the Nernst Equation and Pourbaix Diagrams

7/29/2019 the Nernst Equation and Pourbaix Diagrams

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8/27/12 Do ITPo MS - TLP Lib rary Th e Nern st Eq uatio n an d Po urbaix Diagrams

1/16www.doitpoms.ac.uk/tlplib/pourbaix/printall.php

DoITPoMS

The Nernst Equation and Pourbaix Diagrams

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Contents

Main pages

Aims

Before you start

Introduction

Background

The Nernst equation

Construction of a Pourbaix Diagram

Anatomy of a Pourbaix Diagram

Examples of a Pourbaix Diagram

Constructing a 3D Pourbaix Diagram

Summary

Questions

Going further

Additional pages

Other reference electrodes

Example 1

Example 2

Example 3

Activity

Detailed derivation of the Nerns t equation

Further examples of the Nernst equation

Aims

On completion of this tutorial you should be able to:

Introduce and explain the basic ideas of electrochemis try, including electrochemical potentials, half cell reactions and equilibria.

Describe the mechanisms of aqueous corrosion

Derive the Nernst equation and s how how it can be used to derive Pourbaix diagrams .

Explain the information contained in a Pourbaix diagram, and dem onstrate how this can be used to predict corrosion behaviour.

Before you start

This TLP is largely self-explanatory, but a basic knowledge of logarithms and thermodynamics may be of some help. A general introduction to

relevant thermodynamics can be found here.

Introduction

Corrosion is the wastage of material by the chemical action of its environment. It does not include mechanis ms such as erosion or wear, which are

mechanical.Aqueouscorrosion is the oxidation of a metal via an electrochemical reaction within water and its diss olved compounds. Aqueous

corrosion is dependent on the presence of water to act as an ion conducting electrolyte.


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An understanding of aqueous corros ion is essential for all industries. The lifetime and safety of chemical plants, offshore platforms and ships are

all dependent on controlling and predicting corrosion rates and products.

This TLP introduces the concepts of electrochemical equilibrium reactions, electrode potentials, construction of Pourbaix diagrams using the Nerst

equation and their interpretation. A Pourbaix diagram is a plot of the equilibrium potential of electrochemical reactions agains t pH. It shows how

corrosion mechanism s can be examined as a function of factors such as pH, temperature and the concentrations of reacting species .

Background

Electrode potentials

The electrode potential, E, of a metal refers to the potential difference meas ured (in volts) between a metal electrode and a reference electrode.

E is the equilibrium potential (or reversible potential), which describes the equilibrium between two different oxidation states of the sam e element,

at whatever concentration (or pressure) they occur. E varies with concentration, pressure and temperature. It describes the electrode potential

when the components of the reaction are in equilibrium. This does NOT mean that they are in equilibrium with the standard hydrogen electrode. It

means only that the reaction components are in equilibrium with each other. In the reaction

A + ze =A,

a concentration, C , ofA is in equilibrium with solidA. The reaction moves away from equilibrium only if there is a source or sink for electrons.

If this were the case, then the potential would move away from E .

E , the standard equilibrium potential (or standard electrode potential), is defined as the equilibrium potential of an electrode reaction when all

components are in their standard s tates, measured agains t the standard hydrogen electrode (SHE). It describes the equilibrium between two

different oxidation states of the same element. E is a constant for a given reaction, defined at 298 K. Values ofE for various electrochemical

reactions can be found in data books.

At equi librium, the chem ical driving force for an electrochemical reaction, G is equal to the electrical driving force, E . G corresponds to a charge,

zF, taken through the potential, E . The measured potential for an electrochemical reaction is therefore directly proportional to its free energy

change.

G = -zFE

where zis the number of moles of electrons exchanged in the reaction and Fis Faradays cons tant, 96 485 coulombs per mole of electrons.

Similarly, under standard conditions ,

G = -zFE

Aqueous corrosion

Oxidation of a metal in an aqueous environment is dependent on potential, E, and pH.

