Electrochemistry MAE-295
Dr. Marc Madou, UCI, Winter 2012
Class VII Pourbaix Diagrams
Table of content
 Marcel Pourbaix
 Pourbaix Diagrams
Marcel Pourbaix
 Marcel Pourbaix provided the brilliant means to utilize
thermodynamics more effectively in corrosion science and
electrochemistry in general. This development resulted in four
important books that interpret his work: Thermodynamics of
Dilute Aqueous Solutions, Atlas of Electrochemical Equilibria in
Aqueous Solutions (solid-aqueous equilibria); Lectures on
Electrochemical Corrosion (a teaching text); and, in his last
years, Atlas of Chemical and Electrochemical Equilibria in the
Presence of a Gaseous Phase (solid-gaseous equilibria).

His outstanding work in thermodynamics provided one of the
main underpinnings of electrochemistry, especially in corrosion
science.
Marcel Pourbaix
b. 1904, Myshega, Russia
d. September 28, 1998, Uccle
(Brussels), Belgium
Marcel Pourbaix
 Marcel Pourbaix (1904-1998)
 Marcel Pourbaix was born in Russia, where his father, a Belgian engineer,
was working at the time.
 The significance of Marcel Pourbaix’s great achievement was pointed
out by Ulick R. Evans, widely recognized as the “father of corrosion
science,” in his foreword to Pourbaix’s Thermodynamics of Dilute Aqueous
Solutions: “During the last decade (the 1940s) Dr. Marcel Pourbaix of
Brussels has developed a graphical method, based on generalized
thermodynamical equations, for the solution of many different kinds of
scientific problems, involving numerous types of heterogeneous or
homogeneous reactions and equilibria... Some of these problems have
long been treated from the aspect of thermodynamics... The application
of thermodynamics to typical corrosion reactions is a much newer
development.”
For Mr. Zhang Zhongcheng
As a memory of his stay at Cebelcor in 1984/1985.
With all best wishes from
Marcel Pourbaix
April 26, 1985
Prof Pourbaix, his wife, and Zhang Zhongcheng, in 1985
Prof Pourbaix with his colleagues at Cebelcor in 1984
The E-pH diagram of copper-water system
Pourbaix Diagrams
 Through the use of thermodynamic theory (the
Nernst equation), so-called Pourbaix diagrams
can be constructed. These diagrams show the
thermodynamic stability of species as a function
of potential and pH. Although many basic
assumptions must be considered in their
derivation, such diagrams can provide valuable
information in the study of corrosion phenomena.
The diagram on the right represents a simplified
version of the Pourbaix diagram for the ironwater system at ambient temperature. For the
diagram shown, only anhydrous oxide species
were considered and not all of the possible
thermodynamic species are shown.
 How do we construct this diagram for water?
Pourbaix Diagrams
 Use Nernst Equation:
Oxidation
Faster
Reduction
Slower
Potential
Oxidation
Slower Reduction
E = E0 -
RT
concentration of products
ln 
nF
concentration of reac tan ts
Faster
pH
Rates equal
Pourbaix Diagrams
Besides the use of the Nernst equation the following
relations are used to construct the PourBaix diagrams
 
0
i
ln K eq (= Q*) =
RT lnK
E =
nF
eq
=
RT
EnF
RT
RT

 iln a i 
nF i
 
0
i
or also log K =
i
i
i
i
1,363
=
 ln a
i
i
(a i are products and a 'i are reactants). To derive the Nernst equation from this equation
i
 
i
i
nF
0
i
 
0
:
 
i
0
i
0.059 logK 0.059
0.059
=

 ilog a i  i


 ilog a i or also with E
n
n i
n  23,060
n
i
And finally E
E = E0 -
25 o
= Eo 
i
RT
nE  23,060
i

 iln a i and log K =
=
  ilog a i

nF i
2.303 1.987  298.1
2.303 1.987  298.1 i
i
nE
  ilog a i
0.059 i
To derive the Nernst equation in log terms
E 25o
:
0.059
 ilog a i this is the same expression as
n i
RT
concentration of products
ln 
nF
concentration of reac tan ts
For electrochemical reactions n  0 and for chemical reactions
n = 0.
1 Coulomb - Volt = 1 Joule = 0.239 calorie
1 Faraday - Volt = 96 500 Joule = 23.060 calories
 
i
0
i
0.059
log K = i
o 
n
n  23,060
:
Pourbaix Diagrams
Aqueous solutions cannot be at a lower potential than that
required to reduce water :
2H + + 2e - = H 2 (E 0  0)
 p

