Eh pH or Pourbaix Diagrams

1
Eh pH or Pourbaix Diagrams Eh-pH or Pourbaix
Diagrams are plots of Eh versus pH showing
regions or fields where dissolved species and
precipitates are stable. They can be used to
quickly determine the equilibrium stability
fields for aqueous species. The effective
overall boundaries of the diagram are determined
by the stability field for water. One boundary
is determined by the stability of water with
respect to reduction to H2 at 1 bar 2 e- 2
H2O (l) ------gt H2 (g, 1 bar) 2 OH-
(aq) Writing the usual expression for the Gibbs
free energy change DG DGo R T ln a H2
(g) a2 OH- (aq) / a2 H2O (l) We also have DG
- n F e where F, Faradays constant, is the
charge on a mole of electrons and is equal to
96,570 C, and n is the number of moles of
electrons transferred in the oxidation or
reduction. Using the fact that the activities
of molecular hydrogen at 1 bar and liquid water
can be set equal to 1 gives - n F e DGo
2.303 R T log a2 OH- (aq) or e - DGo / (n
F) - (2.303 R T / (n F) log a2 OH- (aq)
2

• At 25 oC
• 2.303 R T / F 2.303 (8.314 J/mol K) (298.15
  K) / (96,486.8 C)
• 0.05917 V
• Thus
• e - DGo / (n F) - ( 0.05917 V / n
  ) log a2 OH- (aq)
• - DGo / (2 F) - 2 ( 0.05917 V / 2 ) log a
  OH- (aq)
• - DGo / (2 F) - ( 0.05917 V ) log a OH-
  (aq)
• - DGo / (2 F) ( 0.05917 V ) pOH
• - DGo / (2 F) ( 0.05917 V ) ( 14.0 pH
  )
• DGo can be calculated from standard tabulated
  Gibbs free energies of formation at 298.15 K
• DGo 2 DGo m, f, OH- (aq) - 2 DGo m,
  f, H2O (l)
• 2 ( - 157.300 kJ ) - 2 ( - 237.2 kJ )
• 159.8 kJ
• e - DGo / (2 F) ( 0.05912 V ) (
  14.0 pH )
• - ( 159.8 103 J) / (2 (96,570 C) )
  0.8283 V
• - ( 0.05911 V ) pH
• 0 V - ( 0.05911 V ) pH

3
This equation can be plotted on an Eh-pH diagram
to give one of the stablility boundaries for
water
Below this line water is unstable with respect to
reductive decomposition to H2 (g) at 1 bar of
pressure. How would this line change, if the H2
(g) pressure were set at 10 bar or 0.1 bar?
4

• With this background the stability boundary for
  the oxidative decompostion of water to O2 (g) at
  1 bar is relatively easily calculated
• H2O (l) ------gt ½ O2 (g, 1 bar) 2 H (aq)
  2 e-
• Note for consistency in constructing the diagram
  this decomposition must be written as a
  reduction
• ½ O2 (g, 1 bar) 2 H (aq) 2 e- ------gt
  1 H2O (l)
• e - DGo / (n F) - ( 0.05911 V / n ) log a2
  H2O (l) / a O2 (g) a2H (aq)
• - DGo / (2 F) - ( 0.05911 V / 2 ) log
  a-2H (aq)
• - DGo / (2 F) - ( 0.05911 V ) pH
• Calculating DGo in this case gives
• DGo 1 DGo m, f, H2O (l) 1 (
  - 237.2 kJ )
• - 237.2 kJ
• gives
• e - DGo / (2 F) - ( 0.05917 V ) pH
• - (- 237.2 103 J / (2 (( 96,486.8 C
  )) - ( 0.05911 V ) pH
• 1.23 V - ( 0.05911 V ) pH

5
This equation can be plotted on an Eh-pH diagram
to give the other stablility boundary for water
Above this line water is unstable with respect to
oxidative decomposition to O2 (g) at 1 bar of
pressure.
6

