Thermodynamics in the Electrochemical Reactions of Corrosion

CHAPTER 2

Thermodynamics in the Electrochemical Reactions of Corrosion

Chapter Contents 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8

Introduction Electrochemical Corrosion Thermodynamics of Corrosion Processes Equilibrium Electrode Potentials Electrochemical Half-Cells and Electrode Potentials Electromotive Force Series Determination of Electrochemical/Corrosion Reaction Direction by Gibbs Energy Reference Electrodes of Importance in Corrosion Processes 2.8.1 Determination of reversible potential of the hydrogen electrode 2.8.2 Determination of reversible potential of the oxygen electrode 2.8.3 Determination of cell potential of the hydrogen-oxygen cell (fuel cell) 2.8.4 Determination of electrode potential of a standard Weston cell 2.8.5 Determination of electrode potentials for electrodes of the second kind

Corrosion Engineering http://dx.doi.org/10.1016/B978-0-444-62722-3.00002-1

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© 2015 Elsevier B.V. All rights reserved.

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2.8.6 Calomel electrode 2.8.7 Silver-silver chloride electrode 2.8.8 Copper-copper sulfate electrode 2.9 Measurement of Reversible Cell Potential with Liquid Junction Potential 2.10 Measurement of Corrosion Potential 2.11 Construction of Pourbaix Diagrams 2.11.1 Regions of electrochemical stability of water 2.11.2 Construction of pourbaix diagram for zinc 2.11.3 Construction of Pourbaix diagram for tin 2.11.4 Pourbaix diagram for iron 2.11.5 Construction of Pourbaix diagram for nickel 2.12 Case Studies 2.12.1 Activity coefficients 2.12.2 Evaluation of theoretical tendency of metals to corrode 2.12.3 Hydrogen and oxygen electrodes Exercises References

52 53 54 55 56 57 58 59 63 67 68 71 71 73 87 90 91

2.1 INTRODUCTION Corrosion is spontaneous dissolution or destruction of metals due to electrochemical, chemical, or biochemical interactions with aqueous or organic environments. Corrosive environments include moisture, oxygen, inorganic and organic acids, pressure, temperature, and the presence of chlorides. The simplest and most common example of corrosion is the oxide (rust) formation on reinforcing steel rebars in structural concrete. Corrosion is a nonequilibrium electrode process occurring under open circuit conditions without the application of an external current. During the corrosion process, metals tend to convert to more thermodynamically stable compounds such as oxides, hydroxides, salts, or carbonates.

2.2 ELECTROCHEMICAL CORROSION The electrochemical corrosion process consists of two partial electrochemical reactions: the anodic partial reaction, consisting of oxidation/dissolution of the metal, and the cathodic partial reaction, consisting of the reduction of water, hydrogen, or oxygen gas. The energy change of the partial corrosion reactions provides a driving force for the process and controls its direction. Electrochemical corrosion reactions have different thermodynamic and kinetic properties than chemical reactions. For example, if a redox reaction proceeds as a chemical reaction, it is necessary for the reacting particles to come into contact with each other so that electrons can be transferred from one reactant to the other. Thermodynamically, the reaction is controlled by the ratio of the internal energy of the reactants to their activation energy. The collisions of the particles are not limited in

Thermodynamics in the electrochemical reactions of corrosion

the reaction space and may occur in any direction. As a consequence, the electrons also move in any direction in the reaction space. The only requirement is that the path of the charge transfer must be very small. With an electrochemical reaction, the activation energy of corrosion reactions and their kinetic properties depend not only on activity, chemical potential, and temperature, but also on the electrocatalytic properties of the materials. The thermodynamics of corrosion processes provides a tool to determine the theoretical tendency of metals to corrode. Thus, the role of corrosion thermodynamics is to determine the conditions under which the corrosion occurs and how to prevent corrosion at the metal/environment interface. Thermodynamics, however, cannot be used to predict the rate at which the corrosion reaction will proceed [1–6]. The corrosion rate must be estimated by Faraday’s law and is controlled by the kinetics of the electrochemical reaction. Depending on the nature of the metal, the oxidation reaction may occur uniformly (as in carbon steel) or may be localized (as in hard alloys such as Inconel or Monel). In localized corrosion (pitting), the corrosion proceeds through the formation of narrow cracks after penetrating the grains of the metal. Corrosion occurs along the grain boundaries of the metal, known as intercrystalline corrosion. Besides the hydrogen evolution reaction, there are other cathodic depolarization reactions such as: Oxygen reduction in alkaline or neutral solutions : O2 + 2H2 O + 4e
! 4OH


(2.1)

Oxygen reduction in acidic solutions : O2 + 4H + + 4e
! 2H2 O

(2.2)

Metal deposition in galvanic corrosion : M + + e
! M

(2.3)

Reduction of metal ions : M3 + + e
! M2 +

(2.4)

The overall anodic reaction for the corrosion of iron in neutral or alkaline solutions is described as: 2Fe + 2H2 O + O2 ! 2Fe2 + + 4OH
! 2FeðOHÞ2

(2.5)

Ferrous hydroxide produced in Eq. (2.5) is oxidized to ferric salts according to: FeðOHÞ2 + H2 O ! FeðOHÞ3 + H + + e


(2.6)

Corrosion reactions also occur as a replacement reaction: Ni2 + + Fe ! Fe2 + + Ni

(2.7)

Electrochemical corrosion may occur in aqueous electrolytes, gas atmosphere in the presence of moisture on the metal surface (atmospheric corrosion), or as soil corrosion (Fig. 2.1). Corrosive failure may also occur due to electrocorrosion, which is caused by an external electric current.

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Rust [Fe(OH)2] formation

OH−

Fe2+

OH−

OH−

Fe2+ Fe2+

H2O

Electrolyte (water, soil etc.)

O2 Corroding surface

e−

e−

e− Iron

Fig. 2.1 Corrosion cell formed as a result of rusting of iron.

Corrosion is initiated by electrochemical reactions in: 1. Technical metals that contain impurities of other metals: Examples are technical metals such as zinc and tin, which contain silver or iron as impurities. The standard electrode potentials of silver and iron are more electropositive than those of zinc or tin, causing zinc and tin to corrode through a form of galvanic corrosion, while the impurities remain intact. Because of their more positive electrode potentials, silver and iron are cathodically protected by zinc or tin. 2. Identical metals in contact with solutions of different concentrations: The metal dissolves from the electrode immersed in a dilute solution, and is deposited on the electrode that is immersed in a more concentrated solution. The corrosion stops when the electrolyte concentration is homogeneous at the interfaces of both of electrodes. The other type of electrochemical concentration cell is known as a differential aeration cell. The electrode potential difference in this case results from different oxygen aeration of the electrodes. This type of corrosion initiates crevice corrosion in aluminum or stainless steel when exposed to a chloride environment. 3. Identical metals each exposed to a different temperature: The driving force for this type of corrosion results from each electrode having a different temperature when they are immersed in a homogeneous electrolyte. The metal exposed to the higher temperature acts as a cathode. When this metal is in electrical contact with a metal exposed to the lower temperature (anode), the metal dissolves from the lower-temperature electrode (anode) and is deposited on the higher-temperature electrode (cathode).

2.3 THERMODYNAMICS OF CORROSION PROCESSES The energy change of the partial corrosion reactions provides the driving force for the overall reaction and controls its spontaneous direction. Corrosion thermodynamics

Thermodynamics in the electrochemical reactions of corrosion

establishes the quantitative relationship between the electrical energy produced or consumed during the corrosion processes and the chemical energy. The corrosion of iron in an acid environment occurs according to the following reaction: ne

Fe + 2HCl > FeCl2 + H2

(2.8)

The dissolution of iron in an acidic solution releases hydrogen without the formation of any oxide barrier films on the surface. The reaction shown in Eq. (2.8) may be separated into two partial reactions: Fe ! Fe2 + + 2e
ðanodic partial reactionÞ

(2.9a)

2H + + 2e
! H2 ðcathodic partial reactionÞ

(2.9b)

In Eq. (2.9a), the iron atoms are transformed into iron ions while the electrons produced are consumed during the reduction of hydrogen ions to hydrogen gas. In Eq. (2.8), “n” represents the number of elementary charges, e ¼ 4.803  10
10 (1.602  10
19 coulombs) or electrostatic units exchanged during the anodic and cathodic charge transfer reactions. According to sign convention, the stoichiometric numbers are positive for the products and negative for the reactants. For the corrosion reaction presented in Eq. (2.8), the changes in the number of moles of the species in the reaction are proportional to their stoichiometric numbers. The quantity of electricity produced as a result of the chemical reaction is equal to the product of nFE, where E is the electromotive force measured in the case of reversible reactions. The quantity F is the Faraday constant, which can be estimated from the product, F ¼ NAe where NA ¼ 6.02  1023 (Avogadro’s number) and “e” is the elementary charge. The absolute value of the Faraday constant equals 96,485 C (coulomb). For any isothermal process, the reaction described in Eq. (2.8), when performed at constant pressure, decreases the Gibbs free-energy (G). Assuming that the corrosion process proceeds at constant pressure, the change of Gibbs free-energy is the focal point for any thermodynamic analysis of corrosion reactions. The change in the Gibbs free-energy represents the maximum useful work for an isothermal and isobaric conversion for the reaction in Eq. (2.8). G ¼ H + TS

(2.10)

According to the second law of thermodynamics, Eq. (2.10) can be expressed as the difference between two equilibrium states: dG ¼
SdT + V dP, G ¼ f ðT , P Þ

(2.11)

Fundamental thermodynamic aspects are discussed in detail in [7,8]. According to convention, the dG is a negative quantity for the spontaneous direction of any reaction. When the Gibbs free-energy reaches its minimum, the dG is equal to zero. In this state,

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the system is in equilibrium where the rate of the reaction in the forward direction is the same as that in the reverse. Besides the fact that the corrosion process is irreversible in nature, the equilibrium conditions are used to derive all thermodynamic and kinetic expressions. The system can be subjected to both mechanical work (PV) and electrical work (W). Thus, the Gibbs free-energy in Eq. (2.11) can be expressed as: dG ¼
SdT + V dP
dW

(2.12)

According to convention, the negative sign for the electrical work, dW, in Eq. (2.12) means that work is done by the system. For processes occurring at constant pressure and temperature, Eq. (2.12) can be expressed as:
dGT , P ¼ dW

(2.13)

The decrease in Gibbs free-energy in Eq. (2.13) is equal to the electrical work W. Because the electrical work is expressed as: W ¼ nFE

(2.14)

dW ¼ nFdE

(2.15)

dGT , P ¼
nFdE

(2.16)

and

Electrical work is the product of charge multiplied by the electromotive force (emf) potential (E) of the cell. If the work done results from an electrochemical reaction with cell potential, E, and if the charge is defined for one mole of reaction in which “n” moles of electrons are transferred, then the electrical work (
W) done by the cell is equal to nFE. The Faraday constant F (96,485 C/mole) in Eq. (2.16) is necessary to convert moles of electrons to coulombs. During the corrosion process, the concentration of the oxidizing and reducing species change, so the thermodynamic properties of the system must depend on the composition as well as on temperature and pressure. The Gibbs free-energy, nG, is a function of the number of moles of the reduced and oxidized species participating in the corrosion reaction through the following equation: XδðnGÞ dðnGÞ ¼ ðnV ÞdP
ðnSÞdT + dni (2.17) δni P , T nj i The derivative of nG in Eq. (2.17) with respect to the number of the moles of the oxidized and reduced species participating in the corrosion reaction is defined as the chemical potential μi.   δðnGÞ μi ¼ (2.18) δni P , T nj

Thermodynamics in the electrochemical reactions of corrosion

The general equation for d(nG) expressed in terms of the chemical potential μi is: dðnGÞ ¼ ðnV ÞdP
ðnSÞdT +

X μi dni

(2.19)

i

Equation (2.19) is used as a foundation to build the structure of corrosion solution thermodynamics. For one mole, n ¼ 1 of participating reacting species, it can be written in the form in which ni is replaced by a mole fraction xi: X dG ¼ V dP
SdT + μi dxi (2.20) i

At constant temperature and pressure, Eq. (2.19) becomes: XδnG X dðnGÞT , P ¼ dni ¼ μi dni δni P , T , nj

(2.21)

After integration GT , P ¼

X μi ni

Equations (2.16) and (2.21) can be written for electrochemical process as: X X ΔGT , P ¼
nFdE ¼ μi dni or nFE ¼
μi ni

(2.22)

(2.23)

2.4 EQUILIBRIUM ELECTRODE POTENTIALS At standard states, all reactants and products in any electrochemical process are at unit activity. Departure from unit activity can be determined using the Nernst equation, which is derived by assuming that the reaction proceeds isothermally and reversibly in a corrosion system [2,9–11]. nF

½vA A + ½vB B +   $ ½vC C + ½vD D +    Q

(2.24)

According to Eq. (2.16), the reversible potential of the corrosion system ET,P is defined as: ΔGT , P (2.25) nF The general equation for d(nG) is expressed in terms of the chemical potential μi by Eq. (2.19). Each dni in Eq. (2.19) may be replaced by the product viaε, where “a” represents the activity of the reactants, ε is the reaction coordinate and characterizes the extent of the corrosion reaction. In the above equation, “vi” is the stoichiometric number ET , P ¼


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for the species with a chemical potential μi. Thus, at constant pressure and temperature and unit activity, Eq. (2.19) becomes: X dðnGÞ ¼ μi dvi dε (2.26) i

