

;1' we can set p a cell

5t < #!(g) < #+ << 1!+ (aq) < 1(s)

whose net reaction is

#!(g) + 1!+(aq)  !#+ + 1(s)

the potential difference between the platinm and 1 electrodes will be

 E cell  = V  M  – V  solution  V  solution – V  !t 

 bt since the difference V  solution – V  !t  is by definition $ero for the hydrogen half)cell' the cell potential we measre

corresponds to

 E cell  = V  M  – V  solution

which is 9st the potential %relative to that of the *#& of the half)cell whose reaction is

1!+ + !e –   1(s)

Measurement o a standard reduction potential#

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The 1!+;1 half)cell is on the left' and the standard hydrogen cell is on the right. The two half)cells are 9oined

throgh the salt bridge in the middle. The more "active" the metal 1 %the greater its tendency to donate electrons

to #+&' the more negative will be E cell  = >V  = E right  ? E left 

 

*tandard EredctionF potentials are commonly denoted by the symbol E". E" vales for hndreds of electrodes

have been determined %mostly in the period @G!B)HB' dring which time they were referred to as "oxidation

 potentials"& and are sally tablated in order of increasing tendency to accept electrons %increasing oxidi$ing

 power.&

$able 2% some standard reduction

potentials

mch more extensive table can be fondhere. ,ote particlarly that

• nlike the activity series mentioned

above' this table incldes non-

metallic su#stances' and it is

quantitative.

• The more negative the half)cell 14'

the greater the tendency of the

redctant to donate electrons' and thesmaller the tendency of the oxidant to

accept electrons.

• species in the leftmost colmn can

act as an oxidi$ing agent to any

species above it in the redctant

colmn.

• xidants sch as Cl! that are below

#! will tend to decompose water.

o&idant%electron acceptor&

reductant%electron donor&

'() volts

 ,a+  ,a(s)  ?!.J@

Zn!+ Zn(s)  ?.J2

4e!+ 4e(s)  ?.HH

Cd!+ Cd(s)  ?.HD

5b!+ 5b(s)  ?.@!2

2 H*  H2(g) +#+++

gCl(s) g(s) + Cl ? (aq)  +.!!!

#g!Cl!(s) !Cl ? 

(aq) + !#g% & +.!2KC!+ C(s) +.33J

I!(s) ! I ?  +.B3B

4e3+ 4e!+ +.JJ@

g+ g(s) +.JGG

!(g) + H#+ ! #!% & +@.!3

Cl!(g) ! Cl ?  +@.32

Liven the E" vales for two half reactions' yo can easily predict the potential difference of the corresponding

cell: simply add the redction potential of the redction half)cell to the negative of the redction potential %that is'

to the oxidation potential& of the oxidation reaction.

 

Problem '&ample ,

4ind the standard potential of the cell

Cu(s) - Cu2* -- Cl .  - AgCl(s) - Ag(s)

and predict the direction of electron flow when the two electrodes are connected.

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 Solution: The above notation represents a cell in which metallic copper ndergoes oxidation' delivering electrons

to a reactant on the right' which gets redced. 7t what species actally receives the electronM It cannot be g'

 becase metallic elements do not form negative ions. The only redcible species on the right is the g+ contained

within the insolble salt gCl. Nedction of this ion to metallic g is accompanied by a release of Cl ?  ions into the

soltion. The two half)reactions and their standard potentials are

C %s& C!+ %a(& + ! e ?   ?%+D.33J& v

gCl %s& + e ?   g %s& + Cl ? %a(& +D.!!! v

 ,ote that becase C is being oxidi$ed %rather than redced&' we take the negative of the standard redction

 potential.

1ltiplying the second e(ation %bt not its reduction potential & by ! in order to balance electrons' we have the

net reaction

! gCl %s& + C %s& ! g %s& + ! Cl 

 ? %a(& + C!+ %a(&

Combining the two half)cell potentials shown above' the net cell potential is

 E cell  = %?D.33J + D.!!!& v = .+#,,/ v

7ecase this potential is negative' we know that the net cell reaction %and' of corse' the two half reactions&

 proceed in the reverse directions to those depicted above. Ths when the two electrode are connected' electrons

 pass from the silver electrode throgh the external circit to the copper electrode. ,ote that this corresponds to the

rle in noted in Table ! above: gCl acts as an oxidi$ing agent %electron sink& to metallic copper which appears

 below it in the redctant colmn.

If yo are wondering why we did not mltiply E" the for the C!+;C cople by two' the reason for this will be

explained in the next section.

Cell potentials and ree energ0

4rom the above' it shold be apparent that the potential difference between the electrodes of a cell is a measre of

the tendency for the cell reaction to take place: the more positive the cell potential' the greater the tendency for the

reaction to proceed to the right. 7t we already know that the standard free energy change expresses the tendency

for any kind of process to occr nder the conditions of constant temperatre and pressre. Ths >$ and E" 

measre the same thing' and are related in a simple way:

>$" = –n%E" %!&

... or in more detail %see below for explanations of the nits given for voltage&

few remarks are in order abot this very fndamental and important relation:

• The negative sign on the right indicates that a positive cell potential  %according to the sign convention

discssed previosly& implies a negative free energy change' and ths that the cell reaction will

spontaneosly proceed to the right .

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• lectrical work is done when an electric charge q moves throgh a potential difference >V . The right side

of (. ! refers to the movement of n moles of charge across the cell potential E"' and ths has the

dimensions of &or' .

• The vale of >$" expresses the maximm sefl work that a system can do on the srrondings. "sefl"

work is that which can be extracted from the cell by electrical means to operate a lamp or some other

external device. This excldes any !-V  work that is simply a conse(ence of volme change %which cold

conceivably be pt to some seO& and which wold be performed in any case' even if the reactants were

combined directly. This (antity of work ?>L can only be extracted from the system nder the limitingconditions of a thermodynamically reversi#le change' which for an electrochemical cell implies $ero

crrent. The more rapidly the cell operates' the less electrical work it can spply.

• If %  is expressed in colombs per mole of electrons' the electrical work is in 9oles per mole. To relate

these nits to electrical nits' recall that the colomb is one amp)sec' and that po&er ' which is the rate at

which work is done' is measred in watts' which is the prodct of amps and volts.

@ P = @ watt)sec = @ %amp)sec& Q volts

Ths the volt  has the dimensions of 9oles;colomb? the energy prodced per (antity of charge passing throgh

the cell. 7ecase voltage is the (otient of two extensive (antities' it is itself intensive. 8hen we mltiply theanodic and cathodic half)reactions by the stoichiometric factors re(ired to ensre that each involves the same

(antity of charge' the free energy change and the nmber of colombs both increase by the same factor' leaving

the potential %voltage& nchanged. This explains why we do not have to mltiply the E"s of the anode and cathode

reactions by stoichiometric factors when we are finding the potential of a complete cell.

If (. ! is solved for E"' we have

%3&

This states explicitly that the cell potential is a measre of the free energy change per mole of electrons

transferred ' which is a brief re)statement of the principle explained immediately above.

To see this more clearly' consider the cell

C(s) < C!+ << Cl ?  < gCl(s) < g(s)

for which we list the standard redction potentials and $s of the half)reactions:

reaction  E" )n%E"= $"

cathode ! Q EgCl%s& + e –   g%s& + Cl ? F

anode C%s& C!+ + ! e – 

+.!!! v

 ?%+.33J& v

 ?H!KDD P

+2BDDD P

net ! g(s) + ! Cl ? (aq) + C!+(aq)  gCl(s) + C(s)

cell C(s) < C!+(aq) << gCl(s) < Cl ? (aq) < g(s) 

 ?.@@B v +!!!DD P

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#ere we mltiply the cathodic reaction by two in order to balance the charge. 7ecase the anodic reaction is

written as an oxidation' we reverse the sign of its  E" and obtain E cell  = E right  ? E left  = .#,,/ volt for the cell potential.

