POTENTIAL-pH DIAGRAMS' PAUL DELAHAY Louisiana State University, Baton Rouge, Louisiana
MARCEL POURBAIX Universith Libre de Bruxelles, Brussels, Belgium
PIERRE VAN RYSSELBERGHE University of Oregon, Eugene, Oregon
THE fundamental importance and the wide usefulness
Designating by J.,the electric potential on the electrode side of the interface, by J.,the electric potential on the solution side, by p the chemical potentials or partial molal free energies of reactants and products, and by F the faraday, the condition of electrochemical equilibrium for reaction (I) is
of the concept of standard electrode potential in the interpretation of reactions between oxidation-reduction systems hardly need to be emphasized to readers of THISJOURNAL. The tables giving the standard potentials a t pH 0 and 14 (1) give only an incomplete picture of the reactions in which these systems participate, for 1 (z~m f m r x r f mr.- - y p l ~ d- Z ~ R , O ) (11) a t least two reasons; first, it is difficult to build for one- IL. - IL, = self a mental picture of many of these potentials a t pH Separating the 1's into standard p'sand activity terms values different from 0 or 14, and second, some oxidawe get tion-reduction reactions cannot occur a t vH 0 or 14 but can occur a t intermediate pH values. A complete IL. - IL. = 1 (woox m r D n *4- np.- - yroncd- zrDtr,o) graphic representation of potential-pH relationship disRT In a"oama+ poses of these and other difficulties. nF av~,a'n,o As far as we have been able to ascertain. ~ O t e n t i a l - ~ H diagrams were first used by Clark (2) tirepresent the If lve subtract from this general expression the parelectrochemical equilibria of H+ ion with molecular HZ ticular value of the potential difference for the standard and of molecular 0% aith mater. Clark also used other hydrogen electrode (+, = 0 for 1 atmosphere and potential-pH diagrams and Michaelis (8) used them in 25OC., pO,+ = 0, p , having the same value since the his studies of organic Redox systems. The construction two metallic terminals are assumed identical) 15-e ohof uotential-DH diagrams for a number of elements t,ain the "~otential"of system (I): .. ( ~ e ,Cu, c~,-N)hasfirst been described by one of us - 22 ninn- LpaR'O - 0.0591:pH + (4). This construction is entirely based upon the use of E = '""" -. ,-. thermodynamic data. Charlot (5) makes an extensive 0.0591 azo. -- log - (IVJ use of these diaerams to exolain reactions occurring ben a%d tween some redox systems of importance in analytical ~~in volts. the ,,ms --~-~ - - ~ -.-. ~ ~ - in ~ ralorieR chemistry. In all our calculations i t mill be assumed that the acTheobject of the present paper is to give an outline tivity of water is constant and equal to that of pure of the fundamental theory of these diagrams, to explain mater. The activities of t,he solutes are products of in some detail the construction of a typical one, namely molalities with practical activity coefficients. The that of iron, and to point out some typica1,applications molality of water is thus always equal to 55.5 and its of. the diagrams in inorganic, analytical, and electro- nractical activitv coefficient is assumed eonal to one. ----. chemistry. This verv good anvroximatiou may. .. " , however. be insufficient in some cases where information of a high THERMODYNAMIC FVRMULILS order of accuracy might be desired. For many of the Oxidation-Reduction Reactions applications of these diagrams valuable qualitative inWe shall use as the general expression for an oxida- formation can be obtained by reading the activities as tion-reduction reaction-writing always the oxidized (varticularlv in the dilute ranees of conform on the left-hand side-the following: centratioris). 6other c&s the differences betveen (1) xOx+mH++ne-=uRed+rH.O . . molalities ind concentrations, ionic strength effects on activity coefficients, etc., may have to be taken into in which the net charge of y Red 'Ox must be account. The diagrams will nevertheless constitute in to that of m H+ ne-. all cases a convenient point of departure from which information of any desired degree of accuracy can be Paper presented the Division of Chemicd Education of the ~~~~i~~~chemicsl ~ ~at the ~118th ~ i ~ ~ t~ it ~ ~ obtained ~~~ ~t by l- suitable successive approximation. It is to ing in Chicago (September 1950). be noted that the well-known uncertainties about pH
+
-
-
~~I~
+
~.~
~
"
+
-
-
~~
~
~~
~
~
~
684
JOURNAL OF CHEMICAL EDUCATION
determinations, salt effects on pH values, etc., also affect the accuracy of the information obtainable from these diagrams. As a whole, we wish to state that our plan is not to attempt to reach the maximum possible accuracy, or even to mention all necessary refinements, but rather to present a certain body of available information in a novel integrated form which we believe to be a fruitful one for many diverse applications.