Because nG is a state function, the right-hand side of the Eq. (2.19) represents an exact differential expression, it follows that:   X δðGÞ (2.27) μvi ¼ δε T , P P In fact, the quantity μvi represents the rate of the change of the total Gibbs free-energy for the corrosion (electrochemical) process, with the extent of the reaction ε at constant T and P. This quantity is zero at the equilibrium state. Thus, according to Eq. (2.22), X ΔG ¼ μi vi : (2.28) Because the chemical potential is a partial property of the Gibbs free-energy, its value can be calculated from the equation: μi ¼ μoi + RT ln ðai Þ

(2.29)

μoi

where is the standard chemical potential, and ai is the activity of the species in the corrosion reaction. Instead of Eq. (2.28), one may write: X X ΔG ¼ μoi vi + RT vi ln ai (2.30) or ΔG ¼

X avC avD μoi vi + RT ln CvA D aA avBB

(2.31)

Assuming that the reactants and the products are in their standard states, the activities of the species participating in the reaction are equal to unity. Under these conditions, the Gibbs free-energy ΔG is equal to the standard Gibbs free-energy ΔGo and the absolute value is equal to the natural logarithm of the equilibrium constant K. X ΔG ¼ ΔGo ¼ μoi xi ¼ RT lnK (2.32) Because ΔGoi is a property of pure species “i” in their standard state and at constant pressure, value depends only on the temperature. In fact, ΔGo represents the quantity P its o viGi . Therefore, this function is the difference between the Gibbs free-energies of the products and reactants and depends on their stoichiometric coefficients. It is independent of the equilibrium composition or pressure and it is fixed for any given corrosion reaction once the temperature is established. The Gibbs free-energy change is defined according to Eqs. (2.29) and (2.31) as: ΔG ¼ RT ln K + RT ln ∏avi i

(2.33)

Thermodynamics in the electrochemical reactions of corrosion

where Π signifies the product over all species. From Eqs. (2.24) and (2.31), it follows that: RT RT avCC avDD   (2.34) ln K
ln vA vB nF nF aA aB   The logarithmic expression in the second term on the right side of Eq. (2.32), when ai ¼ 1, is equal to zero, and: RT Eo ¼
ln K (2.35) nF Ecell ¼


The potential in Eq. (2.35) is defined as Eo and is called the standard electromotive force of a corrosion system. According to Eq. (2.34), for any equilibrium electrochemical system, the (emf) E is the sum of the standard electromotive force, Eo, and the activities of the products and the reactants participating in the reaction: E cell ¼ E o


RT avCC avDD    ln vA vB nF aA aB  

(2.36)

which is equivalent to: E cell ¼ E o
2:303

RT av C av D log CvA D aA avBB nF

(2.37)

Ecell ¼ E o + 2:303

RT av A av B log vAC vBD aC aD nF

(2.38)

or

Equations (2.37) and (2.38) are well known forms of the Nernst equation. The values of bo ¼ 2:303 RT F in Eq. (2.36) are linear functions of T, and are presented in Table 2.1. The value of bo at room temperature is 0.059 V.

2.5 ELECTROCHEMICAL HALF-CELLS AND ELECTRODE POTENTIALS The overall charge transfer of any corrosion reaction must be the sum of two electrode potentials that are established in the half-cells. Each potential results from the change of the Table 2.1 Values of the Factor b ¼ 2.303RT/F for Different Temperatures T °C b° T °C b°


40 0 +5 +10 +15

0.046 0.054 0.055 0.055 0.057

+25 +30 +40 +60 +100

0.059 0.060 0.062 0.066 0.074

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chemical energy of the respective electrode reaction occurring in the half-cell [1,2,6–11]. Thus, the value of the emf, E, for any electrochemical system at equilibrium is: E ¼ e1 + e2

(2.39)

where, e1 and e2 are the electrode potentials of the half-cell reactions. Equation (2.24) can be now rewritten by using the half-cells of the overall corrosion reaction as follows: nF

vA A +   $ vC C

(2.40)

and nF

vB B +   $ vD D

(2.41)

The Nernst equation defines the single electrode (half-cell) potentials in Eqs. (2.40) and (2.41). These are defined by the Nernst equation as: v

RT aA log AvC aC nF

(2.42)

RT avBB + 2:303 log vD aD nF

(2.43)

e1 ¼ eo1 + 2:303 e2 ¼ eo2

where eo1 and eo2 are standard electrode potentials of the half-cell reactions shown in Eqs. (2.40) and (2.41). The sum of the standard electrode potentials equals the standard electromotive force of the corrosion system: E o ¼ eo1 + eo2

(2.44)

The emf of any corrosion system is the sum of the standard emf and the activities of the half-cells of the overall corrosion reaction, Eqs. (2.42) and (2.43).


ΔG RT avA RT av B ¼ Ecell ¼ eo1 + 2:303 log vAC + eo2 + 2:303 log vBD aC aD nF nF nF

(2.45)

Or E ¼ Eo + 2:303

RT avA avB log vAC vBD aC aD nF

(2.38)

2.6 ELECTROMOTIVE FORCE SERIES The emf series of the standard half-cell electrode potential on the hydrogen scale are given in Table 2.2. The reactions in this table are written as reduction reactions from left to right at T ¼ 25  C. They have the same polarity as the reduction potential, which is measured experimentally. From Eq. (2.38), it is not possible to distinguish which of the participants in the reaction are the reactants (oxidized species) and which are the products (reduced species).

Thermodynamics in the electrochemical reactions of corrosion

Table 2.2 Standard Electrode Potentials at 25  C and Their Isothermal Temperature  Coefficients   [12]  dE  3 V  e (V vs.  10  dT C Electrode Reaction SHE)

Li+|Li Rb+|Rb Cs+|Cs K+|K Ra2+|Ra Ba2+|Ba Ca2+|Ca Na+|Na La3+|La Mg2+|Mg Be2+|Be Al3+|Al Ti2+|Ti Zr4+|Zr V2+|V Mn2+|Mn Zn2+|Zn Cr3+|Cr SbO
2 |Sb Ga3+|Ga S2
|S Fe2+|Fe Cr3+,Cr2+|Pt Cd2+|Cd Ti3+, Ti2+|Pt Tl+|Tl Co2+|Co Ni2+|Ni Mo3+|Mo Sn2+|Sn Pb2+|Pb Ti4+, Ti3+|Pt H+, H2|Pt

Li+ + e
¼ Li Rb+ + e
¼ Rb Cs+ + e
¼ Cs K + + e
¼ K Ra2+ + 2e
¼ Ra Ba2+ + 2e
¼ Ba Ca2+ + 2e
¼ Ca Na+ + e
¼ Na La3+ + 3e
¼ La Mg2+ + 2e
¼ Mg Be2+ + 2e
¼ Be Al3+ + 3e
¼ Al Ti2+ + 2e
¼ Ti Zr4+ + 4e
¼ Zr V2+ + 2e
¼ V Mn2+ + 2e
¼ Mn Zn2+ + 2e
¼ Zn Cr3+ + 3e
¼ Cr

SbO
2 + 2H2O + 3e ¼ Sb + 4OH 3+
Ga + 3e ¼ Ga S + 2e
¼ S2
Fe2+ + 2e
¼ Fe Cr3+ + e
¼ Cr2+ Cd2+ + 2e
¼ Cd Ti3+ + e
¼ Ti2+ Tl+ + e
¼ Tl Co2+ + 2e
¼ Co Ni2+ + 2e
¼ Ni Mo3+ + 3e
¼ Mo Sn2+ + 2e
¼ Sn Pb2+ + 2e
¼ Pb Ti4+ + e
¼ Ti3+ H + + e
¼ ½ H 2


3.045
2.925
2.923
2.925
2.916
2.906
2.866
2.714
2.522
2.363
1.847
1.662
1.628
1.529
1.186
1.180
0.762
0.744
0.670
0.529
0.510
0.440
0.408
0.402
0.369
0.336
0.277
0.250
0.20
0.138
0.126
0.040 0.000

Sn4+, Sn2+|Pt Cu2+, Cu+|Pt Cu2+|Cu Fe(CN)3
6 , Fe (CN)4
6 |Pt OH
, O2|Pt Cu+|Cu I
|I2, Pt MnO-4, MnO24 |Pt

Sn4+ + 2e
¼ Sn2+ Cu2+ + e
¼ Cu+ Cu2+ + 2e
¼ Cu 4

Fe(CN)3
6 + e ¼ Fe(CN)6

+ 0.015 + 0.153 +0.337 +0.360


0.534
1.245
1.197
1.080
0.59
0.395
0.175
0.772 +0.085 +0.103 +0.565 +0.504
0.08 +0.09 +0.468 +0.67 +0.052
0.093
1.327 +0.06 +0.06
0.282
0.451 0.000 (+0.871) +0.073 +0.008 -

½ O2 + H2O + 2e
¼ 2OH
Cu+ + e
¼ Cu I2 + 2e
¼ 2I

2
MnO
4 + e ¼ MnO4

+0.401 +0.521 +0.535 +0.564


0.440
0.058
0.148 Continued

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Table 2.2 Standard Electrode Potentials at 25  C and Their Isothermal Temperature Coefficients [12]—cont'd     dE V  103  e (V vs. dT C Electrode Reaction SHE)

Fe3+, Fe2+|Pt Hg2+ 2 |Hg Ag+|Ag Hg2+|Hg Hg2+, Hg+|Pt Pd2+|Pd Br-|Br2, Pt Pt2+|Pt Mn2+, H+| MnO2, Pt Cr3+, Cr2O2
7 , H+|Pt Cl
|Cl2, Pt Pb2+, H+| PbO2, Pt Au3+|Au + MnO
4, H | MnO2, Pt Ce4+, Ce3+| Pt + SO2
4 , H | PbSO4, PbO2, Pb Au+|Au

Fe3+ + e
¼ Fe2+
Hg2+ 2 + 2e ¼ 2Hg +
Ag + e ¼ Ag Hg2+ + 2e
¼ Hg Hg2+ + e
¼ Hg+ Pd2+ + 2e
¼ Pd Br2 + 2e
¼ 2BrPt2+ + 2e
¼ Pt MnO2 + 4H+ + 2e
¼ Mn2+ + 2H2O

+0.771 +0.788 +0.799 +0.854 +0.910 +0.987 +1.065 +1.200 +1.230

+ 1.188
1.000
0.629
0.661

+
3+ Cr2O2
7 + 14H + 6e ¼ 2Cr + 7H2O

+1.330


1.263

Cl2 + 2e
¼ 2Cl
PbO2 + 4H+ + 2e
¼ Pb2+ + 2H2O

+1.359 +1.455


1.260
0.238

Au3+ + 3e
¼ Au +
MnO
4 + 4H + 3e ¼ MnO2 + 2H2O

+1.498 +1.695


0.666

Ce4+ + e
¼ Ce3+

+1.610

-

+
PbO2 + SO2
4 + 4H + 2e ¼ PbSO4 + 2H2O

+1.682

+0.326

Au+ + e
¼ Au

+1.691

-

The following rules were adopted by the International Union of Pure and Applied Chemistry (IUPAC) in Stockholm in 1953 to solve the question of the signs of electrode potential and to determine which substances should be considered as the reactants and which as products. Any electrochemical cell, according to this agreement, is written from left to right as follows: (i) the material of one of the two electrodes, (ii) the solution in contact with one electrode, (iii) the solution in contact with the second electrode, and (iv) the material of the second electrode. In the written expression, the electrodes are separated from the solutions by a single bar, while the solutions are separated by a double bar, indicating that there is no diffusion potential between the solutions in the cell. Of the two half-cell electrode potentials, only the cell potential E can be measured experimentally. Therefore, it is not possible to measure the absolute values of any single half-cell electrode potential. To solve this problem, Nernst suggested that the potential of

Thermodynamics in the electrochemical reactions of corrosion

the hydrogen electrode at a hydrogen pressure of 1 atm and at unit concentration of hydrogen ion was to serve as an arbitrary zero potential. In Table 2.2, all listed potentials are on the hydrogen scale, in which the half-cell potential of the hydrogen electrode eoH + jH2 is at standard state, and has been arbitrarily taken as a zero reference point in the electromotive force series. The Gibbs free-energy for the hydrogen evolution reaction is not zero. 2H + + 2e
! H 2

(2.9b)

The zero value of the hydrogen reference electrode has been adopted by IUPAC as suggested by Nernst for convenience, in order for the standard hydrogen electrode (SHE) to serve as a reference potential. By using this scale, the electrode potential can be determined at all temperatures. However, the arbitrary zero will be different at different temperatures [12–14]. A half-cell potential of any redox corrosion reaction is measured when the half-cell is coupled with the SHE. An example of measuring the half-cell potential is given for an Sn|Sn2+ electrode in Fig. 2.2. Tin metal is immersed in 1M standard solution of Sn2+ in hydrochloric acid and is separated through a membrane from a H2|H+ reference electrode. This connection establishes a galvanic cell that, according to IUPAC agreement, is written as: Pt,H2 jHCljjSn2 + jSn

(2.46)

Sn + 2H + ! Sn2 + + H2

(2.47)

Both Sn and Sn2+ in the corrosion reaction are at standard state. The potential measured for the Sn|Sn2+ electrode is 0.138 V with Sn|Sn2+ negative vs. the hydrogen reference electrode. Because the potential of the SHE is defined as zero, the standard potential of the Sn2+|Sn redox system is eo ¼
0.138 V, as presented in Table 2.2. Electrodes shown

V

Sn

Pt

(Sn2+) = 1

(H+) = 1

H2 (pH2 = 1 atm.)

Porous barrier

Fig. 2.2 Schematic of electrochemical cell showing the measurement of cell potential.