RT
H2


E = E0 l og 
+ ]2 
nF
[
 H

RT
reduced species
(also E = E 0 l og
nF
(oxidized species) (H + ) m
RT
RT
E = E0 l og p H 2 +
log [ H +]
nF
F
( pH = - log [H + ] and rH 2   l og p H 2 )
2H2O = O2 + 4H+ + 4eEquilibrium potential
falls as 2.0
pH increases
1.6
1.2
or
RT
pH = E = E 0 - 0.059 pH
F
at 1 atm hydrogen (hydrogen bubbles form) !
Aqueous solutions cannot be at a higher potential than that
required to oxidize water :
E = E0
+
0.4
H2O is stable
0.0
2H+ + 2e- = H2
Equilibrium
potential falls as
pH increases
-0.4
-0.8
+ 4e  2H 2O (E  1.229)
[H + ]4 p 
RT
O2

+
l og 
2 

4F
[ H 2 O ] 
-
Potential
0.8
E = E0 -
O 2 + 4H
O2 is stable
0
taking water activity as unity
E = 1.229 + 0.0148 l og p O 2 - 0.059 pH
H2 is stable
-1.2
-1.6
0
7
14
Pourbaix Diagrams
For the general reaction :
 We will consider Cu in an aqueous
aA + bB + cH 2O + mH + + ne = 0 we can write that logK - mpH =
solution as the next exercise: five
different reactions are involved.
nE
(A) a
 log
0.059
(B) b
proton number  m and electron number = n
0.059
0.059
(A) a
(A) a
mpH +
log
with n = 0 logK - mpH =  log
b
n
n
(B)
(B) b
a
1 
(A) 
or pH = logK + log

m 
(B) b 
or E  E 0 
1. Cu 2+  2H 2O  CuO 2 H - + 3H +
 
0
i
log K =
pH =
i
i
=
1, 363
15, 912 - 2  56, 560 + 60, 960
 26.6
1, 363
 
Cu 2+
1 
(Cu 2+ )  1

(26.6

log
)
logK + log

m 
(CuO 2 H - )  3
CuO 2 H -
Cu 


2+
Every time the ratio

CuO 2 H -

increases by a factor of 10, the pH decreases with
At equal concentrations pH = 
1
(26.6)  8.9
3
2. CuO 2 H -  H +  CuO 22
 
i
log K =
i
1, 363
0
i
CuO H 
CuO 
-
 13.2 and pH = -(logK + log
2
22
The pH changes with one unit per decade change in of ratio of reaction partners.
At equal concentrations: pH = 13.2
7

1
of a pH unit.
3
Pourbaix Diagrams
3. Cu 2+  Cu + + e = 0
 
 
Cu 2+
0.059
E = E0 
log
. The potential increases with 0.059 V everytime the ratio of
1
Cu +
Cu 
Cu 
2+
+
increases with a factor of 10. E is independent of the pH.
4. CuO 2 H - + 3H +  e  Cu + + 2H 2O or also CuO 2 H - - Cu + - 2H 2O + 3H +  e = 0


CuO 2 H 0.059
0.059
E = E0 
 mpH +
log
. E will decrease with 0.177 V everytime the pH increases with 1 unit.
n
n
Cu +
At equal concentrations : E = E 0 
 
0.059
 mpH = 1.74 - 0.177pH. At constant pH E increases with 0.059 V everytime
n
with a factor of 10.
5. CuO 2
2-
- Cu
+