If oxidation does occur, the metal species is oxidised and loses electrons, forming metal cations; and a corresponding reduction reaction that

consumes electrons at the cathode

In aqueous corrosion water is the electrolyte, an ion-conducting medium. This m eans that the sites of oxidation and reduction can be spatially

separate. This is different from a gas eous environment, as a gas cannot conduct ions.

A metal oxidising to produce metal ions may dissolve into the water, resulting in corrosion. This is di fferent from corrosion in a gas, where the

oxidised metal s tays where it is produced, as an oxide film on the metal.

e

e

z+ -

Az+

Z+

e

0

0 0

e

e

e

0 0


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Electrochemical half-cell reactions

A half-cell reaction is an electrochemical reaction that results in a net surplus or deficit of electrons. It is the smalles t complete reaction step from

one species to another. Although this reaction may proceed as a sequence of more s imple reactions, these intermediate stages are not stable.

A half-cell reaction can either be a reduction, where electrons are gained, or an oxidation, where electrons are lost.

The following mnemonic is often helpful:

OILRIG: Oxidation Is Loss; Reduction Is Gain (of electrons).

The anode is the s ite of oxidation where electrons are los t.

The cathode is the s ite of reduction where electrons are gained.

Anions, such as O , are negatively charged ions , attracted to the anode.

Cations, such as Fe , are positively charged ions, attracted to the cathode.

Reduction half-cell reactions

Reduction reactions occur at the cathode and involve the consumption of electrons. In corrosion these normally correspond to reduction of oxygen

or evolution of hydrogen, such as:

O + H O + 4e = 4OH

O + 4H + 4e = 2H O

2H O + 2e = H +2OH

2H + 2e = H

Oxidation half-cell reactions

Oxidation reactions occur at the anode and involve the production of e lectrons. For the corrosion of metals , these reactions normally correspond to

the various m etal dissolution or oxide formation reactions, such as:

Fe = Fe + 2e

Fe = Fe + e

Fe + 2OH = Fe(OH) + 2e

2Fe + 3H O = Fe O + 6H + 6e

In addition to causing corrosion, oxidation may result in the formation of apassive oxide. The passive oxide produced may protect the metal

beneath from further corrosion s ignificantly slowing further corrosion. An example of such pass ivation is that of aluminium in water, where

aluminium is oxidised to from a layer of Al O that protects the metal beneath from further oxidation.

Reference electrodes

Since only differences in potential can be measured, a benchm ark electrode is required, against which all other electrode potentials can be

compared. The particular reference electrode used must be s tated as part of the units.

The Standard Hydrogen Electrode (SHE)

The electrode reaction

2H + 2e = H

is defined as having an electrode potential, E /H of zero volts, when all reactants and products are in the standard state. The standard chemical

potential of H at 1 molar (M) concentration is by definition equal to zero.

The standard state is defined as 298 K, 1 bar pressure for gases and a concentration 1 molar (1 mol dm ) for ions in aqueous s olution.

As a direct resul t of this , the standard hydrogen electrode (SHE) is commonly used as a reference electrode. When coupled with an electrode, the

potential difference measured is the electrode potential of that electrode, as the SHE establis hes by definition the zero point on the electrochemical

2-

2+

2 2

- -

2

+ -

2

2

-

2

-

+ -

2

2+ -

2+ 3+ -

-

2

-

2 2 3

+ -

2 3

+ -

2

H+ 2

+

-3


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scale.

The standard hydrogen electrode consists of a platinum electrode suspended in a sulphuric acid solution with a one molar concentration of H .

Purified hydrogen is bubbled through to equilibrate the 2H + 2e = H electrode reaction.

[Pop-up forother reference electrodes]

The diagram above shows how the standard potential, E of nickel can be determined. The nickel electrode contains Ni ions in equilibrium with

nickel metal.

The hydrogen electrode is linked via a salt bridge to the deaerated solution in which the nickel electrode is im mersed. This permits charge transfer

and potential meas urement but not mass transfer of the acid solution in the electrode.