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in Table 2.2 with a large negative eo with respect to a standard hydrogen electrode are strongly reducing. They undergo oxidation and transfer electrons to the other half-cell reaction, where the reduction process occurs at the interface. Electrodes such as Au|Au3+ or Pt|Pt2+ are positive with respect to SHE. They are strongly oxidizing and capture electrons from the other half-cell. In a spontaneous reaction between two half-cells, the half-cell with the more positive potential in Table 2.2 undergoes reduction, while the one with the more negative potential undergoes oxidation. The charge transfer changes the standard electrode potential due to the change of the composition of the electroactive species in the electrolyte. When a final ratio of the activities of the reactive species, as defined in Eq. (2.38), is equal to the equilibrium constant of the reaction, the system will be in equilibrium.

2.7 DETERMINATION OF ELECTROCHEMICAL/CORROSION REACTION DIRECTION BY GIBBS ENERGY The energy change in the partial reactions provides the driving force and determines the direction of the spontaneous reaction. When there are no net current flows in a reversible electrochemical or corrosion cell, Eq. (2.16) is valid: dG ¼
nFdE

(2.16)

Under standard conditions, the standard free-energy of the cell reaction ΔG is directly related to the standard potential difference across the cell Eo: o

(2.48) ΔGo ¼
nFEo X o o vi Gi is the difference between the Gibbs energy of the products and where ΔG ¼ i the reactants of the electrochemical reaction, (weighted by their stoichiometric coefficients) or X ΔGo ¼ ΔGof ðproductsÞ
ΔGof ðreactantsÞ (2.49) Each of the products and reactants is in its standard state as a pure substance at standard temperature and at a fixed pressure. ΔGo is fixed for a given electrochemical reaction and it is independent of equilibrium pressure and composition once the temperature is established. The free-energy of formation of the pure elements arbitrarily is taken to be zero. The values of ΔGoform that are defined at 298 K can be corrected to the reaction temperature of interest ΔGoform(T). The equilibrium Gibbs free-energy is calculated from ΔGform by using Eq. (2.31), which corrects the standard Gibbs free-energy concentrations (defined in the standard state of the pure substances at fixed pressure) with the concentrations of the products and reactants at equilibrium state (actual state of the reaction). The negative sign of the Gibbs free-energy in Eq. (2.16) follows the convention that a

Thermodynamics in the electrochemical reactions of corrosion

positive potential, E, results in a negative free-energy change for a spontaneous electrochemical reaction. Accordingly, ΔG is calculated from ΔGo data from which the potential of the reversible electrochemical cell is estimated. Conversely, the cell potential can be measured experimentally as described above; once the potential is known, ΔG is calculated using Eq. (2.16). Example 2.1 Predict whether or not Sn will dissolve spontaneously in hydrochloric acid. To solve the problem it is necessary to separate the corrosion reaction Sn + 2HCl ! SnCl2 + H2 Ecell ¼ 0:138V into its half-cell reactions: Anodic : Sn ! Sn2 + + 2e
eo ¼ 0:138V


(2.50) (2.51)

Cathodic : 2H + 2e ! H2 e ¼ 0V (2.9b) If reaction in Eq. (2.50) proceeds from left to right, the Gibbs free-energy change must be negative according to Eq. (2.48). To evaluate the Gibbs free-energy change, it is necessary to calculate the electrode potential, E, which is the sum of the half-cell potentials: +

o

(2.39) E ¼ ea + ec In order for the overall corrosion reaction in Eq. (2.50) to proceed as written, one should substitute the potential of the anodic reaction in Eq. (2.39), which as shown in Eq. (2.51) is oxidation of tin to tin oxide. According to IUPAC convention, the sign of the half-cell electrode potential must be reversed from cathodic eo ¼
0.138 V in Table 2.2 to eo ¼ + 0.138 V. The potential of the anodic reaction has the same magnitude but the opposite sign of the cathode half-cell reaction in Table 2.2. Because the potential of the SHE is set to zero, the cell potential for reaction (2.50) is: E ¼ 0:138 + 0 ¼ 0:138 V vs: SHE The calculated Gibbs free-energy using Eq. (2.48) is negative, indicating that the reaction in Eq. (2.50) proceeds spontaneously as written. Therefore, Sn will dissolve spontaneously in hydrochloric acid.

Example 2.2 Calculate the tendency for corrosion to occur in the following metal electrolyte systems: (a) silver in cupric acid and (b) nickel in silver nitrate. (a) Anodic : 2Ag ! 2Ag + + 2e
eoAgjAg + ¼
0:799V vs: SHE Cathodic : Cu2 + + 2e
! Cu eoCu2 + jCu ¼ 0:337V vs: SHE Corrosion reaction : 2Ag + Cu2 + ! Cu + 2Ag + E cell ¼
0:462 V vs: SHE

43

44

Corrosion engineering

Because the cell potential is negative according to Eq. (2.48), the Gibbs free-energy is positive, indicating that the corrosion process will not proceed spontaneously as written. (b) Anodic : Ni ! Ni2 + + 2e
eoNijNi2 + ¼ 0:250 V vs: SHE Cathodic : 2Ag + + 2e
! 2Ag eoAg + jAg ¼ 0:799V vs: SHE Corrosion reaction : Ni + 2Ag + ! 2Ag + Ni2 + Ecell ¼ 1:049Vvs: SHE Corrosion will occur with the displacement of silver ions from the electrolyte in the presence of Ni metal, which has more negative standard potential than silver.

Example 2.3 Predict the spontaneous direction for the reaction: 4OH
+ 2Fe2 + ! O2 + 2Fe + 2H2 O

(2.52)

O2 + 2H2 O + 4e
! 4OH
, eoO2 jOH
¼ 0:401Vvs: SHE

(2.53)

Fe2 + + 2e
! Fe, eoFe2 + jFe ¼
0:440Vvs: SHE

(2.54)

The half-cell reactions are:

and

Assuming that reaction in Eq. (2.52) proceeds from left to right, the half-cell potential for reaction in Eq. (2.53) written as oxidation is eoO2 jOH
¼
0:401Vvs: SHE: According to IUPAC convention, the sign must be reversed because the positive sign for this half-cell reaction in Table 2.2 is written for the reduction reaction. The half-cell potential for the reaction in Eq. (2.54) eFe2 + jFe ¼
0:440Vvs: SHE is correct because the half-cell reaction is a reduction. The cell potential is then Ecell ¼
0.401 + (
0.440) ¼
0.841 V vs. SHE. The potential is negative and reaction in Eq. (2.52) as written does not proceed spontaneously. The opposite reaction in Eq. (2.55) proceeds as: (2.55) O2 + 2Fe + 2H2 O ! 4OH
+ 2Fe2 + The cell potential for reaction in Eq. (2.55) is 0.841 V vs. SHE resulting in negative Gibbs free-energy. Thus, for iron corroding in water near a neutral pH, the half-cell reactions are written as: Fe ! Fe2 + + 2e
Anode Reaction O2 + 2H2 O + 4e
! 4OH
Cathode Reaction The metals with cell potentials that are more negative than the oxygen electrode potential are not thermodynamically stable when in contact with water and air, and a spontaneous reaction occurs in which oxygen will be converted into water.

Thermodynamics in the electrochemical reactions of corrosion

2.8 REFERENCE ELECTRODES OF IMPORTANCE IN CORROSION PROCESSES 2.8.1 Determination of reversible potential of the hydrogen electrode The half-cell of the hydrogen reference electrode consists of platinum foil, which serves as a conductor. The platinum foil is in contact with a sulfuric acid solution that contains H+ cations of unit activity, in equilibrium with H2 gas, in its standard state of 1 atm [12–17]. The standard hydrogen electrode may be represented as: H + jH2 , Pt The charge transfer reaction is: 2H + + 2e
! H2

(2.9b)

According to the Nernst equation: eH + jH2 ¼ eoH + jH2 + 2:303

RT ðaH +Þ2 log PH2 2F

eH + jH2 ¼ eoH + jH2 + 0:059logaH + eH + jH2 ¼
0:059ðpHÞ

(2.56)

The hydrogen electrode potential depends on the hydrogen activity and the partial hydrogen pressure. Under standard conditions, the hydrogen pressure is one atmosphere; thus, its activity is equal to 1 and, therefore, according to IUPAC convention, the hydrogen reference electrode potential is zero. The schematic of a SHE is shown in Fig. 2.3. Connnecting wire

H2

Mercury

Bubbler as atmospheric seal

Electrolyte Platinized platinum Electrolyte bridge

H2

Fig. 2.3 Schematic of the standard hydrogen electrode.

45

46

Corrosion engineering

The hydrogen reference electrode is connected to the other redox system through a solution bridge. The bridge consists of a porous glass membrane that permits only charge transfer, without interference of the mass transfer of the acid solution at the electrode interface. The platinum electrode in Fig. 2.3 serves only as a catalyst for the hydrogen evolution reaction, and has the function of establishing the potential on the surface. The SHE is the primary reference electrode. Its half-cell potentials presented in Table 2.2 are expressed on the basis of the standard hydrogen scale, in which the emf of any cell is equal to the potential of the redox system, relative to the potential of the SHE, which is set equal to zero.

Example 2.4 Determine whether zinc is stable in aqueous solutions of hydrochloric acid with pH between 0 and 5. The initial concentration of ZnCl2 is 10
6 M. Plot the driving emf and the Gibbs free-energy as a function of pH for the overall corrosion reaction. The activity coefficients are assumed to be 1. The hydrogen pressure ¼ 1 atm. Zinc is oxidized at the anode and the H+ is reduced at the cathode. For the overall reaction: Zn + 2H + ! Zn2 + + H2 the only terms that should be considered are the Zn2+ and the H+ concentrations. The activities of metal Zn and H2 are assumed to be unity. Because Zn2+ is the product, it will appear in the numerator of the logarithmic term, and the H+ (reactant) will appear in the denominator. The problem requires changing the pH in order to calculate the cell potential at different pH values. Cell Notation: Zn|Zn2+, Cl
, H+|H2 |Pt In the given reaction, Zn is oxidized at the anode according to: Zn ! Zn2+ + 2e
The hydrogen is evolved at the cathode according to: 2H+ + 2e
! H2 The overall reaction can be written as: Zn + 2H+ ! Zn2+ + H2 The Nernst equation for the anodic reaction can be written as: eH +jH2 ¼ eoH + jH2


2:303RT aH2 log 2F ðaH +Þ2

eZnjZn2 + ¼ eoZnjZn2 +


0:059 log ðaZn2 +Þ 2

At pH ¼ 0, the eZnjZn2 + electrode potential is calculated as eZnjZn2 + ¼ 0:762


  0:059 log 10
6 2

eZnjZn2 + ¼ 0:940Vvs: SHE E cell ¼ ea + ec E cell ¼ eoH + jH2

+ eoZnjZn2 +

RT aZn2 +
2:303 log 2F ðaH +Þ2 aZn

!

Thermodynamics in the electrochemical reactions of corrosion

Table 2.3 The Cell Potential and Gibbs Free-Energy for the Reaction Zn(s) + 2HCl(aq) ! ZnCl2(aq) + H2(g)  kJ  eZnjZn2 + ðV Þ pH Ecell (V) DG mol

0.94 0.94 0.94 0.94

0 1 3 5

0.940 0.881 0.763 0.645


181.42
170.03
147.26
124.48

The cell potential as a function of pH is calculated using the equation: Ecell ¼ eZnjZn2 +
0:059pH The Gibbs free-energy is calculated by using Eq. (2.45): " #   ΔG RT ðaH +Þ2 RT o ¼ eH + jH2 + ln ln aMn +
eoMn + jM +
PH2 nF nF nF

(2.45)

or ΔG ¼
nFEcell; the results are presented in Table 2.3. As shown in Fig. 2.4a and b, for a pH increase of 1, the cell potential decreases by 59 mV. The Gibbs energy change decreases linearly with increase from pH 0-5. For pH where the Gibbs free-energy is negative, the process proceeds spontaneously. Zinc is unstable in solutions with pH 0-5.

2.8.2 Determination of reversible potential of the oxygen electrode An oxygen gas electrode is represented by: O2 , PtjOH
The charge transfer reaction is written as: O2 + 2H2 O + 4e
! 4OH
According to the Nernst equation:

!

RT PO2 eO2 jOH
¼ eoO2 jOH
+ 2:303 log 4F ðaOH
Þ4 0:059 log ðPO2 Þ
0:059log ðaOH
Þ 4 eO2 jOH
¼ 0:401
0:059log ðaOH
Þ

eO2 jOH
¼ eoO2 jOH
+

(2.57)

The oxygen electrode is classified as a metal oxide electrode of the second kind. Due to the tendency of oxygen to react with metals and produce oxides, it is very difficult to construct an oxygen electrode with the potential as described by Eq. (2.57).

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Corrosion engineering

Fig. 2.4 (a) pH vs. Gibbs free-energy (b) pH vs. cell potential for the Zn corrosion cell.

2.8.3 Determination of cell potential of the hydrogen-oxygen cell (fuel cell) In a hydrogen/oxygen fuel cell shown in Fig. 2.5, the electrical energy results from chemical energy that has been released when water is formed: 1 H2 + O2 ! H2 O 2

Thermodynamics in the electrochemical reactions of corrosion

Load 2e−

−

+ H2

Air

e−

H+

H+

e−

H+

H+ H+

H2(g) → 2H+ + 2e− e−

H+

H+

e−

1 O2 + 2e− → O−2 2

H+

H+

2H+ + O2− → H2O(liq.)

H+

H+ Electrolyte (Ion conductor)

H2O, depleted fuel, & product gases out

Depleted oxidant and product gases out (H2O)

Cathode

Anode

Fig. 2.5 Schematic of the hydrogen/oxygen fuel cell.