CuO 2 20.059
0.059
- 2H 2O + 4H  e = 0. E = E 0 
 4pH +
log
1
1
Cu +
+
 

E decreases 0.236 V for every pH unit increase and at equal concentration : E = E 0  0.236 pH
CuO  increases with a factor of 10 (at constant pH), E increases with 0.059V.
Cu 
2-
Every time
2
+
The bolder lines in the Pourbaix diagram represent pH and E values for equal concentrations.
The interesections determine four domains where Cu
2+
+
, CuO 2 H - , CuO 22 and Cu are dominant.
The finer lines are for different ratios of reactants/products [0.1 - 1 - 9; 91 - 99 - 99.9].
CuO H  increases
Cu 
-
2
+
Pourbaix Diagrams
Pourbaix Diagrams
 The diagram shown here shows how the
potentials for reduction and oxidation of water
vary with pH for natural waters. These are the
inner two lines that slope downward from low
pH to high pH. Note that the pH scale only runs
from 2-10 (we are talking here about natural
waters). For both oxidation and reduction of
water, an additional line is shown that lies 0.6V
above (for oxidation of water) or below (for
reduction) the theoretical E. This pair of lines
represents the potentials including an
approximation for the overvoltage. Lastly, there
is a pair of vertical lines at pH=4 and 9. These
are reflective of the fact that most natural
waters have a pH somewhere between these
limits. .
2008
MAE 217-Professor Marc J. Madou
Pourbaix Diagrams
 A Pourbaix diagram is an attempt to overlay the redox
and acid-base chemistry of an element onto the water
stability diagram. The data that are required are redox
potentials and equilibrium constants (e.g. solubility
products). On the right is the Pourbaix diagram for
iron. Below that is the same diagram showing only
those species stable between the water limits.
2008
MAE 217-Professor Marc J. Madou
Pourbaix Diagrams
 Equilibrium Reactions of
iron in Water

1. 2 e- + 2H+ = H2

14.
FeOH+ + H2O = Fe(OH)2(sln) + H+

2. 4 e- + O2 + 4H+ = 2H2O

15.
Fe(OH)2(sln) + H2O = Fe(OH)3- + H+

3. 2 e- + Fe(OH)2 + 2H+ = Fe + 2H2O
16.
Fe3+ + H2O = FeOH2+ + H+

4. 2 e- + Fe2+ = Fe


5. 2 e- + Fe(OH)3- + 3H+ = Fe + 3H2O

17.
FeOH2+ + H2O = Fe(OH)2+ + H+

6. e- + Fe(OH)3 + H+ = Fe(OH)2 + H2O

18.
Fe(OH)2+ + H2O = Fe(OH)3(sln) + H+

7. e- + Fe(OH)3 + 3H+ = Fe2+ + 3H2O

19.
FeOH2+ + H+ = Fe2+ + H2O

8. Fe(OH)3- + H+ = Fe(OH)2 + H2O

20.
e- + Fe(OH)2+ + 2H+ = Fe2+ + 2H2O

9. e- + Fe(OH)3 = Fe(OH)310. Fe3+ + 3H2O = Fe(OH)3 + 3H+

21.


11. Fe2+ + 2H2O = Fe(OH)2 + 2H+

22.
e- + Fe(OH)3(sln) + 2H+ = FeOH+ + 2H2O

12. e- + Fe3+ = Fe2+

23.
e- + Fe(OH)3(sln) + 3H+ = Fe2+ + 3H2O

13. Fe2+ + H2O = FeOH+ + H+
MAE 217-Professor Marc J. Madou
e- + Fe(OH)3(sln) + H+ = Fe(OH)2(sln) + H2O
2008
Pourbaix Diagrams
 Some limitations of Pourbaix diagrams include:
 No information on corrosion kinetics is provided by these




thermodynamically derived diagrams.
The diagrams are derived for specific temperature and pressure
conditions.
The diagrams are derived for selected concentrations of ionic species
(10-6 M for the above diagram).
Most diagrams consider pure substances only - for example the
above diagram applies to pure water and pure iron only. Additional
computations must be made if other species are involved.
In areas where a Pourbaix diagram shows oxides to be
thermodynamically stable, these oxides are not necessarily of a
protective (passivating) nature.
2008
MAE 217-Professor Marc J. Madou
Pourbaix Diagrams
MAE 217-Professor Marc J. Madou
2008