The negative cell potential tells s that this reaction will not proceed spontaneosly.

1hen the electrons dont cancel out

 ,ote' however' that if we are combining two half reactions to obtain a third half reaction' the E" vales are not

additive' since this third half)reaction is not accompanied by another half reaction that cases the charges to

cancel. 4ree energies are always additive' so we combine them' and se >$" = –n%E" to find the cell potential.

Problem '&ample 2 

Calclate E" for the electrode 4e3+;4e(s) from the standard potential of the coples 4e3+;4e!+ and 4e!+;4e(s) 

 Solution: Tablate the vales and calclate the >$"s as follows:

(i)  4e3+ + e –   4e!+  E"@ = .JJ@ v ' >$"@ = ?.JJ@ % 

(ii)  4e!+ + ! e –   4e%s&  E"!= ?.HHD v ' >$"! = +.KKD % 

(iii)  Fe3* * 3 e –  4 Fe5s6  E"3 = M ' >$"3 = +.@DG % 

The free energy for half)reaction (iii) is .@DGn% ' so E"3 = ?.@DG;3 = .#+37 v

 

The fall of the electron

table of standard half)cell potentials smmari$es a large amont of chemistry' for it expresses the relative powers of varios sbstances to donate and accept electrons by listing redction half)reactions in order of

increasing vales' and ths of increasing spontaneity. The greater the vale of ' the greater the tendency of

the sbstance on the left to ac(ire electrons' and ths the stronger this sbstance is as an oxidi$ing agent.

If yo have stdied elementary chemical thermodynamics' yo will have learned abot the role that a (antity

called the $i##s free energy' sally referred to as simply the " free energy"' plays in determining the direction of

any chemical change. The rle is that all spontaneos change %that is' all reactions that proceed to the "right"& is

associated with a fall in the free energy' and the greater the degree of that fall %>$"&' the greater will be the

tendency for the reaction to take place.

If yo are not familiar with the concept of free energy' 9st think of it as something like potential energy' whichsimilarly decreases when spontaneos mechanical events occr' sch as the dropping of a weight.

*ince oxidation)redction processes involve the transfer of an electron from a donor to an acceptor' it makes sense

to focs on the electron and to consider that it falls from a higher)free energy environment %the redctant' or

"sorce"& to a lower)free energy one %the oxidant' or "sink".&

s can be seen from the diagram below' this model makes it far easier to predict what will happen when two or

more oxidants and redcants are combined- the electron "falls" as far as it can' filling p oxidi$ing agents %sinks&

from the bottom p' very mch in the same way as electrons fill atomic orbitals as we bild p larger atoms.

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'lectron!ree energ0 diagram o redo& couples

This chart is essentially an abbreviated form of a table

of standard potentials in which the varios coples are

displayed on a vertical scale corresponding to

= ?>$";n% . ny available sink on the right side will

tend to drain electrons from a sorce above it. 4or

example' immersion of metallic $inc in a soltion of

C*H will reslt in the redction of C!+ to metallic

copper %red arrows.& *imilarly' addition of chlorine to

water will tend to oxidi$e the water' prodcing ! and

Cl ?  %ble arrows.& ,ote especially the positions of the

#!; #+ and #!;!'#

+ coples on this chart' as they

define the range of s for sbstances that will not

decompose water %green region.&

more detailed table with a more complete explanation can be seen on the "4all of the electron" ttorial page- it is

strongly recommended that yo take the time to ac(ire a thorogh nderstanding of this concept.

t this point' it might be worth calling yor attention to the similar way of depicting acid)base reactions as

representing the "fall of the proton" as shown below and described mch more thoroghly here.

Proton!ree energ0 diagram o acid!base

s0stems

cids are proton sources %donors&' bases are proton

 sin's. 5rotons "fall" %in free energy& whenever a

 base is present that presents proton)empty free

energy levels. The red arrows show what happenswhen acetic acid is titrated with a strong base- the

reslts are acetate ion and water. ,ote here again

the crcial role of water' both as a proton acceptor

%forming hydronim ion& and as a proton donor

%forming hydroxide ion.& ,ote also that the p# of a

soltion is a direct measre of the average free

energy of protons in the soltion %relative to #3+.&

n important difference between proton transfer and electron transfer reactions is that the latter can vary greatly inspeed' from almost instantaneos to so slow as to be nobservable. cid)base reactions are among the fastest

known.

/atimer diagrams

Considerable insight into the chemistry of a single element can be had by comparing the standard electrode

 potentials %and ths the relative free energies& of the varios oxidation states of the element. The most convenient

means of doing this is the *atimer diagram. s an example' consider the /atimer diagram for iron:

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The formlas of the species that represent each oxidation state of the element are written from left to right in order 

of decreasing oxidation nmber' and the standard potential for the redction of each species to the next on the right

is written in between the formlas. 5otentials for reactions involving hydrogen ions will be p# dependent' so

separate diagrams are sally provided for acidic and alkaline soltions %effective hydrogen ion concentrations of

@1 and @D ?@H 1' respectively&.

The more positive the redction potential' the greater will be the tendency of the species on the left to be redced

to the one on the right. To see how /atimer diagrams are sed' look first at the one for iron in acid soltion. The

line connecting 4e3+ and 4e!+ represents the reaction

4e3+ + e –   4e!+

whose positive %.HHD v& indicates that metallic iron will dissolve in acidic soltion to form 4e !+. 7ecase the

oxidation of this species to the +3 state has a negative potential %).JJ@v- moving to the left on the diagram reverses

the sign&' the +! state will be the stable oxidation state of iron nder these conditions.

8isproportionation

This /atimer diagram for chlorine illstrates an important principle:

8hen the potential on the left of a species is less positive than that on the right. This indicates that the species can

oxidi$e and redce itself' a process known as disproportionation. s an example' consider Cl! in alkaline soltion.The potential for its redction to Cl ?  is sfficiently positive %+@.32 v& to spply the free energy necessary for the

oxidation of one atom of chlorine to

hypochlorite. Ths elemental chlorine is

thermodynamically nstable with respect to

disproportionation in alkaline soltion' and

the same it tre of the oxidation prodct'

Cl ?  %hypochlorite ion&.

9ehavior o chlorine in :ater

Cl! can oxidi$e water %green arrows' top& and also ndergo disproportionation %prple arrows' bottom&. In the

latter process' one Cl! molecle donates electrons to another.

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7ear in mind that many oxidation)redction reactions' nlike most acid)base reactions' tend to be very slow' so the

fact that a species is thermodynamically nstable does not always mean that it will (ickly decompose. Ths the

two reactions shown in the figre are normally very slow.

Thermodynamics of galvanic cells

The free energy change for a process represents the maximm amont of non) !V  work that can be extracted from

it. In the case of an electrochemical cell' this work is de to the flow of electrons throgh the potential difference

 between the two electrodes. ,ote' however' that as the rate of electron flow %i.e.' the crrent& increases' the

 potential difference mst decrease- if we short)circit the cell by connecting the two electrodes with a condctor

having negligible resistance' the potential difference is $ero and no work will be done. The fll amont of work

can be reali$ed only if the cell operates at an infinitesimal rate- that is' reversibly.