The cell potential is estimated using equation: E H2 , O2 j H2 O ¼ EoH2 , O2 j H2 O + 2:303

  1 RT log PH2 ðPO2 Þ2 4F

This equation was derived considering the partial electrode reaction of hydrogen oxidation and oxygen reduction, H2 ! 2H + + 2e
1 O2 + H2 O + 2e
! 2OH
2 The overall reaction is: 1 H2 + O2 + H2 O ! 2H + + 2OH
2 According to the Nernst equation: PH2 ðPO2 Þ1=2 aH2 O log 4F ðaH +Þ2 ðaOH
Þ2

(2.58) !

RT Ecell ¼ E ocell + 2:303

aH + aOH
¼ Kw

E cell ¼ E ocell
2:303

 RT RT log ðK w Þ + 2:303 log PH2 ðPO2 Þ1=2 F 2F

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50

Corrosion engineering

  RT log ðK w Þ ¼ 0:00 + 0:401
0:059log 10
14 F E cell ¼ 0:00 + 0:41 + 0:83 ¼ 1:23 V  0:059 (2.59) Ecell ¼ 1:23 + log PH2 ðPO2 Þ1=2 2 According to Eq. (2.59), the potential of the fuel cell increases by the log of the partial pressure of both oxygen and hydrogen, and is independent of the pH of the solution. E cell ¼ eoH + jH2 + eoOH
jO2
2:303

2.8.4 Determination of electrode potential of a standard Weston cell The overall reaction in the Weston cell as presented in Fig. 2.6a and b is Cd, Hg|CdSO4| CdSO4|Hg2SO4, Hg. The potential of this cell is very stable with a small temperature coefficient. The left half-cell (anode) reaction in the Weston cell is reversible to cadmium ions, CdðHgÞ ! Cd2 + + 2e
while the right-hand side (cathode) is reversible to sulfate ions: Hg2 SO4 + 2e
! 2Hg + SO2
4

Sat’d CdSO4 soln. CdSO4(S) Hg2SO4(S) Cd(Hg)

Hg(I)

(a)

+

− Hg

Ecell = 1.018 V

(b)

CdSO4 soln.

Cd(Hg)

Fig. 2.6 (a) Schematic of the standard Weston cell and (b) hypothetical electric potential profile in the Weston cell.

Thermodynamics in the electrochemical reactions of corrosion

The overall reaction in the cell is: CdðHgÞ + Hg2 SO4 ! Cd2 + + SO2
4 + 2Hg The emf of the Weston cell is: E cell ¼ eHg2 SO4 jHg
eCd2 + jCd   RT aCd o 2 + eCd jCd ¼ eCd2 + jCd
2:303 log aCd2 + nF   aHg2 + aSO2
RT o 4 log eHg2 SO4 jHg ¼ eHg2 SO4 jHg
2:303 aHg2 SO4 nF   aCd2 + aHg2 + aSO2
RT o 4 Ecell ¼ Ecell
2:303 log aCd aHg2 SO4 nF Because the activities of the solid substances in the above equation are constant and equal to unity, the potential of the standard Weston cell is defined by Eq. (2.60). E cell ¼ E ocell
2:303

RT log ðaCdSO4 Þ nF

(2.60)

2.8.5 Determination of electrode potentials for electrodes of the second kind The half-cell reaction of electrodes of the second kind consists of a metal covered by a low solubility compound of the same metal, (MA), such as a salt, a hydroxide, or an oxide, and is immersed in a solution that contains the same anions as the compound of the metal. Therefore, an electrode of the second kind is represented as: An
jMA, M The electrode reaction is expressed as: MA + ne
! M + An
The Nernst equation written for the electrode potential is:   RT aMA o n
eA j MA ¼ eAn
jMA + 2:303 log aAn
aM nF

(2.61)

Because the solubility of MA is low, the activity of the metal, M, and the solid substance, MA, in Eq. (2.61) are constant. Thus, the equation may be simplified to: eAn
jMA ¼ eoAn
jMA + 2:303

RT log ðaAn
Þ nF

(2.62)

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Corrosion engineering

The electrode potential of this type of electrode is defined by the concentration (activity) of the anions. They are used in corrosion engineering as standard half-cells or reference electrodes. In corrosion engineering practice they are called secondary reference electrodes to differentiate them from the hydrogen electrode, which is a primary reference electrode. The following electrodes of the second kind are of interest in electrochemical and corrosion studies: calomel electrode, silver-silver chloride electrode, and mercurymercurous electrode.

2.8.6 Calomel electrode The calomel electrode shown in Fig. 2.7 consists of a pool of mercury covered with a paste of mercury and calomel (mercurous chloride), immersed in an electrolyte containing a solution of potassium chloride. The reaction of the electrode is a reduction of calomel to metallic mercury and chloride anions. Cl
Hg2 Cl2 jHg Hg2 Cl2 + 2e
! 2Hg + 2Cl


KCl

Hg Hg2Cl2 Porous plug

Porous wick

Fig. 2.7 Schematic of the calomel electrode.

Thermodynamics in the electrochemical reactions of corrosion

The electrode potential is reversible with respect to the chloride ions. eoHg2 Cl2 jHg, Cl
¼ 0:268
0:059log ðaCl
Þ

(2.63)

The saturated calomel electrodes are convenient for corrosion measurements because the diffusion potential initiated at the interface of the saturated potassium chloride solution and the electrolyte is insignificant and can be ignored. The electrode potential of the saturated calomel electrode of 0.241 V is lower than the potential of the standard half reaction of eo ¼ 0.268 V because of the higher chloride activity.

2.8.7 Silver-silver chloride electrode The silver-silver chloride electrode shown in Fig. 2.8 is based on the following redox reaction: AgCljAg,Cl
AgCl + e
! Ag + Cl
The potential of this electrode is defined by the Nernst equation: eAgCljCl
¼ eoAgCljCl

2:303

RT log ðaCl
Þ nF

Ag wire AgCl KCl soln.

Porous junction

Fig. 2.8 Schematic of the silver-silver chloride electrode.

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54

Corrosion engineering

At 25  C: eAgCljCl
¼ 0:222
0:059log ðaCl
Þ

(2.64)

2.8.8 Copper-copper sulfate electrode The copper-copper sulfate reference electrode consists of copper metal immersed in a saturated copper sulfate solution, as shown in Fig. 2.9. A porous frit or wooden plug serves as an electrolytic contact with the cell. The electrode reaction is: Cu2 + + 2e
! Cu The electrode potential is given by: 0:059 eCu2 + jCu ¼ 0:337 + log ðaCu2 +Þ 2 This electrode has a very simple design and is frequently used in corrosion engineering practice to evaluate the corrosion potential of buried pipelines and other buried metallic structures. The disadvantage of using this electrode is its low precision. The conversion of potential from one reference point to another is done by using addition or subtraction.

Copper head Insulating seal

Copper rod

Inert container Copper sulfate solution

Surplus copper sulfate crystals Porous plug Sponge (electrical junction)

Fig. 2.9 Schematic of the copper-copper sulfate reference electrode.

Thermodynamics in the electrochemical reactions of corrosion

Table 2.4 Equilibrium Potential Values for Commonly Used Reference Electrodes Reference Electrode Half-Cell Reaction Potential V vs. NHE

Standard hydrogen Calomel

2H+ + 2e
! H2 Hg2Cl2 + 2 e
! 2Hg + 2Cl-

Silver-silver chloride

AgCl + e
! Ag + Cl-

Mercury-mercurous sulfate Mercury-mercury oxide

HgSO4 + 2e
! Hg + SO24

Copper-copper sulfate

HgO + H2O + 2e- ! Hg + + OH
CuSO4 + 2e
! Cu + SO2
4

0.615 V

Hg/HgSO4

0.318 V

Cu/CuSO4

0.241 V

SCE

0.222 V

Ag/AgCl

0.165 V

Hg/HgO

0.000 V

SHE

0.000 0.283 (1 M KCl, NCE) 0.241 (Sat’d KCl, SCE) 0.236 (Sat’d NaCl, SCCE) 0.222 (KCl, Standard) 0.197 (NaCl, Sat’d) 0.615 (Standard) 0.680 (0.5 M H2SO4) 0.165 (0.1 M NaOH) 0.318 (Sat’d CuSO4)

Fig. 2.10 Hydrogen electrode scale.

For example, the equilibrium reduction potential of iron, which is
0.44 V vs. NHE, will be
0.681 V vs. SCE (saturated calomel electrode). Similarly, a metal that shows a potential of
0.331 V vs. Ag|AgCl will have a potential of
0.109 V vs. SHE and
0.427 V vs. Cu|CuSO4. The potentials of various reference electrodes are given in Table 2.4 and are compared in Fig. 2.10 with respect to the NHE.

2.9 MEASUREMENT OF REVERSIBLE CELL POTENTIAL WITH LIQUID JUNCTION POTENTIAL The potential of two reversible cells can be accurately measured by using the experimental cell setup shown in Fig. 2.11. The cell contains pure zinc and pure platinum electrodes

55

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Corrosion engineering

Cu lead Electrometer eCu/Pt

H2

eZn/Cu

Liquid junction

ej

eH+|H

Pt

Zn

2

H2SO4

eZn/Zn2+

ZnSO4 solution

Fig. 2.11 Schematic of the experimental setup for measuring reversible cell potential.

immersed in zinc sulfate and sulfuric acid solutions, both of unit activity. The cell potential measured by using this apparatus has individual potential contributions from eoZnjZn2 + , eoH + jH2 , eZnjCu , eCujPt , and liquid junction potential, ej : Negligible quantities of contact potentials are also added to the total cell potentials of Zn|Cu and Cu|Pt couples because of the energy required when moving electrons from one metal to another. In most of the cases, their contribution is canceled out because of their opposite signs. However, the half-cell potentials reported in Table 2.2 are incorporated with very small contributions from contact potentials. The liquid junction ej is generated across two solutions of differing concentrations and/or composition due to the migration of ionic species into the solution of lower concentration from higher concentration.

2.10 MEASUREMENT OF CORROSION POTENTIAL The potential of the corroding surface can be monitored periodically by means of a reference electrode. One such example is the corrosion potential measurement of reinforced steel rebar in concrete structures. Corrosion of the steel in reinforced concrete is a major factor in the deterioration of highway and bridge infrastructure. A survey of the condition of a reinforced concrete structure is the first step toward its rehabilitation. A rapid, cost-effective, and nondestructive condition survey offers key information to evaluate the corrosion, aids in quality assurance of concrete repair and rehabilitation,

Thermodynamics in the electrochemical reactions of corrosion

Voltmeter

− +

Copper-copper sulfate reference electrode

Reinforced steel

Fig. 2.12 Corrosion potential measurement of reinforced steel rebar in concrete.

and assists in the prediction of the remaining service life of the material. An effective way to assess the severity of steel corrosion is to measure the corrosion potential because it is qualitatively associated with the steel corrosion rate. Figure 2.12 illustrates the basics of corrosion potential measurements. The reference electrode and the reinforced steel are connected to the positive and negative terminals of a high-resistance (>10 MΩ) voltmeter. One measures the potential difference between a standard portable half-cell standard reference electrode, normally a copper/copper sulfate and the steel by placing the electrode on the surface of the concrete containing the steel reinforcement underneath.

2.11 CONSTRUCTION OF POURBAIX DIAGRAMS The dissolution of a metal and the stability of the products in aqueous solutions depend on the nature of the metal, the solution’s oxidizing power, and the pH of the solution. The stability of different metals is estimated by using potential-pH diagrams suggested by Marcel Pourbaix [18,19]. These diagrams are constructed from calculations based on the Nernst equation and the solubility (activity) data for various metal compounds. Pourbaix diagrams predict the reaction products of the metal that exist at equilibrium at a given electrode potential and pH. The only conditions for constructing the diagram are that all the necessary reactions should be at a given pH and be at a potential of interest. They show the values of pH and potential conditions at which the metal reacts to form complex anions or oxides or where the metal is immune to corrosion. The Pourbaix diagrams are used to (i) predict the spontaneous direction of reactions, (ii) determine the potential/pH regions in which the metal is stable and where the

57

58

Corrosion engineering

corrosion is thermodynamically impossible, (iii) estimate the nature and the composition of corrosion products, and (iv) evaluate the equilibrium conditions of the metal/electrolyte interface. Because the potential-pH diagrams characterize equilibrium thermodynamic properties only, they cannot be used to predict the rates of reactions. They can evaluate the conditions for formation of barrier films on the metals, but they cannot estimate their effectiveness in protecting the metal in different environments. It should be noted that the Nernst equation is used to estimate the electrode potentials and is based on thermodynamic equations, which are not accurate when the concentration of the electroactive species is close to zero. All metals have a limiting critical value of their activities, (a concentration of <10
6 g-ions per liter), below which the Nernst equation does not agree with the experimentally measured Gibbs free-energy.

2.11.1 Regions of electrochemical stability of water Figure 2.13 shows the thermodynamic stability of water at 25  C and at standard pressure, as a function of the potential and the pH of the electrolyte. The regions of electrochemical stability of water are used to predict the properties of a metal in aqueous solutions when the metal’s potential is known at given pH. In Fig. 2.13, the reversible potential of the hydrogen line, line “b” electrode is constructed using the reversible potential for the hydrogen evolution reaction in an acidic solution: 2H + + 2e
! H2

Fig. 2.13 Regions of electrochemical stability of water.