When E orE are measured relative to the SHE (or som e other reference electrode), a voltmeter is used. The voltmeter is required to have a high

impedance to resis t any current flowing between the electrode and the SHE. If a current were allowed to flow, the electrodes would becom e

polarised and would no longer be at equilibrium.

In practice, it is often difficult or imposs ible to determine experimentally the standard electrode potential for electrochemical systems. Many

systems lie outside the water stability zone or are passive. For example, zinc will imm ediately begin to oxidise when immersed in water.

It is very sim ple to determine accurately the s tandard equilibrium potential from the equation linking chem ical driving force with the electrical driving

force,

G = -zFE

Now G , the standard free energy of formation can be expressed as

G = (products) (reactants)

where is the standard chemical potential. By combining these equations,

.

To obtain a standard equilibrium potential, E , for an electrochemical reaction, all that is required is to look up relevant values of standard chemical

potential.

How corrosion of metal occurs

If a metal surface is immersed in an electrolyte such as water, metal ions tend to be los t from the metal into the electrolyte, leaving electrons

behind on the m etal. This will continue to occur until the metal reaches its equilibrium potential and the system comes to equilibrium, with a certain

+

+ -

2

0 2+

e

0

0 0

0

0 0 0

0

0


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concentration of diss olved ions . The metal is at its equilibrium potential, E . If the electrolyte were to be continuously replaced (by water flowing in

through a pipe for example), more and more metal ions would be lost, resulting in continuous corrosion of the metal.

A cathodic reaction may occur that uses up the electrons los t by the metal species . In the reaction,

2H + 2e = H

if the hydrogen gas evolved is lost from the s ystem, the reaction is prevented from reaching equilibrium.

The cathodic reaction acts as a s ink for electrons liberated in the oxidation reaction of the metal. As a result of this, the metal will not reach its

equilibrium potential. The metal oxidation reaction is therefore not in equi librium and carries a net reaction. The difference between the potential, E,of the metal and its equilibrium potential, E is called the overpotential and is given the symbol .

= E E

As corrosion occurs, the mass of metal is reduced due to the conversion of atoms to ions , which are subsequently los t. The sites of oxidation (the

anode) and reduction (the cathode) can both be situated on the sam e piece of metal there is no need for an external electrode to be present for

the process to occur.

Rules for balancing electrochemical equations

The aim of this procedure is to balance electrochemical equations in terms of electronic charge and moles of components, given the main reaction

product and reactant.

By convention, electrochemical reactions are written as the REDUCTION of the species concerned, proceeding to the right. The species with the

lower oxidation s tate is written on the right hand s ide.

The rules are as follows:

1. Write down the m ain reaction components, with the reduced form (the form with the lowes t valency) on the right.

2. Add s toichiometric numbers to balance the number of metal atoms. (Dont worry about charge or oxygen being balanced at this point).

3. Balance the number of oxygen atoms by adding H O to the appropriate side.

4. Balance the number of hydrogen atoms by adding hydrogen ions (H ) to the appropriate side.

5. Balance the residual charge by adding electrons (e ) to the appropriate side.

Now each side of the equation has the same num ber of atoms of each element and the same overall charge.

Examples of balancing electrochemical reactions

Find the electrochemical reaction for an equilibrium between Cr O and CrO

1. Write reduced species on right

CrO

Cr O

2. Balance Cr metal atoms

2 CrO

Cr O

3. Balance oxygen atoms with water

2 CrO

Cr O + 5 H O

4. Balance hydrogen atoms with hydrogen ions

2 CrO + 10 H

Cr O + 5 H O

e

+ -

2

e

e

2

+

-

2 3 4

2-

4

2-

2 3

4

2-

2 3

4

2-

2 3 2

4

2- +

2 3 2


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5. Balance charge with electrons

2 CrO + 10 H + 6 e

Cr O + 5 H O

Check: Each side of the equation has: Two Cr, eight O, ten H and zero residual charge so it is balanced.

Click for more examples :

Example 1

Example 2

Example 3

The Nernst equation

The Nernst equation links the equil ibrium potential of an electrode, E , to its standard potential, E , and the concentrations or pressures of the

reacting components at a given temperature. It describes the value ofE for a given reaction as a function of the concentrations (or pressures ) of all

participating chemical species.