Ro shold recall that this is exactly analogos to the expansion of an ideal gas. The fll amont of work & = !dV 

is extracted only nder the special condition that the external pressre  !  opposing expansion is only

infinitesimally smaller than the pressre of the gas itself. If the gas is allowed to expand into a vacm % !  = D&' no

work will be done.

The total amont of energy a reaction can spply nder standard

conditions at constant pressre and temperatre is given by + .If the reaction takes place by combining the reactants directly

%no cell& or in a short)circited cell' no work is done and the heat

released is > + . If the reaction takes place in a cell that performs

electrical work' then the heat released is diminished by the amont of electrical work done. In the limit of

reversible operation' the heat released becomes

> +  = >$" + ,  > 

8hat yo need to know

1ake sre yo thoroghly nderstand the following essential ideas which have been presented above. It isespecially important that yo know the precise meanings of all the highlighted terms in the context of this topic.

• 8hen we refer to the "standard potential of a half)cell" or "cople" 1 !+;1' we mean the potential

difference E right  ? E left  of the cell

5t < #!(g) < #+ << 1!+ (aq) < 1(s) 

whose left half consists of a standard hydrogen electrode %*#& and whose net reaction is

#!(g) + 1!+(aq)  !#+ + 1(s)

• If the potential difference of this cell is positive % E right  ? E left  SD&' electrons will flow throgh an external

circit from the 5t;#! electrode to the 1 electrode and the cell reaction will spontaneosly proceed in the

direction written. The more positive the cell potential' the greater the tendency of this reaction to occr and

the stronger the oxidi$ing agent 1!+.

• Throgh the relation E" = ? >$".n%  it is apparent that a standard half)cell redction potential is simply the

decrease in the free energy per mole of electrons transferred to #+ ions nder the conditions that define the

*#. *trong redcing agents %good electron donors& have more negative E"s' while strong oxidi$ing agents

%good acceptors& have more positive E"s.

• 4or a more general cell (s) < + << 1!+ < 1(s) ' E" is similarly the fall in free energy per electron)mole

when 1!+ is redced by . This reaction can proceed spontaneosly only if the cell potential is positive

%>L negative.&

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• n electron free energy diagram that displays varios redox coples on a vertical scale of free energies

relative to #+ serves as a convenient means of visali$ing the possible reactions when two or more redox)

active pairs are present in a soltion. The position of a redox cople in relation to those of the # !; #+ and

#!;!'#+ coples is especially significant becase it indicates whether a given species will be

thermodynamically stable in water.

•  *atimer diagrams provide a convenient means of correlating the varios oxidation states of a particlar

element.

#ow cell potentials depend on concentrations

The standard cell potentials we discssed in a previos section refer to cells in which all dissolved sbstances are

at nit activity' which essentially means an "effective concentration" of @1. *imilarly' any gases that take part in

an electrode reaction are at an effective pressre %known as the fugacity& of @ atm. If these concentrations or

 pressres have other vales' the cell potential will change in a manner that can be predicted from the principles

yo already know.

*ppose' for example' that we redce the concentration of Zn!+ in the Zn;C cell from its standard effective vale

of @1 to an to a mch smaller vale:

Zn(s) | Zn2+(aq, .001M) || Cu2+(aq) | Cu(s)

This will redce the vale of / for the cell reaction

Zn(s) + C!+  Zn!+ + C(s)

ths making it more spontaneos' or "driving it to the right" as the *e Ch0telier principle wold predict' and

making its free energy change >$ more negative than >$' so that E  wold be more positive than E".

The relation between the actal cell potential and the standard potential is developed in the following way.

8e begin with the e(ation derived previosly which relates the standard free energy change %for the complete

conversion of prodcts into reactants& to the standard potential

>$" = ? n%E"

7y analogy we can write the more general e(ation

>$ = ? n%E 

which expresses the change in free energy for any extent of reactionU that is' for any vale of the reaction

(otient V. 8e now sbstitte these into the expression that relates L and >$" which yo will recall from the

chapter on chemical e(ilibrim:

>$ = >$" + 1,  ln /

which gives

 –n%E  = –n%E" + 1,  ln /

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which can be rearranged to

(1)

This is the very important 2ernst equation which relates the cell potential to the standard potential and to the

activities of the electroactive species. ,otice that the cell potential will be the same as E" only if / is nity. The

 ,ernst e(ation is more commonly written in base)@D log form and for !BC:

(2)

 Signiicance o the Nernst e;ation

The ,ernst e(ation tells s that a half)cell potential will change by BG millivolts per @D)fold change in the

concentration of a sbstance involved in a one)electron oxidation or redction- for two)electron processes' the

variation will be !K millivolts per decade

concentration change. Ths for the

dissoltion of metallic copper 

C(s)  C!+ + !e – 

the potential

 E  = %? D.33J& ? .D!GB log EC!+F

 becomes more positive %the reaction has a

greater tendency to take place& as the

cpric ion concentration decreases. This'

of corse' is exactly what the /e ChWtelier 

5rinciple predicts- the more dilte the prodct' the greater the extent of the

reaction.

Electrodes with poise

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The e(ation 9st above for the C;C!+ half)cell raises an interesting

(estion: sppose yo immerse a piece of copper in a soltion of pre

water. 8ith /  = EC!+F = D' the potential difference between the

electrode and the soltion shold be infiniteO re yo in danger of 

 being electroctedM Ro need not worry- withot any electron transfer'

there is no charge to $ap yo with. f corse it won6t be very long

 before some C!+ ions appear in the soltion' and if there are only a

few sch ions per liter' the potential redces to only abot !D volts.

1ore to the point' however' the system is so far from e(ilibrim %for 

example' there are not enogh ions to poplate the electric doble

layer& that the ,ernst e(ation doesn6t really give meaningfl reslts.

*ch an electrode is said to be n poised . 8hat ionic concentration is

needed to poise an electrodeM I don6t really know' bt I wold be

sspicios of anything mch below @D ?2 1.

 The Nernst equation works only in dilute ionic solutions

Ions of opposite charge tend to associate into loosely)bond ion pairs in more concentrated soltions' ths

redcing the nmber of ions that are free to donate or accept electrons at an electrode. 4or this reason' the ,ernst

e(ation cannot accrately predict half)cell potentials for soltions in which the total ionic concentration exceeds

abot @D ?3 1.

How the cell potential really  depends

on concentration!

The ,ernst e(ation accrately predicts cell

 potentials only when the e(ilibrim (otient term

/ is expressed in activities. Ionic activities departincreasingly from concentrations when the latter

exceed @D ?H to @D ?B  M ' depending on the si$es and

charges of the ions.

Activities and activity coefcients

If the ,ernst e(ation is applied to more concentrated soltions' the terms in the reaction (otient / mst be

expressed in "effective concentrations" or activities of the electroactive ionic species. The activity coefficient  X

%gamma& relates the concentration of an ion to its activity a in a given soltion throgh the relation a = Xc. *ince

electrode potentials measre activities directly' activity coefficients can be determined by carrying ot appropriate

14 measrements on cells in which the concentration of the ion of interest is known. The reslting  E s can then

 be sed to convert concentrations into activities for se in other calclations involving e(ilibrim constants.

 

Cell potentials and pH: stability diagrams

s most of s recall from or strggles with balancing redox e(ations in beginning chemistry corses' many

electron)transfer reactions involve hydrogen ions and hydroxide ions. The standard potentials for these reactions

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therefore refer to the p#' either D or @H' at which the appropriate ion has nit activity. 7ecase mltiple nmbers

of #+ or # ?  ions are often involved' the potentials given by the ,ernst e(ation can vary greatly with the p#.