Thermodynamics in the electrochemical reactions of corrosion

In an alkaline solution, the equivalent reaction is: 2H2 O + 2e
! H2 + 2OH
The half-cell electrode potential as a function of the pH of the solution is given as: eH + jH2 ¼ eoH + jH2
0:059 pH The area below line “b” corresponds to the area where the water decomposition with hydrogen evolution reaction occurs. The area in Fig. 2.13 between the oxygen equilibrium potentials (line “a”) and the hydrogen line (line “b”) is where the water is stable. In this region, water may be synthesized from oxygen and hydrogen. The area above line “a” corresponds to the region where the water decomposes with the formation of oxygen: 2H2 O ! O2 + 4H + + 4e
and 4OH
! O2 + H2 O + 4e
The Nernst equation for the oxygen equilibrium potentials is defined as: eO2 jH2 O ¼ eoO2 jH2 O
0:059ðpHÞ At pH 0, the equilibrium electrode potential for the reaction is 1.22 V vs. SHE, while that of OH
at pH 14, as shown in Table 2.2, is 0.401 V vs. SHE at unit activity. The area above line “a” corresponds to the region where the water decomposition proceeds with formation of oxygen.

2.11.2 Construction of pourbaix diagram for zinc The zinc system is used to demonstrate the basic principles for the construction of Pourbaix diagrams. Any metal, “M,” reacts anodically in the presence of water through the following general reactions: 1. Oxidation of the metal to aqueous cations: M ! Mn + + ne


(2.65)

2. Oxidation of the metal to oxide or hydroxide: M + nH2 O ! MðOHÞn + nH + + ne


(2.66)

3. Oxidation of the metal to aqueous anions: + M + nH2 O ! MOn
n + 2nH

Thus, the oxidation of zinc to its aqueous solutions is described by the reaction: Zn ! Zn2 + + 2e


(2.67)

59

60

Corrosion engineering

Substituting the zinc standard potential and the zinc concentration into the Nernst equation:   0:059 aZn2 + o eZnjZn2 + ¼ eZnjZn2 + + log aZn n we obtain: 0:059 log ðaZn2 +Þ n For zinc concentration of 1 M, the electrode potential from Table 2.2 is eoZnjZn2 + ¼
0:762Vvs: SHE: As shown in Fig. 2.14, if the concentration of zinc ions is unity, the zinc standard potential is constant at all pH. However, the standard concentration represents an unrealistically high concentration of (Zn2+) in corrosion solution. More realistic for corrosion process would be lower value at the metal/electrolyte interface such as (Zn2+) ¼ 10
6 M resulting in eZnjZn2 + ¼
0:94 V vs. SHE at all pH. The half-cell potential for formation of zinc cation is independent of pH because hydrogen cation is not involved in zinc dissolution reaction. Rather, it depends on the concentration of zinc ions in the solution. Thus, the two horizontal straight lines in Fig. 2.14 result from two different concentrations of zinc in the electrolyte. The zinc oxidation reaction to zinc oxide is expressed by the following equation: eZnjZn2 + ¼
0:762 +

Zn + H2 O ! ZnO + 2H +

Fig. 2.14 Potential-pH diagram showing the cation formation reaction [Zn2+] of 1 and 10
6 M.

Thermodynamics in the electrochemical reactions of corrosion

The reduced and oxidized species, Zn and ZnO, are solids. Their activities in the Nernst equation are unity, which eliminates their contribution to the overall electrode potential. The Nernst equation reduces to: eZnjZnO ¼ eoZnjZnO
0:059pH eZnjZnO ¼
0:439
0:059pH eoZn|ZnO ¼
0.439 V

vs. SHE. where In Fig. 2.15, this equation represents a straight line with a slope of
0.059. At pH ¼ 0, the potential corresponds to the standard zinc eoZn|ZnO electrode potential of
0.439 V vs. SHE. The lines representing the cation and the oxide formation are labeled in Fig. 2.15 as (1) and (2) and they intercept each other at different pH values. The intercept depends on the concentration of Zn2+. In fact, above these concentrations, the Zn2+ cations react with water to form zinc oxide: Zn2 + + H2 O ! ZnO + 2H +

(2.68)

Below this pH, the zinc oxide dissolves to Zn2+ cations. Notice that the charge transfer reaction does not occur in reaction shown in Eq. (2.68) because the oxidation state of Zn2+ does not change. The equilibrium of this reaction is determined by the concentration (activities) of the zinc cations and is independent of the potential. The pH at equilibrium where line (1) and line (2) intersect is estimated by using the value of the equilibrium constant for the reaction in Eq. (2.68) of K ¼ ðaH +Þ2 =ðaZn2 +Þ ¼ 10
10:96 :

Fig. 2.15 Potential-pH diagram showing ZnO superimposed on Fig. 2.14.

61

62

Corrosion engineering

Thus, for Zn2+ activities of 10
6 M, the pH value of 8.48 is calculated from the known value of the equilibrium constant: log ðaZn2 +Þ ¼ 10:96
2pH

(2.69)

log ðK Þ ¼ 2 log ðaH +Þ
log ðaZn2 +Þ ¼
2pH
log ðaZn2 +Þ
log ðK Þ log ðaZn2 +Þ 10:96 6
¼ + ¼ 8:48 2 2 2 2 The lines in Fig. 2.15 are vertical because the pH is independent of the potential. At high potentials, the zinc cations are stable at pH lower than 8.48, while ZnO is stable at pH higher than 8.48. The reaction that corresponds to the formation of aqueous for zinc is: pH ¼

+
Zn + 2H2 O ! ZnO2
2 + 4H + 2e

The Nernst equation is:  0:059 log aZnO2
2 2 2 The Nernst potential, as shown in Fig. 2.16, depends on the pH and the concentration of
6 M, and an anion concentra(ZnO2
2 ) anions. Lines for an anion concentration of 10 tion of 1 M, are shown in Fig. 2.16. The pH slopes for both concentrations are
0.118. The standard value of eoZnjZnO2
, estimated from the intercept at pH ¼ 0, is equal to 2 0.441 V vs. SHE. eoZnjZnO2
¼ 0:441
0:118pH +

Fig. 2.16 Potential-pH diagrams showing aqueous anion formation for Zn metal.

Thermodynamics in the electrochemical reactions of corrosion

At pH values higher than 11, ZnO dissolves to form ZnO2
2 , according to the reaction: + Zn + 2H2 O ! ZnO2
2 + 2H Because there is no charge transfer or a valence change, this reaction is independent of the potential. Thus, the transition from ZnO to ZnO2
2 is calculated from the equilibrium constant. The equilibrium pH in Fig. 2.16 is estimated to be 11.89 and 14.89 for concentrations of aZnO2
¼ 10
6 M and 1 M, respectively, independent of potential. 2  ¼
29:78 + 2ðpHÞ log aZnO2
2  ¼ 1, pH ¼ 14:89 for aZnO2
2  for aZnO2
¼ 10
6 , pH ¼ 11:89 2 When (Zn2+) ¼ 10
6 M, the equilibrium is represented as straight vertical lines at pH ¼ 11.89. In Fig. 2.16, at high potentials, the oxides are stable below a pH of 11.89 and the anion is stable above this pH. At unit activity, the zinc anion is stable above pH ¼ 14.89. The following regions are clearly outlined in Fig. 2.16: (i) immunity, in which the metal is considered to be immune from corrosion attack; (ii) corrosion region, in which the metal corrodes and forms soluble species; and (iii) passive region, in which the metal is coated with oxide or hydroxide. By decreasing the potential (cathodic protection), the metal can move from the active corrosion region to the immunity region. Zinc, because of its equilibrium potential, is used as a sacrificial anode to protect the iron from corrosion.

2.11.3 Construction of Pourbaix diagram for tin The Pourbaix diagram for tin was constructed by using six reduction and oxidation reactions over a pH range of 0-14. All dissolved species were assumed to have activities of 10
6 M. The diagram is plotted at 25  C. The following reactions were considered in the construction of the diagram: SnH4 ! Sn + 4H + + 4e
eoSnH4 jH + ¼
1:076Vvs: SHE Sn ! Sn2 + + 2e
eoSnjSn2 + ¼
0:136Vvs: SHE +
Sn + 2H2 O ! HSnO
eoSnjH +, HSnO
¼ 0:333Vvs: SHE 2 + 3H + 2e 2

Sn

2+

+ 2H2 O ! SnO2 + 4H + 2e +




eoSn2 + jH +

¼
0:077Vvs: SHE

Sn + 2H2 O ! SnO2 + 4H + + 4e
eoSnjH + ¼
0:106 V vs: SHE +
eoHSnO
jH + ¼
0:546 V vs: SHE HSnO
2 ! SnO2 + H + 2e 2

63

64

Corrosion engineering

Derivation of Equilibrium Equations: The Nernst equations were used to derive the equilibrium potentials as a function of pH. Equilibrium (1) SnH4 ! Sn + 4H + + 4e
eoSnH4 jH + ¼
1:076Vvs: SHE eSnH4 jH + ¼ eoSnH4 jH + +

  0:059 0:059 log ðaH +Þ4
log ðaSnH4 Þ 4 4

eSnH4 jH + ¼
1:076
0:059pH


0:059 log ðaSnH4 Þ 4

Equilibrium (2) Sn ! Sn2 + + 2e
eoSnjSn2 + ¼
0:136V vs: SHE eSnjSn2 + ¼ eoSnjSn2 + +

0:059 log ðaSn2 +Þ 2

eSnjSn2 + ¼
0:136 +

0:059 log ðaSn2 +Þ 2

Equilibrium (3) +
Sn + 2H2 O ! HSnO
eoSnjH + , HSnO
¼ 0:333V vs: SHE 2 + 3H + 2e 2

eSnjH + , HSnO
2 ¼ eoSnjH + , HSnO
+ 2

eSnjH + , HSnO
2 ¼ 0:333


  0:059   0:059 log ðaH +Þ3 + log aHSnO
2 2 2

  3  0:059 0:059 pH + log aHSnO
2 2 2

Equilibrium (4) Sn2 + + 2H2 O ! SnO2 + 4H + + 2e
eoSn2 + jH + ¼
0:077 V vs: SHE eSn2 + jH + ¼ eoSn2 + jH + +

  0:059 0:059 log ðaH +Þ4
log ðaSn2 +Þ 2 2

eSn2 + jH + ¼
0:077
2  0:059pH


0:059 log ðaSn2 +Þ 2

Equilibrium (5) Sn + 2H2 O ! SnO2 + 4H + + 4e
eoSnjH + ¼
0:106V vs: SHE

Thermodynamics in the electrochemical reactions of corrosion

eSnjH + ¼ eoSnjH + +

  0:059 log ðaH +Þ4 4

eSnjH + ¼
0:106
0:059pH Equilibrium (6) +
eoHSnO
jH + ¼
0:546 V vs: SHE HSnO
2 ! SnO2 + H + 2e 2

eHSnO
2 jH + ¼ eoHSnO
jH + + 2

  0:059 0:059 log ðaH +Þ + log aHSnO
2 2 2

  0:059 0:059 pH + log aHSnO
2 2 2 The various regions in potential-pH diagram are determined using the equilibrium equations. The following regions exist in Figs. 2.17 and 2.18: (i) immunity region, in which the metal is considered immune to corrosion attack; (ii) passive region, in which the metal is coated with oxide or hydroxide, serving as a barrier film against corrosion; and (iii) corrosion region, in which the metal corrodes and forms soluble species. In addition to the six reactions described above, other chemical reactions may occur, such as: eHSnO
2 jH + ¼
0:546


+ SnO2 + H2 O ! SnO2
3 + 2H

Because there is no charge transfer or valence change in this reaction, it is independent of the potential. The pH, where the transformation of SnO2 to SnO2
3 occurs, is calculated from the equilibrium constant.

Fig. 2.17 Pourbaix diagram for tin.

65

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Corrosion engineering

Fig. 2.18 Areas of stability, passivity, and corrosion for tin.

Fig. 2.19 Pourbaix diagram for tin with added chemical reactions.

 ¼
31:16 + 2pH log aSnO2
3 For a concentration of 10
6 M, this equation is a vertical line at pH ¼ 12.58. The resulting Pourbaix diagram is shown in Fig. 2.19, while the regions of corrosion, passivity, and stability are given in Fig. 2.20.

Thermodynamics in the electrochemical reactions of corrosion

Fig. 2.20 Regions of stability, corrosion, and passivity for tin.

2.11.4 Pourbaix diagram for iron The Pourbaix diagram for iron is constructed by using nine reduction and oxidation reactions over a pH range of 0-14. All dissolved species are assumed to have activities of 1 M. The diagram is plotted at 25  C. The following reactions were used to construct the diagram: Reaction (1) Fe ! Fe2 + + 2e
eFejFe2 + ¼
0:440 +

0:059 log ðaFe2 +Þ 2

Reaction (2) Fe + 2H2 O ! FeðOHÞ2 + 2H + + 2e
eFejFeðOHÞ2 ¼
0:047 + 0:059pH Reaction (3) +
Fe + 2H2 O ! HFeO
2 + 3H + 2e

eFejHFeO
2 ¼ 0:493


  3  0:059 0:059 pH + log aHFeO
2 2 2

Reaction (4) Fe + 2H2 O ! FeðOHÞ2 + 2H + pH ¼ 6:65
0:5 log ðaFe2 +Þ

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Corrosion engineering

Reaction (5) + FeðOHÞ2 ! HFeO
2 +H

  pH ¼ 14:30
log aHFeO
2 Reaction (6) Fe2 + + 3H2 O ! FeðOHÞ3 + 3H + + e
eFe2 + jFeðOHÞ3 ¼ 1:057
3  0:059pH
0:059log ðaFe2 +Þ Reaction (7) Fe2 + + 3H2 O ! FeðOHÞ3 + 3H + 1 pH ¼ 1:613
log ðaFe2 +Þ 3 Reaction (8)
HFeO
2 + H2 O ! FeðOHÞ3 + 2e

  eHFeO
2 jFeðOHÞ3 ¼
0:810
0:059log aHFeO
2 Reaction (9) FeðOHÞ2 + H2 O ! FeðOHÞ3 + H + + e
eFeðOHÞ2 jFeðOHÞ3 ¼ 0:271
0:059pH Iron does not corrode below the horizontal line at
0.44 V vs. SHE. The vertical lines in Reaction (4) represent a chemical reaction without the exchange of electrons. The pH at which this reaction occurs is calculated from the equilibrium constant. The sloping lines in Fig. 2.21a and b are constructed from the processes described in Reactions (2), (3), (6), (7), and (9). The stability of iron in this region increases as the solution pH increases.