EVOLUTION OF OXYGEN
I
'
1
Examples of Application of Equation (IV)
+
(a) Equilibrium Fe+++ e- = Fe++: One finds in Latimer's tables (1) that pa,+++ = -2530 cal. and pop.++= -20,310 cal. a t 25%. We thus have
+
+
+
(b) Equilibrium Mn04- 8H+ 5e- = Mn++ 4Hz0: From the tables porn,,- = -100,600 cal., pox.++ = -48,600 cal., and p",,, = -56,690 cal. Hence
rimre 2.
Potentid-pH Diamsm for wstsr. Hyd.opn, and 01m.n
Example of Application of Equation VIII
+
+
For the equilibrium Fe (OH)% 2H+ = Fe++ 2Hz0 we 6nd (1) p0 = -115,660 cal., pox.++ = -20.310 cal.. uo,., = -56.690 cal. and hence
,
Reactions without Changes i n Oxidation Numbers Reactions of the form pA
+ m H + = qB + z H20
(v)
The three types of equilibrium represented on Figure in which the charge of pB-pA is equal to that of m H+ 1 are self-explanatory. The first and third cases corhave equilibrium constants respond to changes of oxidation numbers, the second case to constant oxidation numbers. The potentials are plotted as ordinates and the pH values as abscissas. As potentials move upward on the vertical axis they b e and, since pox+ = 0, come nobler, i.e., more positive when one considers them as differences from electrode to solution, more negative log K = PP'A - ~ P ' B - ZP'H~O ( V W in the opposite case (1). 2.3RT in which 2.3RT = 1363 cal. a t 25°C. THERMODYNAMIC'STABILITY OF WATER When A is a hydroxide and B the corresponding oosi- Equilibrium between Hydrogen Ion and Hydrogen Gas tive ion we have The reaction 2H+ 2 e = HZ corresponds to the equilibrium potential
+
(VIII)
I
h
E = -0.0591 pH - 0.0295 log PE,
I
XOx+ mH+ne-= y Red+3 H,O
Equilibrium State Independent of pH
.
Equilibrium Btate Independeat of Potential N-.
l
Equilibrium state Dependent on pH and Potential
in which PH, represents the gaseous hydroeen Dressure in eauilibrium with the dissolved hydroxen. his E-pH equation is represented by the straight line 1 in Figure 2. The slope of thisline is -0.0591. There me also, above and below line 1, oarallel lines corresoondine to oressure of lo-% and lo+%atiospher& ofhydrogen. of potential and pH above line 1 correspond to a predominance of HzO (oxidized form H+), while states of potential and DH below l i e 2 corresoond to a o r e dominance of H2 (reduce2 form). 'The
68s
DECEMBER. 1950
vertical distance from line 1to each one of these parallel lines is 0.0591 volt.
FeOt--
+ 8Hf + 3e-
+
Equilibrium between Oxygen and Water
Fe0,--
+ 5H+ + 3e-E == Fe(OH)s + HnO (12) 1.6 - 0.0985 pH + 0.0197 log ap.0,--
= hi++4Hz0 E = 1.7 - 0.157 pH
+ 0.0197 log
(11)
The reaction
+
+ 4e-
0, 4H+
=
2H20
corresponds to the equilibrium potential (1) E = 1.229 0.0591 pH 0.0148 log P*
--
+
which is represented by the straight line 2 in Figure 2. The positions of the parallel lines for pressures of 10-2 and 10+2atmospheres of oxygen show that the region above line 2 corresponds to the predominance of Oz, the region below to the predominance of H 2 0 which is therefore stable between lines 1 and 2. The vertical distance from line 2 to each one of the parallel lines is 0.0295 volt. Figure 2 is similar to one originally presented by Clark (8). A complete representation of the oxygen-water system should include lines corresponding to the reduction of O2to Hz02and of H,Oz to HzO. Ozone should also be considered. These additional aspects of the complete 0%-H20diagram will be examined elsewhere. POTENTIAL-pH DIAGRAM FOR IRON
The method which will now be outlined for the construction of the potential-pH diagram for iron is general for all diagrams of this type. The successive stages of the construction are represented in Figure 3. Only the lines corresponding to unit activities or to unit activity ratios have been drawn, except in the cases of lines 8, 9, and 10 for which the activity represented is lo-=. The limes corresponding to equations 11 and 12 below have not been drawn on account of the uncertainty of the thermodynamic information concerning the Fe0,-- ion. The reactions and corresponding equilibrium equations used in the construction of the diagram are as follows: Fe++
+ 2e-
=
Fe
E
=
-0.440
+ 2H+ = Fet+ + 2Hz0
Fe(OH)2
+ 0.0295 log ape++
(1)
log as,++ = 13.23 - 2 pH (2)
+ 3HC = Fet++ + 3Hs0 log a=.+++ = 4.62 3pH (4) E = -0.049 - 0.0591 Fe(OH)1 + 2HC + 2e- = Fe + 2H,O PH (5) E = 0.262 - 0.0591 Fe(OHh + H C + e- = Fe(0HX + H,O PH (6) Fe(OHh + 3H+ + e- = Fe++ + 3He0 (7) E = 1.044 - 0.177 pH - 0.0591 log HFeOp- + H + = Fe(OH), log aaa.G- = -18.30 + pH ( 8 )
Fe(OH),
ap.++
Fe(OH)#
+ e-
=
HFeOs-
+ EH,O= -0.839
(lo) - 0.0591 log a a ~ . a -
r i m - 3.