It is fre(ently sefl to look at the sitation in another way by considering what combinations of potential and p#

allow the stable existence of a particlar species. This information is most seflly expressed by means of a  E )vs.)

 p# diagram' also known as a !our#ai3 diagram.

Staility o! water

s was noted in connection with the shaded region in the figre below' water is sb9ect to decomposition by

strong oxidi$ing agents sch as Cl! and by redcing agents stronger than #!. The redction reaction can be written

either as

!#+ + !e –   #!(g)

or' in netral or alkaline soltions as

#! + ! e –   #!(g) + ! # ? 

These two reactions are e(ivalent and follow the same ,ernst e(ation

which' at !BC and nit #! partial pressre redces to

 E  = E" ) %.DBG;!& Q ! p# = ?D.DBG p#

*imilarly' the oxidation of water 

! #! !(g) + H #+ + H e – 

is governed by the ,ernst e(ation

which similarly becomes E  = @.!3 ? D.DBG p#' so the E-vs)p# plots for both processes have identical slopes and

yield the stability diagram for water shown below.

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Stabilit0 5Pourbai&6 diagram or :ater

The two vales shown at the left refer to "standard"

conditions of nit #+ activity %p#=D& and gas pressres of @

atm. t combinations of p# and E  that lie otside the shaded

area' the partial pressres of ! or #! exceed @ atm'

signifying the decomposition of water. The nity partial

 pressres are of corse arbitrary criteria- in a system open to

the atmosphere' water can decompose even at mch lower

#! partial pressres' and at oxygen pressres below D.! atm.

4ortnately' these processes are in most cases (ite slow.

The above diagram has special relevance to electrochemical corrosion of metals. Ths metals above hydrogen in

the activity series will tend to ndergo oxidation %corrosion& by redcing #+ ions or water.

Chlorine in water

7ecase chlorine is widely sed as a disinfectant for drinking water' swimming pools' and sewage treatment' it is

worth looking at its stability diagram. ,ote that the effective bactericidal agent is not Cl ! itself' bt its oxidation

 prodct hypochloros acid #Cl which predominates at p# vales below its p0 a of J.3. ,ote also that

• Cl! is nstable in water except at very low p#- it decomposes into #Cl and Cl ? .

• #ypochloros acid and its anion are stronger oxidants than ! and ths sb9ect to decomposition in water.

The only stable chlorine species in water is Cl ? .

• Yecomposition of #Cl occrs very slowly in the dark' bt is cataly$ed by snlight. 4or this reason the

chlorine in otside swimming pools mst be fre(ently renewed.

• Yecomposition of Cl! and #Cl by reaction with organic material in mnicipal water spply systems

sometimes makes it necessary to in9ect additional chlorine at otlying locations.

 

Stabilit0 diagram or chlorine in :ater

ach solid line represents a combination of and p# at whichthe two species on either side of it can coexist- at all other

 points' only a single species is stable. ,ote that e(ilibria

 between species separated by diagonal lines are dependent on

 both E  and p#' while those separated by hori$ontal or vertical

lines are affected by p# only or E  only' respectively.

"ron

*tability diagrams are able to condense a great amont of information into a compact representation' and are

widely employed in geochemistry and corrosion engineering. The 5orbaix diagram for iron is one of the more

commonly seen examples.

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Pourbai& diagram or iron

Three oxidation states of iron %D' +!

and +3& are represented on this

diagram. The stability regions for the

oxidi$ed iron states are shown only

within the stability region of #!.

(ilibria between species separated

 by vertical lines are dependent on p#

only.

The +3 oxidation state is the only

stable one in environments in which

the oxidation level is controlled by

atmospheric !. This is the reason thearths crst contains iron oxides'

which developed only after the

appearance of green plants which are

the sorce of !.

Iron is attacked by #+ to form #! and

4e%II&- the latter then reacts with ! 

to form the varios colored 4e%III&

oxides that constitte [rst\.

 ,meros other species sch as

oxides and hydros oxides are not

shown. really [complete\ diagram

for iron wold need to have at least

two additional dimensions showing

the partial pressres of ! and C!.

 

Concentration cells

4rom yor stdy of thermodynamics yo may recall that the process

solte (concentrated)  solte (dilute)

is accompanied by a fall in free energy' and therefore is capable of doing work on the srrondings- all that is

re(ired is some practical way of captring this work. ne way of doing this is by means of a concentration cell

sch as

C(s) < C,3(45 M) << C,3(465 M) < C(s)

cathode: C!+(45 M) + !e –   C(s)

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anode: C(s)  C!+(465 M) + !e – 

net: C!+(45 M) C!+(465 M)

which represents the transport of cpric ion from a region of higher concentration to one of lower concentration.

The driving force for this process is the free energy change >L associated with the concentration gradient

%C! ? C@&' sometimes known as the free energy of diltion:

>Ldiltion = 1,  ln%C 7 – C 5&

 ,ote' however' that C!+ ions need not physically move between the two compartments- electron flow throgh the

external circit creates a "virtal" flow as copper ions are created in the low)concentration side and discharged at

the opposite electrode. ,itrate ions mst also pass between the cells to maintain electro netrality.

The ,ernst e(ation for this cell is

 E = E" ) %D.DBG; 2 & log / = D ) D.!G log D.@ = +D.!KB v

 ,ote that E" for a concentration cell is always $ero' since this wold be the potential of a cell in which the electro

active species are at nit activity in both compartments.

 

What you need to know

1ake sre yo thoroghly nderstand the following essential ideas which have been presented above. It is

especially important that yo know the precise meanings of all the highlighted terms in the context of this topic.

•  The Nernst equation relates the e#ective concentrations $activities% o! the co&ponents o! acell reaction to the standard cell potential' (or a si&ple reduction o! the !or& )n+ + ne– * )it tells us that a hal!,cell potential will chan-e y ./0n &illivolts per 1,!old chan-e in theactivity o! the ion'

• "onic concentrations can usually e used in place o! activities when the total concentration o! ions in the solution does not e3ceed aout aout '1M'

• "n those reactions in which 4+ or 546 ions take part the cell potential will also depend on thep4' 7lots o! E vs. p4 showin- the staility re-ions o! related species are very use!ul &eans o! 

su&&ari8in- the redo3 che&istry o! an ele&ent'

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Polariation and ts "#ect on Corrosion

5olari$ation is the change of potential from a stabili$ed state' e.g. from the open)circit electrode

 potential- as the reslt of the passage of crrent. It also refers to the change in the potential of an

electrode dring electrolysis' sch that the potential of an anode becomes more noble' and that of a

cathode more active' than their respective reversible potentials. ften accomplished by formation of a

film on the electrode srface.

5olari$ation is sometimes also referred to as "overvoltage" or "overpotential". In some

electrochemistry books' there is a differentiation between overvoltage and overpotential. The former 

refers to the difference between the actal electrode potential at which appreciable electrolysis begins

and the reversible electrode potential %the standard redox potential&- the latter refers to the potential

deviation from the e(ilibrim potential of a system.

In the context of corrosion' polari$ation refers to the potential shift away from the open circit

 potential %free corroding potential& of a corroding system. If the potential shifts in the "positive"

direction %above corr   &' it is called "anodic polari$ation". If the potential shifts in the "negative"

direction %below corr  &' it is called "Cathodic polari$ation".

4or all metals and alloys in any a(eos environment' cathodic polari$ation always redce the

corrosion rate. Cathodic protection is essentially the application of a cathodic polari$ation to a

corroding system.