2.11.5 Construction of Pourbaix diagram for nickel The equilibrium equations for a nickel system used to construct the boundaries of the areas presented in Fig. 2.22a and b are given in Table 2.5. The boundaries between areas represent the equilibrium between the stable chemical species and the chemical species that participate in the chemical reaction. The regions in Fig. 2.22a and b are labeled as immunity, corrosion, and passivation regions. Nickel possesses typical metallic properties with high electrical and thermal conductivities. It is resistant to attack by air or

Thermodynamics in the electrochemical reactions of corrosion

Fig. 2.21 (a and b) Pourbaix diagrams for iron.

water at ordinary temperatures and is used as a protective coating in the galvanizing industry. The metal dissolves in dilute mineral acids. It passivates only in nitric acid. At low nonoxidizing potentials, Ni is stable and immune to corrosion attack. The corrosion areas represent regions where the metal is susceptible to corrosion, and is transformed into stable cationic (Ni2+) or anionic species (HNiO
2 ). In the passive region, the Ni is coated with oxides NiO2 or Ni2O3. NiO2 is insoluble in water, but dissolves in acids at

69

Fig. 2.22 (a and b) Pourbaix diagram for nickel showing the immunity, corrosion, and passivation regions. Table 2.5 Various Equilibrium Reactions for the Ni System Reaction Relationship Between E and pH

(1) (2) (3) (4) (5) (6) (7) (8)

Ni ¼ Ni2++2e
Ni + 2H2O ¼ HNiO-2 + 3H++2e
Ni + H2O ¼ NiO + 2H++2e
2Ni+2 + 3H2O ¼ Ni2O3 + 6H+ + 2e
2NiO + H2O ¼ Ni2O3 + 2H+ + 2e
Ni2+ + 2H2O ¼ HNiO2
+ 3H+ Ni2+ + H2O ¼ NiO + 2H+ NiO + H2O ¼ HNiO2
+ H+ (a) 2H2O + 2e
¼ H2 + 2OH
(b) O2 + 2H2O + 4e
¼ 4OH


E ¼
0.250 + 0.0296log[Ni2+] E ¼ 0.648 + 0.0296log[HNiO
2 ]
0.0887pH E ¼ 0.110
0.0591pH E ¼ 1.753
0.0591log[Ni2+]
0.1774pH E ¼ 1.020
0.0591pH log[HNiO2
]/[Ni2+] ¼
30.40 + 3pH Log[Ni2+] ¼ 12.18
2pH log[HNiO2
] ¼
17.99 + pH E ¼
0.0591pH E ¼ 1.229
0.0591pH

Thermodynamics in the electrochemical reactions of corrosion

potentials higher than 0.4 V vs. SHE. NI2+ cation is stable at a low pH, while HNiO
2 anion is stable at high pH. NiO is stable at pH between 9 and 12.

2.12 CASE STUDIES 2.12.1 Activity coefficients The dissociation constant of a weak acid is defined as: K HA ¼

aH + aA
aHA

(2.70)

Equation (2.70) contains the ions activity aH + and aA
instead of the concentration of the ions C+ and C
[2,20]. Once the activity coefficients are defined, the dissociation constant remains the same and does not depend on the total concentration of the electrolyte. Table 2.6 summarizes the methods used to define the activities in electrolytes. The activity is defined as a product of the concentration and the variable defined as activity coefficient. Ionic activities of the individual ions are given by: a + ¼ n + f  ðmsalt =mo Þ

(2.71)

a
¼ n
f  ðmsalt =mo Þ

(2.72)

where n+ is the number of cations, f is the mean molal activity coefficient, and the ratio (msalt/mo) is the molal concentration. The activity coefficients cannot be determined from experimental data. Also, the activity of the single ionic species cannot be estimated using the activity equations. Using the equations, one can calculate only the product of the activities of all ions of a given electrolyte. The mean activity is a geometrical mean activity of the positive and negative ions in the electrolyte. If any electrolyte dissociates into A+ positive and B
negative ions, the mean activity is defined as:  +
1=ðA + + B
Þ a ¼ aA+ aB


(2.73)

For a binary electrolytes, the above expressions simplifies to: pffiffiffiffiffiffiffiffiffiffiffiffiffiffi a ¼ ða + a
Þ

(2.74)

Table 2.6 Methods Used to Define the Composition of the Electrolyte Unit Definition

Concentration

Activity

Molarity Molality Mole fraction

C m N

ac am aN

Mole/liter of solution Mole/kg of solvent Number of moles of solute/total number of moles in solution

71

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Corrosion engineering

The mean molal activity coefficients of any electrolyte that dissociates into A+ positive and B
negative ions are estimated using a similar equation:  +
1=ðA + + B
Þ (2.75) f  ¼ f +A aBf
or for binary electrolytes: f¼

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ðf + f
Þ

(2.76)

Problem 2.1 Using the mean molal activity coefficients listed in Table 2.7, calculate the activities of the following ions at 298 K in: (a) 0.01 molal aqueous solutions of HNO3 (b) 0.01 molal aqueous solutions of ZnCl2 (c) 0.1 molal aqueous solutions of MgCl2 Table 2.7 Mean Molal Activity Coefficients at 25  C 0.001 0.003 0.01 0.03 msalt/mo

0.1

0.3

1

3

HNO3 LiNO3 AgNO3 Cu(NO3)2 Al(NO3)3 LiOH NaOH HCl LiCl NH4Cl NaCl KCl MgCl2 CuCl2 ZnCl2 FeCl2 NiCl2 AlCl2 H2SO4 Li2SO4 Na2SO4 K2SO4 MgSO4 CuSO4 ZnSO4 NiSO4 Al2(SO4)3

0.79 0.79 0.73 0.51 0.20 0.76 0.77 0.80 0.79 0.77 0.78 0.77 0.53 0.51 0.52 0.52 0.52 0.34 0.27 0.47 0.45 0.44 0.15 0.15 0.15 0.15 0.04

0.74 0.74 0.61 0.44 0.15 0.67 0.71 0.76 0.74 0.69 0.71 0.69 0.48 0.43 0.43 0.45 0.46 0.30 0.18 0.36 0.32 0.32 0.09 0.08 0.08 0.08 0.02

0.72 0.74 0.43 0.46 0.19 0.55 0.68 0.81 0.80 0.60 0.66 0.60 0.57 0.42 0.34 0.51 0.54 0.54 0.13 0.28 0.20

0.91 0.97 0.25 0.90 1.02 0.49 0.78 1.32 1.34 0.56 0.71 0.57 2.32 0.52 0.29

0.05 0.04 0.04 0.04 0.02

0.05 0.04 0.04

0.97 0.97

0.97 0.96 0.97 0.97

0.94 0.94 0.94

0.9 0.9 0.9

0.85 0.85 0.84

0.91 0.94 0.94 0.94 0.94 0.94

0.90 0.90 0.90 0.90 0.90

0.83 0.85 0.84 0.84 0.83 0.85 0.85

0.82 0.81

0.72 0.71

0.62 0.62

0.83

0.61

0.54

0.40

0.89 0.89

0.82 0.81

0.71 0.71

0.59 0.59

0.74 0.70

0.63 0.54

0.44 0.39

0.25 0.24

10

2.44 0.11

3.23 10.40 9.40

0.90

1.69 0.14 0.29 0.14 0.56

Thermodynamics in the electrochemical reactions of corrosion

Solution: (a) HNO3 >H + + NO
3 a + ¼ n + f  ðmsalt =mo Þ a
¼ n
f  ðmsalt =mo Þ aH + ¼ 1  0:9  0:01 ¼ 0:009 aNO
3 ¼ 1  0:9  0:01 ¼ 0:009 (b) ZnCl2 >Zn2 + + 2Cl
aZn2 + ¼ 1  0:71  0:01 ¼ 0:0071 aCl
¼ 2  0:71  0:01 ¼ 0:0142 (c) MgCl2 >Mg2 + + 2Cl
aMg ¼ 1  0:53  0:1 ¼ 0:053 aCl
¼ 2  0:53  0:1 ¼ 0:106

2.12.2 Evaluation of theoretical tendency of metals to corrode

Problem 2.2 Using the free-energy data given in Table 2.8, calculate the standard equilibrium potentials of: (a) Pb2+/Pb (b) Zn2+/Zn (c) Ni+2/Ni Solution: (a) Pb2 + + 2e
¼ Pb X ΔGo ¼ ni μi

Products




X

ni μi

Reactants

ΔGo ¼ μPb
μPb2 + ΔGo ¼ 0
ð
24:3Þ ¼ 24:3kJ=mol ΔGo ¼
nFE o ΔGo 24:3  1000 ¼
¼
0:126V vs: SHE eoPb2 + jPb ¼
nF 2  96485

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Corrosion engineering

Table 2.8 Standard Chemical Potentials (kJ/mol) of Ions in Aqueous Solution at 25  C Relative to the Hydrogen Ion Cation mm Anion mm

Ag+ Al3+ Au3+ Ca2+ Cd2+ Cr2+ Cr3+ Cu+ Cu2+ Fe2+ Fe3+ Hg(I) as Hg2+ 2 Mg2+ NH+4 Na+ Ni2+ Pb2+ Pb4+ Pt2+ Sn2+ Sn4+ Ti2+ Zn2+

+77.1
483.1 + 410.8 + 555.1
77.6
164.6
205.0 + 50.4 + 66.6
84.9
10.6 +162.5
450.9
79.3
261.8
48.2
24.3
824.1 +231.0
26.3 + 2.9
157.0
147.2

Br
Cl
F
I
OH
S2
HS
CN
CO2
3
ClO
4 MnO4
CrO4 NO
2 NO
3 PO3
4 SO2
4

(b) Zn2 + + 2e
! Zn ΔGo ¼ μZn
μZn2 + kJ mol ΔGo 147:2  1000 ¼
eoZn2 + jZn ¼
¼
0:763V vs: SHE nF 2  96485

ΔGo ¼ 0
ð
147:2Þ ¼ + 147:2

(c) Ni2 + + 2e
! Ni ΔGo ¼ μNi
μNi2 + kJ ΔGo ¼ 0
ð
48:2Þ ¼ 48:2 mol o ΔG 48:2  1000 eoNi2 + jNi ¼
¼
¼
0:250V vs: SHE nF 2  96485


102.8
131.1
274.8
51.6
157.2 +98.0 +12.3 +163.7
528.7
44.8
717.0
420.8
35.3
109.8
1008.0
736.6

Thermodynamics in the electrochemical reactions of corrosion

Problem 2.3 Calculate the standard equilibrium single potentials using Gibbs free-energy data given in Table 2.8 for: (a) Cu2+/Cu (b) Fe2+/Fe Solution: (a) Cu2 + + 2e
>Cu ΔGo ¼ μCu
μCu2 + ¼ 0
66:6 ¼
66:6kJ=mol ! ΔGo ¼
nFeo eo ¼
ΔGo =nF ¼

66:6  1000 ¼ 0:345V vs: SHE 2  96485

(b) Fe2 + + 2e
>Fe ΔGo ¼
nFeo ΔGo ¼ μFe
μFe2 + ¼ 0
ð
84:9Þ ¼ + 84:9kJ=mol eoFe2 + jFe ¼
ΔGo =nF ¼


84:9  1000 ¼
0:44V vs: SHE 2  96500

Problem 2.4 Calculate the half-cell potential of Ni in 0.1 M NiCl2 solution. The half-cell is represented as: Ni|Ni2+, Cl
(0.1 M). Solution: Ni2 + + 2e
! Ni eoNi2 + jNi ¼
0:250V vs: SHE   RT aNi 0:059 o ¼
0:250 + eNi2 jNi ¼ eNi2 + jNi
2:303 log log ðaNi2 +Þ aNi2 + 2F 2 eNi2 jNi ¼
0:250 +

0:059 log ð0:1MÞ ¼
0:280V vs: SHE 2

75

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Corrosion engineering

Problem 2.5 If one mole of tin is consumed in the corrosion cell Sn/Sn2+//Cu2+/Cu, calculate the change of the Gibbs free-energy, ΔG. Solution: Sn2 + + 2e
! Sn eoSn2 + jSn ¼
0:138V vs: SHE Cu2 + + 2e
! Cu eoCu2 + jCu ¼ 0:337V vs: SHE Tin will corrode when coupled with the copper. Eocell ¼ eoCu2 + jCu
eoSn2 + jSn ¼ 0:337 + 0:138 ¼ 0:475V vs: SHE The Gibbs free-energy change when one mole of tin is consumed is: ΔG ¼
nFEo ¼
2  96, 485  0:475 ¼
91:7kJ

Problem 2.6 Estimate the equilibrium constant for the reaction: 2Fe3 + + Zn2 + ! 2Fe2 + + Zn Solution: The half cell reactions are: Fe3 + + e
! Fe2 + eoFe3 + jFe2 + ¼ 0:771 V vs: SHE Zn2 + + 2e
! Zn eoZn2 + jZn ¼
0:762V vs: SHE Because ΔGo ¼
2:303RT ln K ¼
nFE ocell , nE ocell 0:059 The electrode potentials for the individual half-cell reactions are:   RT a 2+ eFe3 + jFe2 + ¼ 0:771
2:303 log Fe aFe3 + 2F   RT aZn log eZn2 + jZn ¼
0:762
2:303 aZn2 + 2F log K ¼

Because the equilibrium constant is a ratio between the activities of the products and reactants, it follows that:     RT aFe2 + RT aZn ¼
0:762
2:303 log log 0:771
2:303 aFe3 + aZn2 + 2F 2F   2 + 2 + a + aZn ð0:771 + 0:762Þ  2 ¼ ¼ 52 ¼ log ðK Þ log Fe aFe3 + + aZn 0:059 K ¼ 1052

Thermodynamics in the electrochemical reactions of corrosion

Problem 2.7 What is the emf of a cell constructed from a lead electrode in lead sulfate of pH ¼ 1 with activity of Pb2+ ¼ 0.01 and a hydrogen electrode? Solution: + Cell Notation: Pb|Pb2+, SO2
4 , H |H2 Cell Reactions (assumption): Pb ! Pb2 + + 2e
ðanodeÞ 2H + + 2e
! H2 ðcathodeÞ Pb + 2H + ! Pb2 + + H2 ðoverallÞ ! RT P H2 log eH + jH2 ¼ 0
2:303 2F ðaH +Þ2   RT a 2+ log Pb ePbjPb2 + ¼ 0:126
2:303 aPb 2F ! RT aPb2 + Ecell ¼ 0:126
2:303 log 2F ðaH +Þ2 ! 0:059 0:01 Ecell ¼ 0:126
log ¼ 0:126 V vs:SHE 2 ð0:1Þ2 The cell potential is positive, indicating that the reaction proceeds spontaneously. The lead will corrode, while the hydrogen electrode will serve as the cathode.