s u c w s sstages i~ in c o ~ t r u ~ t i oofnpotantid-pa ~ k g r a n r of iron
JOURNAL OF CHEMICAL EDUCATION APPLICATION TO INORGANIC CHEMISTRY
The iron diagram of Figure 4 explains, among other things, the following well-known facts: Metallic iron causes evolution of hydrogen from water, as is shown by the relative positions of line 1and of the line corresponding to the reaction 2H+ 2e- = Hz. Ferric hydroxide is much less soluble than ferrous hydroxide, as is shown by the position of lines 2 and 4. Freshly precipitated ferrous hydroxide is oxidized by oxygen, as is shown by line 6 and by the line corresponding to the reaction 0% 4H+ 4e- = 2H20. Many interesting facts can be deduced from the simple principle illustrated in Figure 5 which involves the superposition of the diagrams of two elements: The oxidant Oxl oxidizes the reductant Redn because the equilibrium line I is above line 11. Figure 6, for instance, explains why chlorine oxidizes water with evolution of oxygen while bromine requires an acid medium for the same reaction and why iodine practically does not oxidize water. Figure 6, which is very incomplete because it neglects all compounds of the types HC10, CIO-, etc., has been constructed on the basis of the following reactions and equations:
+
+
+
Below line 1 and on the right of line 2 the activity of the Fe++ ion is smaller than one. Above line 3 the ratio a,,*++/a,.++is greater than one, etc. In a complete diagram one should also take into account the ferrite ion FeOz- resulting from the ionization of Fe(OH)*in very alkaline media (see ( I ) , p. 214), the magnetic oxide Fe,04 and other mixed oxides (see (4), p. 85), the ferry1 ion FeO++ (see ( I ) , p. 208), and possibly other compounds. Figure 4 is a somewhat complete potential-pH diagram giving most of the essential aspects of the behavior of iron and of its ions and hydroxides in presence of water. The thick lines 1, 2,3, 4, 5, 6, and 7 represent equilibria between two solid phases (lines 5 and 6), equilibria between a solid and an ion a t activity one in solution (lines 1, 2, 4, and 7), and an equilibrium b e tween two ions in solution with an activit,y ratio equal to one (line 3). The thin lines parallel to 1, 2, and 7, as well as lines 8, 9, and 10 represent equilibria between a solid and ions at activity in solution. I t will be noted that lines 3,4, and 7, lines 2,6, and 7, and lines 1, 2, and 5 have common points of intersection. The two dotted lines represent the eouilihria between water and Hz and O2 already given in Figure 2. They are the limits of the domain of thermodynamic stability of water xith respect to H2 (lower line) and 0% (upper line) a t one atmosphere. I t should be pointed out thatthe intervalof activities 1 to includes practically the whole range of concentrations normally encountered in chemistry.
+ 2e- = E2CI= 1.358 + 0.0295 log PC,,- 0.0591 IogaciBr. + 2e- = 2BrE = 1.065 + 0.0295 log PB,,- 0.0591 log aerCI.
I2
+ 2e-
=
21E = 0.535
+ 0.0295 log PI, - 0.0591 log a,-
(13)
(14) (15)
and 0.
+ 4H+ + 4e-E == 2HsO 1.229 - 0.0591 pH + 0.0148 log Po,
01
r
0 Fisure 6.
2
4
6
8
10
I
12 14
Frwrnentary Potentid-pH Diamanr for Chlorine. Bromin. and lodin.
?