In its most fundamental forms, the Nernst equation for an electrode is written as:

or

[Click here for a full derivation of Nernst equation popup]

Ris the universal gas constant (8.3145 J K mol )

Tis the absolute temperature

zis the num ber of moles of electrons involved in the reaction as written

Fis the Faraday constant (96 485 C per mole of electrons)

The notation [reduced] represents the product of the concentrations (or pressures where gases are involved) of all the species that appear on the

reduced side of the electrode reaction, raised to the power of their stoichiometric coefficients. The notation [oxidised] represents the same for the

oxidised side of the electrode reaction.

Explanation ofActivity

Example 1

In the reaction O + 4H + 4e = 2H O

water is the reduced s pecies and the oxygen gas is the oxidised species . By convention, electrochemical half-equations are written as

Oxidised State + ne-

Reduced State

Taking into account the s toichiometric coefficients of the species, the log term of the Nernst equation for this reaction appears as

Some of the species that take part in electrode reactions are pure solid compounds . The standard s tate for these compounds is unit mole fraction,and as they are pure, and are in their standard states. In dilute aqueous solutions , water has an overwhelming concentration, so it may be

considered pure. The standard state for a gas is taken as 1 atm (or 1 bar) and the standard state for solutes (such as ions) is taken as 1 mol dm .

The log term of the Nernst equation can now be reduced to

4

2- + -

2 3 2

e

0

e

-1 -1

2+ -

2

-3


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The Nernst Equation under standard conditions:

At 298.15 K (25 C), the num eric values of the cons tants can be combined to give a simpler form of the Nernst equation for an electrode under

standard conditions:

This equation can be applied both to the potentials of individual electrodes and the potential differences across a pair of half-cells. However, it is

generally more convenient to apply the Nernst equation to one e lectrode at a time.

Click here for 2 other examples

General expression of the Nernst Equation

Taking the general equation for a half-cell reaction as,

aA + mH + ze = bB + H O

the Nernst equation becomes

Construction of a Pourbaix Diagram

A Pourbaix diagram plots the equilibrium potential (E ) between a metal and its various oxidised species as a function of pH.

The extent of half-cell reactions that describe the dis solution of metal

M = M + ze

depend on various factors, including the potential, E, pH and the concentration of the oxidised species, M . The Pourbaix diagram can be thought

of as analogous to a phase d iagram of an alloy, which plots the lines of equilibrium between different phases as temperature and composi tion are

varied.

To plot a Pourbaix diagram the relevant Nernst equations are used. As the Nerns t equation is derived entirely from thermodynamics, the Pourbaix

diagram can be us ed to determine which species is thermodynamicallystable at a given Eand pH. It gives no information about the kinetics of the

corrosion process.

Constructing a Pourbaix Diagram

The following animation illustrates how a Pourbaix diagram is constructed from first principles , using the example of Zinc.

+

2

e

z+ -

z+


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Note: This animation requires Adobe Flash Player 8 and later, which can b e downloaded here.

Anatomy of a Pourbaix Diagram

The Pourbaix diagram provides much in formation on the behaviour of a system as the pH and potential vary.

The following animation explains how a Pourbaix diagram is built up from fundam entals.


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Examples of a Pourbaix Diagram

Golds Pourbaix diagram explains why it is the most imm une substance known. It is imm une in all regions in which cathodic reactions can take

place. So gold never*corrodes in an aqueous environment.

Immunity of aluminium only occurs at lower potentials. Therefore, unless under conditions that cause it to pass ivate, it is m uch more s usceptible to

corrosion than gold or zinc.

* provided that the water is pure; that no ion complexes are present to provide a cathodic half cell reaction that occurs at a potential higher than +1.5

V(SHE).


A Pourbaix Diagram does not have to be lim ited to two dimens ions . Three (or higher) dim ens ion diagrams can be constructed by varying other

parameters s uch as concentration or temperature.