4or a non)passive system %e.g. steel in seawater&' anodic polari$ation always increases the corrosion

rate. 4or systems showing active)to)passive transition' anodic polari$ation will increase the corrosion

rate initially and then case a drastic redction in the corrosion rate. nodic protection is essentially

the application of anodic polari$ation to a corroding system.

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$he %asics o& Cathodic Protection$a<ea:a0% Cathodic protection is one method sed to prevent corrosion in pipelines' ships' offshore oil platforms'

and other steel strctres.

Corrosion is a natrally occrring phenomenon commonly defined as the deterioration of a sbstance %sally a

metal& or its properties becase of a reaction with its environment. The tendency of a metal to corrode depends on

the grain strctre of the metal' its composition as formed dring alloying' and the temperatre or deformation of a

single metal srface developed dring fabrication.

Corrosion occrs as a reslt of an electrochemical reaction driven by a potential difference between two

electrodes' an anode and a cathode' connected by an electronic path and immersed in the same electrolyte. In the

case of niform corrosion' a mltitde of microscopic anodic and cathodic sites exist on the srface of the metal

strctre.

There are varios time)proven methods for preventing and controlling corrosion. ne of these is cathodic

 protection %C5&. #ere well take a look at cathodic protection' its types' and how it6s sed to protect bried

 pipelines against corrosion.

What is Cathodic Protection' The &etallic sur!aces e3posed to an electrolyte have a &ultitude o! &icroscopic anodic and

cathodic sites' 9here anodes are &ore electrone-ative than cathodes a potential di#erence is

created etween the& allowin- !or corrosion to occur'

The fnction of cathodic protection is to redce the potential difference between anodes and cathodes to a

neglected vale. This redction is de to the polari$ation of cathodes to the potential of most active anodes. In this

way' corrosion crrent is mitigated according to hms law.

Cathodic protection can be accomplished by sending a crrent into the strctre from an external electrode and

 polari$ing the cathodic sites in an electronegative direction.

Cathodic Protection Criteria"n order to achieve adequate C7 the protected structure &ust e polari8ed to a certain value' The

polari8ed potential is &easured with respect to a certain re!erence electrode' A copper0copper

sul!ate re!erence electrode $CSE% is the &ost co&&on electrode used in soil and !reshwater'

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There are two types of criteria for assessing cathodic protection. ither one may be sed depending on the

circmstances' althogh the first is considered sperior in many cases.

1' $he Potential Criterion The polari8ed potential o! the protected structure is to e equal to or &ore ne-ative than,:. &illivolts $&;% with respect to CSE'

2' $he Polariation hi&t Criterion The protected structure is to e polari8ed y 1 &; with respect to CSE !ro& its corrosionpotential'

Note: These criteria are for carbon steel; criteria may i!er for vario"s metal ty#es.

$ypes o& Cathodic Protection There are two types o! cathodic protection<

1' al*anic +node Cathodic Protection

o "n this type o! C7 protection is achieved y connectin- the protected structure to asacri=cial anode which is placed close to the protected structure'

o Sacri=cial anodes are &ade !ro& active &etals such as 8inc alu&inu& or&a-nesiu& which are considered the &ost active &etals accordin- to the -alvanicseries'

o C7 current is created y the potential di#erence etween sacri=cial anodes and the

protected structure'

o  The type o! anode used depends on electrolyte resistivity and the che&icalco&positions o! the electrolyte to which the sustrate is e3posed'

2' mpressed Current Cathodic Protection

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o "n this type o! C7 protection is achieved y connectin- the protected structure to ananode ed throu-h a trans!or&er recti=er $ T>%' The anode ed is a series o! uriedanodes that are electrically connected and surrounded y certain ack=ll to reducetheir resistance to the earth' The anode ed should e placed re&otely !ro& theprotected structure'

o  Three types o! anodes are used< Solule anodes $alu&inu& and steel% se&i,soluleanodes $-raphite and hi-h silicon cast iron $4SC"%% and non,solule anodes $platinu&&i3ed &etal o3ide and poly&er%

o  The &ain co&ponent o! this type o! C7 is the T> which !orces the current to ?ow !ro&the anodes to the protected structure $cathode%'

o  The type o! anodes used depends on the che&ical co&position o! the electrolyte towhich the sustrate is e3posed and the area to e protected'

+pplication o& Cathodic Protection ystems on %uried Pipelines

7ipelines are used !or transportin- water petroleu& products natural -as and other utilities' There@s a hu-e network o! pipin- syste&s used in every country all over the world' 7ipelines &ay

e onshore or o#shore and are suect to corrosion in oth cases' "! corrosion isnBt &iti-ated

dan-erous and e3pensive da&a-e can e the result'

There are several corrosion control techni(es sed on pipelines- cathodic protection is one of them. It can be

applied either to coated pipelines to mitigate the corrosion attack on areas where coating (ality may be poor. It is

also sed on bare pipelines. 7oth types of C5 can be applied to bried pipelines. The application of either of these

types depends on several factors' sch as the re(ired crrent'  soil resistivity' and the area to be protected.

C5 aims to polari$e a pipeline to a minimm potential of )KBD mv' for carbon steel and for ade(ate C5. The

 polari$ed potential is to be measred throgh test stations' which are to be installed at the following locations

along the rote of pipeline:

• At !requent intervals $e'-' 2 k& 0 1'2D &iles%

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• At crossin-s with !orei-n structures

• At points o! electrical isolation

• At so&e -alvanic anode locations

• At casin-s

• Near sources o! electrical inter!erence

• At the location o! stray current dischar-e to earth

Problems Created by Cathodic Protection"n lar-e pipeline networks there are a lot o! crossin-s parallelis& and approaches wherein the

pipeline has its applied C7 syste&' C inter!erence &ay occur etween pipelines acceleratin-

corrosion' "n order to overco&e this prole& pipelines can e electrically coupled either directly or

throu-h resistance'

4or coated pipelines' where the applied coating (ality is poor' cathodic disbondment may occr de to high C5levels. #igher temperatres may also promote cathodic disbondment. #igh 5# environments are also a concern in

terms of stress)corrosion cracking. In sch cases' the polari$ed potential of the pipeline mst be kept at a minimm

vale of )KBD m].

Nemember' cathodic protection is 9st one method sed to prevent corrosion' not 9st in pipelines' bt in ships'

offshore oil platforms' and other steel strctres. 8hether it6s the best application for the 9ob' or the only one to be

sed' is often specific to the strctre being protected.

Polariation

Defnition - What does Polarization mean?

5olari$ation is a mechanism that typically reslts in a change in the potential of an electrode dring electrolysis'

when the anodes potential becomes nobler than that of the cathode. It has the effect %based on conditions& of

decreasing the otpt voltage of batteries' increasing the voltage re(ired for electrolysis cells or lowering

crrents.

5olari$ation can also be described as a kinetic deviation from e(ilibrim de to an electric crrent passing

throgh a galvanic cell. 5olari$ation may occr at the cathode %cathodic polari$ation& or at the anode %anodic

 polari$ation&.The more common form of polari$ation is cathodic polari$ation.

Corrosionpedia explains Polarization

5olari$ation as an electrochemical phenomenon is of importance in the corrosion process. 4or all metals and alloys

in any a(eos environment' cathodic polari$ation always redces the corrosion rate. Cathodic protection refers to

the application of a cathodic polari$ation to a corroding system.