• The regions within the stability field for water
  where Fe3 and Fe2 are stable can be determined
  by considering the reduction of iron (III)
  to iron (II)
• Fe3 (aq) ------gt Fe2 (aq) e
• DGo DGom, f, Fe2 - DGo m, f,
  Fe3
• ( - 78.87 kJ ) - ( - 4.6 kJ )
• - 74.27 kJ
• e - DGo / (n F) - ( 0.05911 V / n )
  log a Fe2 / a Fe3
• - ( -74.27 103 J / (1 (( 96,570 C ))
• - ( 0.05911 V / 1 ) log a Fe2 / a Fe3
• 0.769 V - ( 0.05911 V ) log a Fe2 / a
  Fe3
• To further develop this equation requires making
  a choice about the activities of Fe3 and Fe2.
  The usual choice is to take the activities of
  dissolved species as 10-6, although other choices
  can be made.
• e 0.769 V - ( 0.05911 V ) log
  10-6 / 10-6
• 0.769 V
• Notice that e is independent of pH, because the
  reduction we were considering did not involve, H
  (aq) or OH- (aq) and will plot as a straight line
  parallel to the pH axis on the Eh-pH diagram.

7
Note that the more oxidized species, in this case
Fe3, is stable at the higher Eh.
8

• Now consider the relative stability of Fe3 (aq)
  and FeO(OH) (s), the mineral goethite
• FeO(OH) (s) 3 H (aq) ------gt Fe3 (aq)
  2 H2O (l)
• Note that in this equilibrium no species is being
  oxidized or reduced.
• DGo DGom, f, Fe3 2 DGom, f, H2O
  (l) - DGo m, f, FeO(OH) (s)
• ( - 4.6 kJ ) 2 ( - 237.2 kJ ) - ( -
  488.57 kJ )
• 9.6 kJ
• Why was DGom, f, H not included in this
  calculation?
• (n 0 ) e - DGo / F - ( 0.05911 V ) log
  a Fe3 / a FeO(OH) (s)
• - ( 0.05911 V ) 3 pH
• 0 - ( 9.6 103 J ) / ( 96,570
  C )
• - ( 0.05911 V ) log 10-6 / 1
• - ( 0.05911 V ) 3 pH
• ( - 9.94 10-5 V ) - 6 (- 0.05911 V ) -
  ( 0.1773 V ) pH
• 0.255 V - ( 0.1773 V ) pH
• pH 1.44
• Notice that when the equilibrium did not involve
  and oxidation or reduction, pH is independent of
  e and will plot as a straight line parallel to
  the e axis on the Eh-pH diagram.

9
(No Transcript)
10

• Now consider the relative stability of Fe2 (aq)
  and FeO(OH) (s)
• FeO(OH) (s) 3 H (aq) e- ------gt Fe2
  (aq) 2 H2O (l)
• DGo DGom, f, Fe2 2 DGom, f, H2O
  (l) - DGo m, f, FeO(OH) (s)
• ( - 78.87 kJ ) 2 ( - 237.2 kJ ) - ( -
  488.57 kJ )
• - 64.7 kJ
• e - DGo / (n F) - ( 0.05911 V / n )
  log a Fe2
• - ( 0.05911 V ) 3 pH
• - ( - 64.7 103 J / (1 (( 96,570 C ))
• - ( 0.05911 V / 1 ) log 10-6
• - ( 0.05911 V ) 3 pH
• 0.670 V 0.355 V - ( 0.1773 V ) pH
• 1.025 V - ( 0.1773 V ) pH

11
Any oxidation or reduction equilibrium that
involves H (aq) or OH- (aq) will plot as a
sloped line on these Eh-pH diagrams.
12

• Now consider the relative stability of FeO(OH)
  (s) and Fe3O4 (s), magnetite
• 3 FeO(OH) (s) H (aq) e- ------gt Fe3O4
  (s) 2 H2O (l)
• DGo DGo m, f, Fe3O4 (s) 2 DGo m,
  f, H3O (l) - 3 DGo m, f, FeO(OH) (s)
• ( - 1015 kJ ) 2 ( - 237.2 kJ ) - 3 ( -
  488.57 kJ )
• - 24.13 kJ
• e - DGo / (n F) - ( 0.05911 V ) 1 pH
• - ( - 24.13 103 J / (1 (( 96,570 C ))
• - ( 0.05911 V ) 1 pH
• 0.250 V - ( 0.05911 V ) pH