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Summary

In this package:

the concepts of equilibrium potential and their measurement are introduced.

electrochemical half-cells are defined and treatment of electrochemical equations dem onstrated.

the physical and chemical processes which lead to aqueous corrosion are examined.

the Nernst Equation has been derived and the way in which it links measured potentials at various conditions with standard equilibrium

potentials is discussed.the way in which some electrochemical reactions have equilibrium potentials that vary as a function of pH is cons idered and the concept and

derivation of a Pourbaix diagram introduced.

through the use of specific examples, the characteristics of Pourbaix diagrams and their uses are examined. The stability of water is

demonstrated through the use of the Pourbaix diagram.

cathodic and anodic reaction lines on Pourbaix diagrams are discussed and the way in which a point on the diagram corresponds to physical

corrosion examined.

Please follow this link if you would like to provide a short review for this TLP

Questions


Quick questions

You should be ab le to answer these questions without too much difficulty after studying this TLP. If not, then you should go through it again!

1.

2.


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3.

4.

5.

6.

7.

Going furtherBooks

J.M. West: "Basic Oxidation and Corrosion"

Ellis-Horwood L.L. Shreir, R.A. Jarman and G.T. Burstein: "Corrosion", third edition, Butterworth-Heinemann


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Websites

Kinetics of Aqueous Corrosion TLP - introduces the mechanism of aqueous corrosion and the associated kinetics (DoITPoMS).

Other reference electrodes

It is often impractical to use the s tandard hydrogen electrode owing to the clumsy nature of using hydrogen gas. In practice, a range of alternative,

secondary electrodes are used.

The potentials of these electrodes are precise ly known with respect to the SHE, so a m easured potential can be eas ily converted to an equivalent

one relative to the SHE. Three of the mos t common secondary electrodes are:

The saturated calomel electrode (SCE),

The s ilver/silver chloride electrode

The copper-copper(II) sulphate e lectrode.

The saturated calomel electrode (SCE)

The reaction is based on the reaction between this elemental mercury (Hg) and mercury(I) chloride (Hg Cl , "calomel").

A one molar solution of potassium chloride in water forms the aqueous phas e in contact with the mercury and the mercury(I) chloride.

The Nernst equation for this e lectrode can be expressed as

In cell notation the electrode is written as: Cl | Hg Cl | Hg | Pt

The meas ured potential, E, of the SCE is +0.241 V (SHE) for a saturated chloride ion solution at 298 K.

The silver/silver chloride electrode

This is based on the reaction is between the s ilver metal (Ag) and s ilver(I) chloride (AgCl). The half-cell reaction is

AgCl + e = Ag + Cl

which gives a Nernst equation of

.

Changing the electrolyte concentration with this electrode changes the equilibrium electrode potential, so fixed values of chloride concentration are

required.

In cell notation, this is written as Ag | AgCl | KCl .

The measured potential, E = +0.235 V (SHE) at 298 K.

The copper-copper(II) sulphate electrode

The copper-copper(II) sulphate electrode is based on the redox reaction between copper metal and its salt - copper(II) sulphate.

The corresponding equation can be presented as follows:

Cu + 2e = Cu

The Nernst equation below shows the dependence of the potential of the copper-copper(II) sulphate electrode on the concentration copper-ions:

2 2

-

(saturated) 2 2(s) (l)

- -

(1M)

2+ -


13/16



The equilibrium potential of a copper-copper su lphate electrode is -0.318 Vwith respect to the s tandard hydrogen e lectrode for a saturation

concentration of copper ions at 298 K.

Example 1

Find the electrochemical reaction for an equilibrium between Zn and Zn(OH)


Zn(OH)

Zn

2. Balance zinc atoms

Zn(OH)

Zn


Zn(OH)

Zn + 4 H O


Zn(OH) + 4 H

Zn + 4 H O


Zn(OH) + 4 H + 2 e

Zn + 4 H O

Check: Each side of the equation has: One Zn, four O, four H and zero residual charge s o it is balanced.

Example 2

Find the electrochemical reaction for an equilibrium between NO and NO.