5olari$ation can occr in three ways:

• Concentration polari8ation

• >esistance polari8ation

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• Activation polari8ation

Concentration polari$ation of an electrode is the reslt of formation of a diffsion layer ad9acent to the srface of

the electrode where there is a gradient of ion concentration. Yiffsion of the ions throgh the layers controls the

electrochemical reaction and is important for processes sch as electroplating and corrosion. Concentration

 polari$ation may be redced by increasing agitation or raising the temperatre of the electrolyte.

Nesistance polari$ation describes the potential drop de to the high resistivity of the electrolyte srronding the

electrode. It may also be a reslt of the inslation effect of the film on the electrode srface formed by the reaction prodcts. Nesistance polari$ation is expressed by the hm6s law.

ctivation polari$ation occrs when the electrochemical reaction proceeds throgh several sccessive steps. The

speed of the overall reaction is determined by the slowest step %known as the rate)determining step& of the process.

4or example' in a hydrogen redction reaction' the reaction may proceed as follows:

1' 4ydro-en ions are asored !ro& the solution onto the anode sur!ace'

2' Electron trans!er occurs !ro& the anode to the hydro-en ions to !or& hydro-en'

F' The hydro-en ato&s !or& hydro-en -as &olecules'

D' 4ydro-en -as ules are !or&ed'

Corrosion Potential

Defnition - What does Corrosion Potential mean?

The corrosion potential of a given material is the electromotive force or the voltage condcted by its srface. This

is determined by immersing the material and a reference electrode in an electrolyte' casing the material6s srface

to release electrons.

Corrosionpedia explains Corrosion Potential 

In simple terms' corrosion potential is the characteristic or property of metal and nonmetal srfaces to lose

electrons in the presence of an electrolyte. Yring the process of corrosion' two electrodes are formed

spontaneosly' a cathode and an anode. Corrosion potential is the electrode potential that the material srface

ac(ires atomatically in its environment.

The corrosion potential of a material is a sefl parameter in estimating the present and ftre corrosion damage

and detection' as well as monitoring the electrochemical reaction casing corrosion' both at the work site as well

as in the laboratory. #ence' the stdy of this variable is important for designers of pipelines' e(ipment' systems as

well as strctres' and also for maintenance engineers in order to redce economic losses de to material

deterioration and its detection expenses' costly and high risk failres as well as repair and replacement costs.

Corrosion potential can be measred by finding the potential difference between an appropriate referenceelectrode and the material6s srface' sally a metal srface' when immersed in a given electrolyte. This

measrement is done by sing a high impedance voltmeter with high accracy to observe and record small

voltages withot re(iring significant crrent flow. higher crrent flow can affect the accracy of the voltage

measrement. 1easrement of corrosion potential is sed in evalation of effectiveness of protective coating on

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 pipelines and other e(ipment' as well as strctres. It also enables detection of defects in the coated srfaces'

sch as pinholes' lack of adhesion and porosity.

etting tarted with "lectrochemical Corrosion ,easurement

-e*iew o& the "lectrochemical %asis o& Corrosion

1ost metallic corrosion occrs via electrochemical reactions at the interface between the metal and an electrolyte

soltion. 4or example' a thin film of moistre on a metal srface forms the electrolyte for atmospheric corrosion.

second example is when wet concrete is the electrolyte for reinforcing rod corrosion in bridges. lthogh most

corrosion takes place in water' corrosion in non)a(eos systems is not nknown.

Corrosion normally occrs at a rate determined by an e(ilibrim between opposing electrochemical reactions.

ne reaction is the anodic reaction' in which a metal is oxidi$ed' releasing electrons into the metal. The other is

the cathodic reaction' in which a soltion species %often ! or #+& is redced' removing electrons from the metal.

8hen these two reactions are in e(ilibrim' the flow of electrons from each reaction is balanced' and no net

electron flow %electrical crrent& occrs. The two reactions can take place on one metal or on two dissimilar metals

%or metal sites& that are electrically connected.

4igre @ sketches this process. The vertical axis is electrical potential and the hori$ontal axis is the logarithm of

absolte crrent. The theoretical crrent for the anodic and cathodic reactions is represented as straight lines. The

crved line is the total crrent: the sm of the anodic and cathodic crrents. This is the crrent that yo measre

when yo sweep the potential of the metal with yor potentiostat. The sharp point in the crve is actally the point

where the crrent reverses polarity as the reaction changes from anodic to cathodic' or vice versa. The sharp pointis cased by plotting along a logarithmic axis. The se of a logarithmic axis is necessary becase of the wide range

of crrent vales that mst be recorded dring a corrosion experiment. 7ecase of the phenomenon of passivity'

the crrent often change by six orders of magnitde dring a corrosion experiment.

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Figure ,# Corrosion process showing anodic and cathodic components of crrent.

The potential of the metal is the means by which the anodic and cathodic reactions are kept in balance. Nefer to

4igre @. ,otice that the crrent from each half reaction depends on the electrochemical potential of the metal.

*ppose that the anodic reaction releases too many electrons into the metal. xcess electrons ths shift the

 potential of the metal more negative' which slows the anodic reaction and speeds p the cathodic reaction. This

conteracts the initial pertrbation of the system.

The e(ilibrim potential assmed by the metal in the absence of electrical connections to the metal is called the

open)circit potential' oc. In most electrochemical corrosion experiments' the first step is the measrement of oc.

The vale of either the anodic or cathodic crrent at oc is called the corrosion crrent' Icorr . If we cold measre

Icorr ' we cold se it to calclate the corrosion rate of the metal. nfortnately' Icorr  cannot be measred directly.

#owever' it can be estimated sing electrochemical techni(es. In any real system' I corr  and corrosion rate are afnction of many system parameters' inclding type of metal' composition of the soltion' temperatre' movement

of the soltion' metal history' and many others.

The above description of the corrosion process does not say anything abot the state of the metal srface. In

 practice' many metals form an oxide layer on their srface as they corrode. If the oxide layer inhibits frther

corrosion' the metal is said to passivate. In some cases' local areas of the passive film break down' allowing

significant metal corrosion to occr in a small area. This phenomenon is called pitting corrosion or simply pitting.

7ecase corrosion occrs via electrochemical reactions' electrochemical techni(es are ideal for the stdy of the

corrosion processes. In electrochemical stdies' a metal sample with a srface area of a few s(are centimeters is

sed to model the metal in a corroding system. The metal sample is immersed in a soltion typical of the metals

environment in the system being stdied. dditional electrodes are immersed in the soltion' and all the electrodes

are connected to a device called a potentiostat. potentiostat allows yo to change the potential of the metal

sample in a controlled manner and measre the crrent that flows as a fnction of applied potential.

7oth controlled)potential %potentiostatic& and controlled)crrent %galvanostatic& polari$ation are sefl. 8hen the

 polari$ation is done potentiostatically' crrent is measred' and when it is done galvanostatically' potential is

measred. This discssion will concentrate on controlled)potential methods' which are mch more common than

galvanostatic methods. 8ith the exception of open)circit potential verss time' electrochemical noise' galvaniccorrosion' and a few others' potentiostatic mode is sed to pertrb the e(ilibrim corrosion process. 8hen the

 potential of a metal sample in soltion is forced away from oc' it is referred to as polari$ing the sample. The

response %that is' reslting crrent& of the metal sample is measred as it is polari$ed. The response is sed to

develop a model of the samples corrosion behavior.

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Guantitative Corrosion Theory

In the previos section we pointed ot that Icorr  cannot be measred directly. In many cases' yo can estimate it

from crrent)verss)voltage data. Ro can measre a logarithmic crrent verss potential crve over a range of

abot one half volt. The voltage scan is centered on oc. Ro then fit the measred data to a theoretical model of

the corrosion process.