Problem 2.8

Determine whether tin is stable in 10
6 M Sn2+ acid solution of pH ¼ 2. Estimate (a) the Gibbs free-energy change and (b) the cell potential for the corrosion cell. The activity coefficients are assumed to be 1. The hydrogen pressure is 1 atm. Solution: Half-cell reactions: Sn + ! Sn2 + + 2e
ðanodeÞ 2H + + 2e
! H2 ðcathodeÞ Sn + 2HCl ! SnCl2 + H2 ðoverallÞ ! RT P H2 log eH + jH2 ¼ 0
2:303 2F ðaH +Þ2   RT aSn2 + log eSnjSn2 + ¼ 0:138
2:303 aSn 2F Ecell ¼ ea + ec

77

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Corrosion engineering

! RT PH2 aSn2 + Ecell ¼ 0 + 0:138
2:303 log 2F ðaH +Þ2 aSn 0:059 10
6 log Ecell ¼ 0:138
2 2 ð10
2 Þ

! ¼ 0:197V vs: SHE

The Gibbs free-energy is calculated by using the Eq. (2.45):   2    a + ΔG RT RT
eoMn +jM +
¼ Ecell ¼ eoH +jH2 + ln H ln ðaMn +Þ P H2 nF nF nF

(2.45)

or ΔGSn ¼
nFEcell ¼
2  96;500  0:197 ¼
38:021

kJ mol

Because Gibbs free-energy change is negative, tin dissolves at pH ¼ 2.

Problem 2.9

For the cell at 25  C, Cu|Cu2+ (a ¼ 1)//Fe2+|Fe (a ¼ 1) determine if the reaction will proceed spontaneously as written? Cell Reactions: Solution: Cu ! Cu2 + + 2e
Fe2 + + 2e
! Fe E ocell ¼ eoFe2 + jFe + eoCujCu2 + ¼
0:440
0:337 ¼
0:777V vs: SHE ΔGo ¼
nFEocell ¼
2  96; 485  ð
0:777Þ ¼ 150

kJ >0 mol

The reaction will not proceed spontaneously as written. The spontaneous reaction is: Cu2 + + Fe ! Cu + Fe2 +

Problem 2.10

Determine whether Fe is stable in 10
6 M aerated water solution of Fe2+ at a pH of 8. Estimate (a) the Gibbs free-energy change and (b) the cell potential of the corrosion cell. The activity coefficients are assumed to be 1. The hydrogen pressure is 1 atm.

Thermodynamics in the electrochemical reactions of corrosion

Solution: Fe ! Fe2 + + 2e
ðanodeÞ 1 O2 + H2 O + 2e
! 2OH
ðcathodeÞ 2 FeðsÞ + 1=2O2 ðgÞ + H2 OðlÞ ! FeðOHÞ2 ðaq:Þ ðoverallÞ ! RT ðaOH
Þ2 log eO2 jOH
¼ 0:401
2:303 PO 2 2F   RT a 2+ log Fe eFejFe2 + ¼ 0:440
2:303 aFe 2F ! RT ðaOH
Þ2 aFe2 + Ecell ¼ 0:401 + 0:440
2:303 log PO2 aFe 2F This simplifies to:   2 0:059 log 10
6 10
6 ¼ 1:372V vs: SHE 2 The Gibbs free-energy is calculated by using the Eq. (2.45)      ΔG RT aH + 2 RT
eoMn + jM + ¼ Ecell ¼ eoH + jH2 + ln ln ðaMn +Þ
PH2 nF nF nF kJ ΔGFejO2 ¼
nFE ¼
2  96; 485  1:372 ¼
264:8 mol Because the Gibbs free-energy is negative, the reaction will proceed spontaneously as written. Iron will dissolve in aerated solution at pH of 8. E cell ¼ 0:841


Problem 2.11

Estimate the theoretical tendency for zinc to corrode (emf) when immersed in 10
6 to 10
1 M ZnCl2 solution at pH of 3. The corrosion cell is described as: ZnðsÞ + 2HClðaqÞ ! ZnCl2 ðaqÞ + H2 ðgÞ Solution: The overall reaction can be written as: Zn + 2H + ! Zn2 + + H2 The Nernst equations for the anode, cathode, and overall reactions are as follows:   RT aZn2 + o 2 + ðanodeÞ log eZnjZn ¼ eZnjZn2 +
2:303 aZn 2F ! RT aH2 eH + jH2 ¼ eoH + jH2
2:303 log ðcathodeÞ 2F ðaH +Þ2

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Fig. 2.23 Plot of ZnCl2 concentrations vs. cell potential for the Zn corrosion cell.

! Ecell ¼ eH + jH2 + eZnjZn2 +

¼ eoH + jH2

+ eoZnjZn2 +

RT aH2 aZn2 +
2:303 log 2F ðaH +Þ2 aZn

ðoverallÞ

! 0:059 aZn2 + E cell ¼ 0 + 0:762
log 2 ðaH +Þ2 For pH 3, the above equation can be written as: 0:059 log ðaZn2 +Þ
0:059pH 2 By substituting the ZnCl2 concentrations at pH ¼ 3 in the above expression, the tendency of zinc to corrode in volts was calculated and presented in Fig. 2.23. The results indicate that the tendency of zinc to corrode increases with decreasing the concentration of zinc ions at the electrode interface. Ecell ¼ 0:762


Problem 2.12 Estimate the hydrogen pressure (fugacity) necessary to stop the corrosion of cobalt in 0.1 M Co2+ solution at pH of 1, 3, 5, and 7. Solution: To stop the corrosion process, the EMF of the cell should be zero or positive. The standard equilibrium potential for the reaction: Co ! Co2 + + 2e
is 0:277V vs: SHE: The Nernst equation for the reaction:

Thermodynamics in the electrochemical reactions of corrosion

Fig. 2.24 Dependence of fugacity on pH for the cobalt system.

Co + 2H + ! Co2 + + H2 is written as: aCo=Co2 + PH2 RT log
2:303 2F ½aH +2 ! 0:059 ½0:1  P H2 E cell ¼ 0:277
log ¼0 2 ½aH +2

Ecell ¼ eoCojCo2 +

!

+ eoH + jH2

P H2 ¼

10

0:2772 2 0:059 ðaH +Þ

0:1 The hydrogen pressure necessary to stop corrosion of Co is calculated by substituting appropriate pH values in the above equation and equating to zero. The plot of pH vs. hydrogen pressure (Fig. 2.24) indicates that below pH ¼ 3, the hydrogen pressure cannot stop cobalt from corroding. Thus, increasing hydrogen pressure is not a feasible solution to stop the corrosion of cobalt in acidic solutions.

Problem 2.13 Determine the tendency of zinc to corrode in 0.6 M ZnCl2 solution at pH between 0 and 5. Cell notation: Zn∣Zn2+, Cl
, H+∣H2∣Pt Cell reactions: Zn ! Zn2+ + 2e
(anode) 2H + + 2e
! H2 ðcathodeÞ Solution: Zinc is oxidized at the anode and the H+ is reduced at the cathode. The only terms that one should consider are those for the Zn2+and the H+ concentrations. The activities of

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Fig. 2.25 Dependence of cell potential on pH for the Zn system.

metallic Zn and H2 are assumed to be unity. Because Zn2+ is formed (product), it will appear in the numerator of the logarithmic term, and the H+ (reactant) will appear in the denominator. The problem requires changing the H+ concentration in line with the pH in order to calculate the cell potential at different pH values. The general Nernst equation for the overall reaction is: ! RT aZn2 + o o log Ecell ¼ eH + jH2 + eZnjZn2 +
2:303 2F ðaH +Þ2 ! 0:059 aZn2 + E cell ¼ 0 + 0:762
log 2 ðaH +Þ2 Ecell ¼ 0:762


0:059 log ð0:6Þ
0:059pH 2

E cell ¼ 0:769V vs: SHE ðfor pH ¼ 0Þ The plot of pH vs. the cell potential (Fig. 2.25) indicates that, for an increase of the pH of 1, there is a decrease in the cell potential of 0.059 mV.

Thermodynamics in the electrochemical reactions of corrosion

Problem 2.14 Calculate the theoretical tendency of nickel to corrode (in volts) with evolution of hydrogen when immersed in 0.02 M NiCl2, acidified to pH ¼ 6. Cell Notation : NijNi2 + , Cl
,H + jH2 jPt Cell Reactions : Ni ! Ni2 + + 2e
ðanodeÞ H2 ! 2H + + 2e
ðcathodeÞ Ni + 2H + ! Ni2 + + H2 ðoverallÞ Solution: The Nernst equation for the overall reaction can be written as:

!

RT PH2 aNi2 + log
2:303 E cell ¼ eH + jH2 + eNijNi2 + 2F ðaH +Þ2 aNi ! RT ðaH +Þ2 Ecell ¼ 0 + 0:250 + 2:303 log aNi2 + 2F ! 2 0:059 ð10
6 Þ E cell ¼ 0:250 + log 0:02 2 ¼ eoH + jH2

+ eoNijNi2 +

E cell ¼
0:05V vs: SHE The Gibbs free-energy is calculated by using the expression: ΔG ¼
nFE ΔG ¼
2  96; 485  ð
0:05Þ ¼ 9:65kJ=mol Nickel does not corrode at pH ¼ 6.

Problem 2.15 Calculate the driving emf for the corrosion cell and write the spontaneous reaction for the following cell: PtjjFe3 + ðactivity ¼ 0:1Þ,Fe2 + ðactivity ¼ 0:001Þ,Zn2 + ðactivity ¼ 0:01Þ jj Zn The iron redox reaction is assumed to be the cathode. The half-cell reactions and the overall reaction are: Zn ! Zn2 + + 2e
ðanodeÞ 2Fe3 + + 2e
! 2Fe2 + ðcathodeÞ Zn + 2Fe3 + ! Zn2 + + 2Fe2 + ðoverallÞ

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Solution: The Nernst equations for the anode, cathode, and overall reactions are as follows:   RT aZn2 + o ðanodeÞ log eZnjZn2 + ¼ eZnjZn2 +
2:303 aZn 2F ! RT ðaFe2 +Þ2 o log eFe3 + jFe2 + ¼ eFe3 + jFe2 +
2:303 ðcathodeÞ 2F ðaFe3 +Þ2 E cell ¼ eFe3 + jFe2 + + eZnjZn2 + ¼ eoFe3 + jFe2 +

+ eoZnjZn2 +

RT ðaFe2 +Þ2 aZn2 + log
2:303 2F ðaFe3 +Þ2

!

RT ð0:001Þ2 0:01 Ecell ¼ 0:762 + 0:771 + 2:303 log 2F 0:1

ðoverallÞ !

E cell ¼ 1:326V vs: SHE The Gibbs free-energy is calculated by using the expression: ΔG ¼
nFE cell Because ΔG is negative, the Fe cation will oxidize zinc to zinc ion by reducing itself to Fe+2. 3+

Problem 2.16 Calculate the theoretical tendency of cobalt to corrode (in volts) in deaerated water of pH ¼ 5, 6, 7, and 8. Assume corrosion products are hydrogen and Co(OH)2. The CoðOHÞ2 ¼ ½Co2 + ½OH
2 ¼ 1.6  10
17. solubility product: K sp Cell Notation : CojCo2 + , H + jH2 Cell Reactions: CoðOHÞ2 ! Co2 + + 2OH
 ðOHÞ2 K Co ¼ Co2 + ½OH
2 ¼ 1:6  10
17 sp  2 + 1:6  10
17 Co ¼ 2 ½10
pH  Co ! Co2 + + 2e
ðanodeÞ 2H + + 2e
! H2 ðcathodeÞ Co + 2H + ! Co2 + + H2 ðoverallÞ ! RT PH 2 log eH + jH2 ¼ 0
2:303 2F ðaH +Þ2

Thermodynamics in the electrochemical reactions of corrosion

Table 2.9 pH and Corresponding Potential of Cobalt System pH Potential (V) vs. SHE

5 6 7 8

0.132 0.014
0.104
0.222   RT a 2+ log Co aCo 2F ! RT aCo2 + log E cell ¼ 0:227
2:303 2F ðaH +Þ2

eCojCo2 + ¼ 0:227
2:303

(2.77)

Solution: The Co2+ concentration is estimated at different pH from the Ksp. Next, the potential is calculated using Eq. (2.77) and presented in Table 2.9. Cobalt is stable at pH values 7 and 8 and starts to corrode at a pH of 6, as indicated by the positive potential.