APPLICATION TO ANALYTICAL CHEMISTRY
The potential-pH diagrams lead to many intereshg consequences for redox titrations. We shall consider two typical examples. Titration of Ferrous Ion by DichromaJe
The reduction of CrnOi--(or Cr04-- ) to Cr+++occurs according to the following reactions and electrochemical equilibrium equations: Cr20r--
+ 14H+ + 6eE = 1.37
+ 7HzO
2Cr+++ 0.138 pH
=
-
(16)
a o.,o,-+ 0.00985 log +
DECEMBER, 1950 Cr207-
Cr04--
+ 8HtE =+ 1.14 6 e - = 2Cr(OH)a + H%O - 0.0788 pH + 0.00985 log +
+ 4Ht + 3 E
=
e = Cr0.2H.O 0.94 - 0.0788 pH
+
(17) ac,pr--
(19) 0.0197 log- ar.or-(Ic10.-
These equations have been used in the construction of Figure 7 in which the HCrOp- ion has been neglected because the corresponding equilibrium lines are very close to those of Cr*Or--. This potentiahpH diagram for the Cr(+6)/Cr(+3) system, when compared with the iron diagram of Figure 4, shows that the oxidation of Fe++ is possible and that, therefore, a titration method can be worked out.
O&dation of Ferrocyanide to Ferricyanide by Cr%07-and Oxidation of Cr (+S) to Cr(+6) by Ferricyanide The following reaction and equation have been added to Figure 7:
The corresponding acids have not been taken into account. One sees, on the basis of Figure 7, that in acid solution Cr,07-- oxidizes ferrocyanide while in basic solution Cr(+3) is oxidized to Cr(+6) by ferricyanide. We thus have a rational explanation for two well-established titration methods whose details are available in the literature (6). Many other such titrations can be based upon potential-pH diagrams which therefore appear as a most useful tool in this field.
Determination of Lead Pb++ by Anodic Oridation to PbO, Figure 8 is a fragmentary potential-pH diagram for lead based upon the following equations: Pb++ Pbi4
+ 2e-
+ 2e-
=
=
Pb
Pb++
+ 0.0295 log am** h' = 1.691 + 0.0295 log -
E
=
-0.126
apb+* a ~ b
Figure 7. superposition of Partial Chromium Diagram and of F m Femkyanide Equilibrium
systematic study of electrolytic oxidation and reduction. The first step in this study is the establishment of the conditions of electrochemical equilibrium. The experimental study, through polarization curves, shows then whether reversible or irreversible behavior prevails. The diagrams are thus an essential adjunct to the study of overvoltage. CONCLUSIONS
A number of features and advantages of the diagrams are the following: They give a clear and rational explanation of the properties of the various elements. They can be used by students who have not had any preparation in thermodynamics. Drawn or projected on a large scale they can be used with advantage in courses of inorganic and analytical chemistry. The svstematic studv of these diazrams shows the gaps in our thermodynamic and electrochemical data. For some elements, tungare practically sten for instance, no there dat,a F2
-
(21) (22)
Lines 22, 23, and 24 have been represented for activities 10-8 of Pb+' and Pb++ on account of the low solubility of PbOz. Figure 8 shows that Pb++ can be oxidized anodically to PbOz vhich is very insoluble even a t high acidities. The practical method of cleaning the electrode based upon the reduction of PbOz to P b f + by oxalic acid is also conveniently explained by this diagram. APPLICATION TO ELECTROCHEMISTRY
One of the most useful fields of application of the potential-pH diagrams is that of corrosion. One of us (M. P.) has insisted on the usefulness of the diagrams for corrosion studies and research in a number of publications (4). The diagrams also lend themselves to the
available. The diagrams lend them1.2 selves to the planning of research programs in a 08 variety of fields: dissolu0.4 tion of metals, equilibria betweenmetalsand oxides,etc. They also emphasize the contrast between reversible and irreversible conditions -0.4 and, as alreadv stated., thev. - 2 0 2 4 6 are essential a t least as rig, 8. F I . . ~ . po~t.,.-~ ~ t'd-pH n s m a m *- h a d points of departure in the study of overvoltage. As a whole the diagrams constitute the thermodynamic frame within which all these reactions can take place. LITERATURE CITED (1) LATIMER, W. M., "The Oxidation States of the Elements and Their Potentids in Aqueous Solutions," Prentice-Hall, PITew York, 1938.
JOURNAL OF CHEMICAL EDUCATION (2) CWLRK, W. M., "The Determination of Hydrogen Ion," 3rd edition. Williams and Wilkins. Baltimore. 1928. See p. 387. (3) MICAABLEL., "Oxidation-Reduction Potentials," Lippincotti Philadelphia, 1930. Seep. 89. (4) Pomrslux, M., "Thermodynttmique des Solutions Aqueuses DiluBes. ReprBsentation Graphique du Rdle du pH et du
Potentiel," Meinema, Delft, 1945. Also BBranger, Paris, 1948. English translation by J. N. AGAR,Arnold, London, 1949. (5) CBARMT, G., "ThBorie et MBthode Nouvelle d'Analyse Qualitative," 3rdedition: Masson, Paris, 1949. ( 6 ) M ~ L L E RM. . E.. '(Die Elektrometrische Massanalyse," 6th 1942. edition, ~ t e i n k b ~ fDresden, f,