The model we se for the corrosion process assmes that the rates of both the anodic and cathodic processes are

controlled by the kinetics of the electron)transfer reaction at the metal srface. This is generally the case forcorrosion reactions. n electrochemical reaction nder kinetic control obeys (. @' the Tafel e(ation.

 

In this e(ation'

 8  is the crrent reslting from the reaction

 8 6 is a reaction)dependent constant called the exchange crrent

 E  is the electrode potential

 E 6 is the e(ilibrim potential %constant for a given reaction&

 9  is the reactions Tafel constant %constant for a given reaction' with nits of volts;decade.

The Tafel e(ation describes the behavior of one isolated reaction. In a corrosion system' we have two opposing

reactions: anodic and cathodic.

The Tafel e(ations for the anodic and cathodic reactions in a corrosion system can be combined to generate the

7tler)]olmer e(ation %(. !&.

where

 8  is the measred crrent from the cell in amp^res

 8 corr  is the corrosion crrent in amp^res

 E  is the electrode potential

 E corr  is the corrosion potential in volts

 9 a is the anodic _ Tafel constant in volts;decade

_c is the cathodic _ Tafel constant in volts;decade

8hat does (. ! predict abot the crrent)verss)voltage crveM t corr ' each exponential term e(als one. The

cell crrent is therefore $ero' as yo wold expect. ,ear corr ' both exponential terms contribte to the overall

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crrent. 4inally' as the potential is driven far from corr  by the potentiostat' one exponential term predominates and

the other term can be ignored. 8hen this occrs' a plot of logarithmic crrent verss potential becomes a straight

line.

plot of log I verss is called a Tafel plot. The Tafel plot in 4igre @ was generated directly from the 7tler)

]olmer e(ation. ,otice the linear sections of the cell crrent crve.

In practice' many corrosion systems are kinetically controlled and ths obey (. !. crve of logarithmic crrent

verss potential that is linear on both sides of corr  is indicative of kinetic control for the system being stdied.

#owever' there can be complications' sch as:

• Concentration polari8ation where the rate o! a reaction is controlled y the rate at whichreactants arrive at the &etal sur!ace' 5!ten cathodic reactions show concentrationpolari8ation at hi-her currents when di#usion o! o3y-en or hydro-en ion is not !ast enou-hto sustain the kinetically controlled rate'

• 53ide !or&ation which &ay or &ay not lead to passivation' This process can alter thesur!ace o! the sa&ple ein- tested' The ori-inal sur!ace and the altered sur!ace &ay havedi#erent values !or the constants in Eq' 2'

• 5ther e#ects that alter the sur!ace such as pre!erential dissolution o! one co&ponent o! analloy can also cause prole&s'

• A &i3ed control process where &ore than one cathodic or anodic reaction occurssi&ultaneously &ay co&plicate the &odel' An e3a&ple o! &i3ed control is the si&ultaneousreduction o! o3y-en and hydro-en ion'

• (inally potential drop as a result o! cell current ?owin- throu-h the resistance o! your cellsolution causes errors in the kinetic &odel' This last e#ect i! it is not too severe &ay ecorrectale via ">,co&pensation in the potentiostat'

In most cases' complications like those listed above case non)linearities in the Tafel plot. se with cation the

reslts derived from a Tafel plot withot a well)defined linear region.

Classic Tafel analysis is performed by extrapolating the linear portions of a logarithmic crrent verss potential

 plot back to their intersection. *ee 4igre ! %which is 4igre @ reprinted with annotations that demonstrate the

analysis&. The vale of either the anodic or the cathodic crrent at the intersection is I corr . nfortnately' many real)

world corrosion systems do not provide a sfficient linear region to permit accrate extrapolation. 1ost modern

corrosion test software' sch as Lamry Instrments YC@DB YC Corrosion Techni(es software' performs a more

sophisticated nmerical fit to the 7tler)]olmer e(ation. The measred data are fit to (. ! by ad9sting the

vales of corr ' Icorr ' _a' and _c. The crve)fitting method has the advantage that it does not re(ire a flly developed

linear portion of the crve.

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Figure 2# Classic Tafel analysis.

Polariation -esistance

(. ! can be frther simplified by restricting the potential to be very near to corr . Close to corr ' the crrent)verss)

voltage crve approximates a straight line. The slope of this line has the nits of resistance %`&. The slope is'

therefore' called the polari$ation resistance' N  p. n N  p vale can be combined with an estimate of the _ coefficients

to yield an estimate of the corrosion crrent.

If we approximate the exponential terms in (. ! with the first two terms of a power)series expansion % & and

simplify' we get one form of the *tern)Leary e(ation:

In a polari$ation resistance experiment' yo record a crve of crrent verss voltage as the cell voltage is swept

over a small range of potential that is very near to oc %generally @D m]&. nmerical fit of the crve yields a

vale for the polari$ation resistance' N  p. 5olari$ation resistance data do not provide any information abot the

vales for the _ coefficients. Therefore' to se (. 3' yo mst provide _ vales. These can be obtained from a

Tafel plot' or estimated from yor experience with the system yo are testing.

Calculation o& Corrosion -ate &rom Corrosion Current

The nmerical reslt obtained by fitting corrosion data to a model is generally the corrosion crrent. 8e are

interested in corrosion rates in the more sefl nits of rate of penetration' sch as millimeters per year. #ow is

corrosion crrent sed to generate a corrosion rateM ssme an electrolytic dissoltion reaction involving a

chemical species' *:

  S H Sn+ + ne6

Ro can relate crrent flow to mass via 4aradays /aw.

G I n() Eq' D

where

/ is the charge in colombs reslting from the reaction of species *

n is the nmber of electrons transferred per molecle or atom of *

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 %  is 4aradays constant = G2 HKB colombs;mole

 M  is the nmber of moles of species * reacting

more sefl form of (. H re(ires the concept of e(ivalent weight. The e(ivalent weight %8& is the mass of

species * that will react with one 4araday of charge. 4or an atomic species' 8 = 8 .n %where 8 is the atomic

weight of the species&.

Necalling that M  = m;8 and sbstitting into (. H we get:

 

where m is the mass of species * that has reacted.

In cases where the corrosion occrs niformly across a metal srface' the corrosion rate can be calclated in nits

of distance per year. 7e carefl: this calclation is only valid for niform corrosion- it dramatically nderestimates

the problem when locali$ed corrosion occrsO

4or a complex alloy that ndergoes niform dissoltion' the e(ivalent weight is a weighted average of the

e(ivalent weights of the alloy components. 1ole fraction' not mass fraction' is sed as the weighting factor. If the

dissoltion is not niform' yo may have to measre the corrosion prodcts to calclate 8.

Conversion from a weight loss to a corrosion rate %CN& is straightforward. 8e need to know the density' d' and the

sample area' . Charge is given by V = It' where t is the time in seconds and I is a crrent. 8e can sbstitte in the

vale of 4aradays constant. 1odifying (. B'

 

where

Icorr  The corrosion crrent in amp^res

0 constant that defines the nits for the corrosion rate

8 The e(ivalent weight in grams;e(ivalent

d Yensity in g;cm3

*ample area in cm!