Problem 2.17 Tin is immersed in a solution of CuCl2 with activity of Cu2+ ¼ 0.2. Determine the concentration of Sn2+ at which the corrosion will stop. Solution: Sn ! Sn2 + + 2e
Cu2 + ! 2e
+ Cu Sn + Cu2 + ! Cu + Sn2 + Eocell ¼ eoSnjSn2 + + eoCu2 + jCu   0:059 a 2+ Ecell ¼ Eocell
log Sn aCu2 + 2 The reaction stops when the cell emf is zero.     0:059 a 2+ 2  0:475 a 2+ ¼0 Ecell ¼ Eocell
log Sn ¼ log Sn aCu2 + aCu2 + 2 0:059 0:95

aSn2 + ¼ 100:059  aCu2 + ¼ 2:53  1016 M The corrosion will stop when Sn2+ concentration reaches 2.53  1016 M at the electrode interface.

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Problem 2.18 (a) Calculate the pressure (fugacity) of hydrogen required to stop corrosion of nickel immersed in 0.05 M NiCl2, pH ¼ 2. (b) Compare the results for the fugacity to stop the corrosion of iron immersed in 0.05 M FeCl2 at a pH of 2. Solution: (a) Ni in NiCl2 at pH ¼ 2 Cell Notation Ni ! Ni2 + + 2e
ðanodeÞ 2H + + 2e
! H2 ðcathodeÞ Ni + 2H + ! Ni2 + + H2 ðoverallÞ ! RT PH 2 eH + jH2 ¼ 0
2:303 log 2F ðaH +Þ2   RT aNi2 + eNijNi2 + ¼ 0:250
2:303 log aNi 2F

! RT PH2 aNi2 + Ecell ¼ 0 + 0:250
2:303 log 2F ðaH +Þ2 aNi This simplifies to:

!

0:059 PH2 aNi2 + Ecell ¼ 0 ¼ 0:250 + log 2 ðaH +Þ2

0:059 0:05PH2 log ¼ 0:250
2 ðaH +Þ2 ! 0:05PH2

0:500 ¼ log 2 0:059 ð10
2 Þ  0:500=0:059 
2 2 10 ð10 Þ ¼ 5:965  105 atm PH 2 ¼ 0:05 (b) For FeCl2 at a pH of 2: Cell Notation: Fe ! Fe2 + + 2e
ðanodeÞ 2H + + 2e
! H2 ðcathodeÞ Fe + 2H + ! Fe2 + + H2 ðoverallÞ ! RT PH 2 log eH + jH2 ¼ 0
2:303 2F ðaH +Þ2   RT a 2+ eFejFe2 + ¼ 0:440
2:303 log Fe aFe 2F

!

Thermodynamics in the electrochemical reactions of corrosion

! RT PH2 aFe2 + log 2F ðaH +Þ2 aFe

E cell ¼ 0 + 0:440
2:303 This simplifies to:

!

!

0:059 PH2 aFe2 + Ecell ¼ 0 ¼ 0:440 + log 2 ðaH +Þ2

0:059 0:05PH2 log ¼ 0:440
2 2 ð10
2 Þ ! 0:05PH2

0:880 ¼ log 2 0:059 ð10
2 Þ  PH2 ¼

0:880 2 100:059 ð10
2 Þ

0:05

¼ 1:645  1012 atm:

The pressure to stop the Ni corrosion cell is much less than the pressure to stop the iron corrosion cell. Iron is more thermodynamically active with standard potential of
0.44 V vs. SHE when compared with nickel with standard electrode potential of eo ¼
0.250 V vs. SHE.

2.12.3 Hydrogen and oxygen electrodes

Problem 2.19 Plot the half-cell potential for a hydrogen electrode at pH 0-14, pressure of hydrogen of 1 atm, and temperatures of 25, 30, 40 and 50  C. Solution: For a hydrogen electrode, the reaction can be written as: 2H + + 2e
! H2 The Nernst equation for this reaction is: ! eH + jH2 ¼ eoH + jH2

RT PH 2 log
2:303 2F ðaH +Þ2

At 25  C, the Nernst equation for the reaction becomes: eH + jH2 ¼ 0
0:059pH By substituting the given temperature and pH values, the half-cell potential of the hydrogen electrode can be calculated. The results are presented in Table 2.10 and graphically shown in Fig. 2.26a and b.

87

Table 2.10 pH and Potential Relationship of the Hydrogen Electrode at Different Temperatures pH E (25 °C) E (30 °C) E (40 °C) E (50 °C)

1 2 3 4 5 6 7 8 9 10 11 12 13 14


0.059
0.118
0.177
0.237
0.296
0.355
0.414
0.473
0.532
0.591
0.650
0.710
0.769
0.828


0.060
0.120
0.180
0.240
0.301
0.361
0.421
0.481
0.541
0.601
0.661
0.721
0.782
0.842


0.062
0.124
0.186
0.248
0.311
0.373
0.435
0.497
0.559
0.621
0.683
0.745
0.807
0.869


0.064
0.128
0.192
0.256
0.320
0.385
0.449
0.513
0.577
0.641
0.705
0.769
0.833
0.897

Fig. 2.26 Plot of pH vs. cell potential for the hydrogen electrode. (a) pH ¼ 0-7 and (b) pH ¼ 8-14.

Thermodynamics in the electrochemical reactions of corrosion

Problem 2.20 The oxygen discharge electrode reactions at pH ¼ 0 and pH ¼ 14 are as follows: 2H2 O ! O2 + 4H + + 4e
ðpH ¼ 0Þ 4OH
! O2 + 2H2 + 4e
ðpH ¼ 14Þ For unit activity of H+, the standard potential for the first discharge reaction is eo1 ¼ 1.229 V vs. SHE. Calculate the standard potential for the oxygen electrode, eo2, at pH ¼ 14. Solution: The oxygen electrode reactions taking place at different pH values are as follows: 2H2 O ! O2 + 4H + + 4e
ðpH ¼ 0Þ 4OH
! O2 + 2H2 O + 4e
ðpH ¼ 14Þ The electrode potentials for the respective oxygen electrodes can be represented as: e1 ¼ eo + 0:059 log ðaH +Þ ðpH ¼ 0Þ e2 ¼ eo2
0:059 log ðaOH
Þ ðpH ¼ 14Þ Because both reactions represent the oxygen electrode: e2
e1 ¼ 0 ¼ eo2
eo1 + 0:059 log ðaOH
ÞðaH +Þ ðaH +ÞðaOH
Þ ¼ K w ¼ 10
14   eo2
eo1 + 0:059 log 10
14 ¼ 0 eo2
eo1 ¼ + 0:8288 eo1 ¼ eo2
0:8288 ¼ 0:401V eo1 ¼ 1:2298
0:8288 ¼ 0:401 V vs: SHE The electrode potential, eo, for the reaction 4OH
! O2 + 2H2O + 4e
is 0.401 V vs. SHE.

Problem 2.21 Plot the half-cell potential of the hydrogen electrode in a solution of pH 7 with partial pressures of hydrogen of 0.5, 1, 1.5, 2, 3, and 5 atm at 25  C. The cell notation is Pt|H2|H+ Solution: The H2/H+ standard potential is equal to zero. By substituting the hydrogen partial pressure values in the Nernst equation one can obtain the potential of a hydrogen electrode under the conditions described in the problem. The general Nernst equation for the half-cell electrode reaction is: ! RT ðPH2 Þ o log eH + jH2 ¼ eH + jH2
2:303 2F ðaH +Þ2

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Corrosion engineering

Fig. 2.27 Dependence of the hydrogen electrode potential on hydrogen pressure at pH 7.

Because under standard conditions, eoH + jH2 ¼ 0

!

RT PH 2 log eH + jH2 ¼ 0
2:303 2 2F ð10
7 Þ For the case of hydrogen partial pressure of 0.5 atm., the equation becomes:   0:059 0:5 + eH jH2 ¼ 0
log 2 10
14 eH + jH2 ¼
0:405 V vs: SHE Substituting the other hydrogen partial pressure values in the above equation, the respective half-cell potential values are obtained and shown in Fig. 2.27. The results indicate that by increasing the pressure from 0.5 to 5 atm., the hydrogen reference potential decreases by 30 mV at pH of 7.

EXERCISES E2.1. Calculate the half-cell potential of cadmium in 0.1 M CdCl2. E2.2. Calculate the theoretical tendency of tin to corrode (in volts) with the evolution of hydrogen when immersed in 0.01 M SnCl2 acidified to pH ¼ 2, 3, 4, and 5. E2.3. Plot the hydrogen pressure (fugacity) necessary to stop corrosion of nickel in 0.1 M Ni2+ solution at pH ¼ 1, 3, 5, and 7.

Thermodynamics in the electrochemical reactions of corrosion

E2.4. Plot the hydrogen pressure (fugacity) necessary to stop corrosion of tin in 0.1 M Sn2+ solution at pH ¼ 1, 3, 5, and 7. E2.5. Determine which electrode will corrode in a cell made up of iron and zinc electrodes when the cell is short circuited. The electrodes are immersed in a solution of Fe+2 and Zn+2 of equal activity. E2.6. A cell, constructed from tin (anode) and a hydrogen electrode (cathode), is immersed in 0.2 M SnCl2 solution. Estimate the cell potential as a function of pH (pH ¼ 1, 3, 5, and 7). E2.7. Calculate the theoretical tendency of zinc to corrode (in volts) with the evolution of hydrogen when immersed in 0.05 M ZnCl2 at pH ¼ 1 through 5. E2.8. Plot the emf of an electrode constructed of zinc (anode) and a hydrogen electrode (cathode) immersed in 0.6 M ZnCl2 at pH 0, 1, 2, 3, 4, and 5. E2.9. Calculate the concentration of Zn2+ ions required to stop zinc corrosion when Zn is immersed in a solution of FeCl2 with activity of Fe2+ ¼ 0.1 M. E2.10. (a) Calculate the cell potential of a concentration cell constructed from a zinc electrode in 0.2 M ZnSO4 and 0.6 M ZnSO4 solution. Neglect the liquid junction potential. (b) Write the spontaneous reaction of the cell and indicate which electrode is the anode. E2.11. If the concentration of H+ decreases from 0.5 to 10
6 M, estimate how much 2+ the oxidizing power of the (MnO
4 /Mn ) couple will be reduced. E2.12. Determine whether iron is stable in an aqueous solution at pH ¼ 3, 5, and 7. Plot the driving EMF and the Gibbs free-energy as a function of pH. Assume PH2 ¼ 1 atm. and [Fe2+] ¼ 10
6 M.

REFERENCES [1] H.H. Uhlig, R. Winston, Corrosion and Corrosion Control, third ed., John Wiley & Sons, New Jersey, 1985. [2] L.I. Antropov, Theoretical Electrochemistry, Translated from Russian by Artavaz BeknazarovMir Publishers, Moscow, 1972. [3] R.H. Perry, D. Green, Perry’s Chemical Engineers’ Handbook, seventh ed., McGraw-Hill, New York, 1997. [4] J.M. West, Basics Corrosion and Oxidation, second ed., Holsted Press: A Division of John Wiley & Sons, New York, 1986. [5] J.M. West, Electrodeposition and Corrosion Processes, D. Van Nostrand Co., New York, 1965 [6] D.R. Gaskell, Introduction to Metallurgical Thermodynamics, Taylor and Francis, United Kingdom, 1981. [7] J.M. Smith, H.C. Van Ness, M.M. Abbot, Introduction to Chemical Engineering. Thermodynamics, seventh ed., McGraw Hill, New York, 2005. [8] S.I. Sandler, Chemical and Engineering Thermodynamics, third ed., John Wiley & Sons, New York, 1999. [9] D.A. Jones, Principles and Prevention of Corrosion, second ed., Prentice Hall, New Jersey, 1996. [10] M.G. Fontana, Corrosion Engineering, McGraw Hill, New York, 1986.

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[11] L.L. Shrier, Corrosion Control, second ed., Newnes-Butterworths, Sevenoaks, Kent, England, 1976. [12] A.H. Bard, R. Parsons, J. Jordan, Standard Potentials in Aqueous Solutions, Marcel Dekker, New York, 1985. [13] D.J.G. Ives, G.J. Janz, Reference Electrodes, NACE International, Houston, 1996. [14] D.R. Lide, Handbook of Physics and Chemistry, CRC Press, New York, 1997. [15] J.O.M. Bockris, R.A. Fredlein, A Workbook of Electrochemistry, Plenum Press, New York, 1973. [16] H. Kaesche, Metallic Corrosion, NACE Publication. NACE International, Houston, 1985. [17] D.J.G. Ives, G.J. Janz, Reference Electrodes: Theory and Practice, Academic Press, New York, 1961. [18] M. Pourbaix, Atlas of Electrochemical Equilibria in Aqueous Solutions, NACE, Houston, 1974. [19] M. Pourbaix, Lectures on Electrochemical Corrosion, Plenum Press, New York, 1971. [20] J.O.M. Bockris, A.K.N. Reddy, Modern Electrochemistry, Plenum Press, New York, 1971.