NO

NO

2. Balance nitrogen atoms

NO

NO


NO

NO + 2 H O


NO + 4 H

NO + 2 H O

4

2

42

4

2

4

2

2

4

2 +

2

4

2 + -

2

3

-

3

-

3

-

3

-

2

3

- +

2


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NO + 4 H + 3e

NO + 2 H O

Check: Each side of the equation has: One N, three O, four H and zero residual charge so it is balanced.

Example 3

Find the electrochemical reaction for an equilibrium between MnO and MnO


MnO

MnO

2. Balance Mn atoms

MnO

MnO


MnO

MnO + 2H O


MnO + 4 H

MnO + 2H O


MnO + 4 H + 3 e

MnO + 2H O

Check: Each side of the equation has: One Mn, four O, four H and zero residual charge so it is balanced.

Activity

When the concentration of a s pecies is high or a com plex is involved, concentration should be replaced by the term, activity. The system can be

more or less active than its concentration sugges ts.

Detailed derivation of the Nernst equation

Consider the following reaction at equilibrium:

This can be expressed as two half equations:

A + ze = A and

The left hand reaction represents the equilibrium between atoms ofA on a metal surface andA ions in s olution. The term equilibrium refers to

the fact that the rate of reaction in one direction equals the rate of the reverse reaction.

For the above reaction, the free energy change, G, is given by

3

- + -

2

4

-

2

4

-

2

4

-

2

4

-

2 2

4

- +

2 2

4

- + -

2 2

z+ -

z+


15/16



whereX is the mole fraction ofA in the metal and C is the concentration ofA in solution. When the metal,A, is pure, X = 1. Also, the standard

statesX and C can be omitted, as the standard state for the metal phase is unit mole fraction, and for the dissolved ions is 1 m ol dm .

Thus, the free energy change can be expressed as

(1)

At equi librium, the chem ical driving force, G is always equal to the electrical driving force, E . As dis cussed previously, this can be expressed as

G = -zFE

where zis the number of moles of electrons exchanged in the reaction and Fis Faradays cons tant, 96 485 coulombs per mole of electrons. Under

standard conditions,

.G = -zFE

From the fundamental thermodynamic equation

G = -RTln K

E can therefore be expressed as

where Kis the equi librium cons tant for the reaction.

However, only the s tandard equilibrium potential, E , is related directly to K. The non-standard potential, E is not.

Equation (1) can now be expressed in terms of electrode potential by subs tituting forG and .G

The equilibrium potential is therefore given by

It is conventional to work in decadic logs rather than natural logs , since this is arithmetically more convenient and thepHscale is expressed in the

decadic form: lnX= 2.303 logX so the equation may be written as:

Note that for this sim ple reaction, the Nernst equation s hows that the equilibrium potential, E is independent of thepHof the solution. Many half-

cell reactions contain H ions and their Nernst equations therefore depend on thepH.

For the half-cell reaction

MnO + 4H + 3e = MnO + 2H O , E0= 0.588 V(SHE)

the Nernst equation appears as

A A

z+

A0

A

0

Az+

-3

e

0

e

0 0

0

0

0

e

0

e+

4

- + -

2 2


16/16


= 0.588 + 0.197 log [MnO ] - 0.789 pH

The Nernst equation can therefore be generalised as

The notation [reduced] represents the product of the concentrations (or pressures where gases are involved) of all of the species that appear on

the reduced side of the electrode reaction, raised to the power of their stoichiometric coefficients. The notation [oxidised] represents the same for

the oxidised side of the electrode reaction.

Solutions in which components, such as Cl ions, can complex with the metal ions require a different treatment.

Further examples of the Nernst equation

Academic consultant:G. Tim Burstein (University of Cambridge)

Content development: Andy Bennett, Andy Collier, Carol Newby

Photography and video: Brian Barber and Carol Best

Web development: Lianne Sallows and David Brook

DoITPoMS is funded by the UK Centre for Materials Education.

Additional support for the developm ent of this TLP came from the Worshipful Com pany of Armourers and Bras iers '

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Documents

the Nernst Equation and Pourbaix Diagrams