 

$able ,# Corrosion "ate Constants

nits for corrosion rate 0 nits

mm;year %mmpy& 3!J! mm %)cm)year&

milli)inches;year %mpy& @.!KK Q @DB milli)inches %)cm)year&

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IR Compensation

8hen yo pass crrent between two electrodes in a condctive soltion' there are always regions of different

 potentials in the soltion. 1ch of the overall change in potential occrs very close to the srface of the

electrodes. #ere the potential gradients are largely cased by ionic concentration gradients set p near the metal

srfaces. lso' there is always a potential difference %a potential drop& cased by crrent flow throgh the

resistance in the blk of the soltion.

In an electrochemical experiment' the potential that yo wish to control or measre is the potential of a metal

specimen %called the 8orking lectrode& verss a Neference lectrode. 8e are normally not interested in the

 potential drops cased by soltion resistances becase they are negligible in typical electrolyte soltions sch as @

1 #!*H or B ,aCl.

Lamry Instrments potentiostats' like all modern electrochemical instrments' are three)electrode potentiostats.

They measre and control the potential difference between a non)crrent)carrying Neference lectrode and one of

the two crrent)carrying electrodes %the 8orking lectrode&. The potential drop near the other crrent)carrying

electrode %the Conter lectrode& does not matter when a three)electrode potentiostat is sed.

Carefl placement of the Neference lectrode can compensate for some of the IN)drop reslting from the cell

crrent' I' flowing throgh the soltion resistance' N. Ro can think of the Neference lectrode as sampling the

 potential somewhere along the soltion resistance. The closer it is to the 8orking lectrode' the closer yo are to

measring a potential free from IN errors. #owever' complete IN compensation cannot be achieved in practice

throgh placement of the reference electrode' becase of the finite physical si$e of the electrode. The portion of

the cell resistance that remains after placing the Neference lectrode is called the ncompensated resistance' N .

Lamry potentiostats can se crrent)interrpt or positive)feedback IN compensation to dynamically correct

ncompensated resistance errors. In the crrent)interrpt techni(e' the cell crrent is periodically trned off for a

very short time. 8ith no crrent flowing throgh the soltion resistance' its IN drop disappears instantly. The

 potential drop at the electrode srface remains constant on a rapid time scale. The difference in potential with the

crrent flowing and withot is a measre of the ncompensated IN drop.

The potentiostat makes a crrent)interrpt measrement immediately after it ac(ires each data point. The

 potentiostat actally takes three potential readings: @ before the crrent is trned off' and ! and 3 while it is off

%see 4igre 3&. ,ormally' the latter two are sed to extrapolate the potential difference' ' back to the exact

moment when the crrent was interrpted. The timing of the interrpt depends on the cell crrent. The interrpt

time is HD s on the higher crrent ranges. n lower crrent ranges' the interrpt lasts longer.

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Figure 3. Crrent)interrpt potential verss time.

In controlled potential modes' the applied potential can be dynamically corrected for the measred IN error in oneof several ways. In the simplest of these' the IN error from the previos point is applied as a correction to the

applied potential. 4or example' if an IN free potential of @ ] is desired' and the measred IN error is D.! ]' the

 potentiostat applies @.! ]. The correction is always one point behind' for the IN error from one point is applied to

correct the applied potential for the next point. In addition to this normal mode' a Lamry Instrments potentiostat

offers more)complex feedback modes in which the two points on the decay crve are averaged.

7y defalt in the controlled potential modes' the potential error measred via crrent)interrpt is sed to correct

the applied potential. In the controlled crrent modes' no correction is re(ired. If IN compensation is selected' the

measred IN error is sbtracted from the measred potential. ll reported potentials are therefore free from IN

error.

4or a detailed theoretical discssion of ncompensated resistance' see 0eith 7. ldham' et al.' nalytical

Chemistry' J! %!DDD&' 3GJ! and 3GK@.

Current and Voltage Conventions

Crrent polarities in electrochemical measrements can be inconsistent. crrent vale of ?@.! m can mean

different things to workers in different branches of electrochemistry or in different contries or even to different

 potentiostats. To an analytical electrochemist it represents @.! m of anodic crrent. To a corrosion scientist it

represents @.! m of cathodic crrent. Lamry Instrments potentiostat in defalt mode follows the corrosion

convention for crrent in which positive crrents are anodic and negative crrents are cathodic. 4or the

convenience of or sers arond the world' Lamry Instrments potentiostats can provide the crrent polarity as

 per yor preference with a simple software command.

The polarity of the potential can also be a sorce of confsion. In electrochemical corrosion measrement' the

e(ilibrim potential assmed by the metal in the absence of electrical connections to the metal is called the open)

circit potential' oc. 8e se the term corrosion potential' corr ' for the potential in an electrochemical experiment

at which no crrent flows' as determined by a nmerical fit of crrent)verss)potential data. In an ideal case' the

vales for oc and corr  are identical. ne reason the two voltages may differ is that changes have occrred to the

electrode srface dring the scan.

8ith most modern potentiostats' all potentials are specified or reported as the potential of the working electrode

with respect to either the reference electrode or the open)circit potential. The former is always labeled as [vs.

ref \ and the latter as [vs. oc\. The e(ations to convert from one form of potential to the other are:

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  E vs' Eoc I $E vs' Ere! % 6 Eoc

  E vs' Ere!  I $E vs' Eoc% + Eoc

Negardless of whether potentials are verss ref  or verss oc' one sign convention is sed. The more positive a

 potential' the more anodic it is. 1ore anodic potentials accelerate oxidation at the 8orking lectrode. Conversely'

a negative potential accelerates redction at the 8orking lectrode.

ome -e&erences on Corrosion $heory and "lectrochemical Corrosion $ests

YC lectrochemical Test 1ethods' ,.L. Thompson and P.#. 5ayer' ,ational ssociation of Corrosion ngineers.I*7,: @)KJJG@H)23)D.

5rinciples and 5revention of Corrosion' Yenny . Pones' 5rentice)#all' @GG2. I*7, D)@3)3BGGG3)D.

5olari$ation Nesistance 1ethod for Yetermination of Instantaneos Corrosion Nates' P.N. *clly' Corrosion' B2

%!DDD&' @GG.

*everal electrochemical corrosion techni(es are approved by the *T1 %merican *ociety for Testing and

1aterials' @DD 7arr #arbor Yrive' 8est Conshohocken' 5 @GH!K. They may be fond in ]olme 3.D! of the

*T1 *tandards:

L B: 5otentiostatic and 5otentiodynamic nodic 5olari$ation 1easrements

L BG: 5olari$ation Nesistance 1easrements

L 2@: Cyclic 5olari$ation 1easrements for /ocali$ed Corrosion *sceptibility of Iron)' ,ickel)' and Cobalt)

7ased lloys

L @DD: Cyclic Lalvanostaircase 5olari$ation

L @D2: ]erification of lgorithm and (ipment for lectrochemical Impedance 1easrements

L @DK: lectrochemical 5otentiokinetic Neactivation %5N& for Yetecting *ensiti$ation

L @BD: lectrochemical Critical 5itting Temperatre Testing of *tainless *teels

lectrochemical Techni(es in Corrosion ngineering' ,ational ssociation of Corrosion ngineers' @GK2.

Corrosion Testing and valation' *T5 @DDD' d. N. 7aboian and *.8. Yean' merican *ociety for Testing and

1aterials' 8est Conshohocken' 5' @GG@. I*7, D)KD3@)@HD2)D.

lectrochemical Corrosion Testing' *T5 J!J' d. 4. 1ansfeld and . 7ertocci' merican *ociety for Testing and

1aterials' 8est Conshohocken' 5' @GJG.

Corrosion and Corrosion Control' 3rd ed.' #erbert #. hlig' Pohn 8iley and *ons' ,ew Rork' @GKB.