13
(No Transcript)
14

• Now consider the relative stability of Fe2 (aq)
  and Fe3O4 (s), magnetite
• Fe3O4 (s) 8 H (aq) 2 e- ------gt 3 Fe2
  (aq) 4 H2O (l)
• DGo 3 DGom, f, Fe2 4 DGom, f,
  H2O (l) - DGo m, f, Fe3O4 (s)
• 3 ( - 78.87 kJ ) 4 ( - 237.2 kJ ) - ( -
  1015 kJ )
• - 170 kJ
• e - DGo / (n F) - ( 0.05911 V / n )
  log a3 Fe2
• - (( 0.05911 V ) 8 / 2 ) pH
• - ( - 170 103 J / (2 ( 96,570 C )))
• - 3 ( 0.05911 V / 2 ) log 10-6
• - (( 0.05911 V ) 8 / 2 ) pH
• 0.880 V 0.532 V - ( 0.1773 V ) pH
• 1.025 V - ( 0.2364 V ) pH

15
Note that Fe2 (aq) - Fe3O4 (s) line meets the
intersection of the FeO(OH) (s) - Fe3O4 (s) and
Fe2 (aq) - FeO(OH) (s) lines, as, of course, it
should. These expectations can be used to reduce
the effort required to construct these
diagrams. Based on the above diagram what iron
species and what iron equilibria would you expect
to dominate natural waters containing iron?
16
How does the Eh-pH diagram change if activities
of the aquesous ions involved in the various
equilibria are changed by a factor of 10 in
either direction from the 10-6 values that have
been used so far? Using the result for the Fe2
(aq) and Fe3O4 (s) equilibria previously derived
for aFe2 10-6 e 0.880 V - 3 ( 0.05911
V / 2 ) log 10-6 - ( 0.1773 V )
pH equations can be quickly derived for aFe2
10-5 e 0.880 V - 3 ( 0.05911 V / 2 ) log
10-5 - ( 0.1773 V ) pH 1.323 V - (
0.1773 V ) pH and for aFe2 10-7 e
0.880 V - 3 ( 0.05911 V / 2 ) log 10-7 -
( 0.1773 V ) pH 1.500 V - ( 0.1773 V )
pH The positions of the other lines of
equilibria can relatively quickly established
based on the intersections of the above lines
with lines that dont shift and the fact the
changing these activities does not affect the
slope of the lines.
17
Note that where the aqueous ionic species is in
the products of the equilibria used to derive
these lines, decreasing that ionic species
activity increases its stability field.
18

• Where does elemental iron occur in this Eh-pH
  diagram?
• Consider the reduction of Fe2 (aq) to Fe (s)
• Fe2 (aq) 2 e ------gt Fe (s)
• DGo DGom, f, Fe (s) - DGo m, f,
  Fe2
• ( 0 kJ ) - ( - 78.87 kJ )
• 78.87 kJ
• e - DGo / (n F) - ( 0.05911 V / n )
  log 1 / a Fe2
• - ( 78.87 103 J / (2 (( 96,570 C ))
• - ( 0.05911 V / 2 ) log 1 / a Fe2
• - 0.4084 V - ( 0.05911 V / 2 ) log 1 /
  10-6
• - 0.4084 V - 0.1773 V
• - 0.5857 V

19

• Also consider the reduction of magnetite to
  elemental iron
• Fe3O4 (s) 8 H (aq) 8 e- ------gt 3 Fe
  (s) 4 H2O (l)
• DGo 4 DGom, f, H2O (l) - DGo m, f,
  Fe3O4 (s)
• 4 ( - 237.2 kJ ) - ( - 1015 kJ )
• 66.2 kJ
• e - DGo / (n F - (( 0.05911 V ) 8 /
  8 ) pH
• - ( 66.2 103 J / (8 ( 96,570 C )))
• - ( 0.05911 V ) pH
• - 0.086 V - ( 0.05911 V ) pH

20
Plotting these lines on the Eh-pH diagram gives
Would you expect to find elemental iron in a wet
oxygen rich environment? Under what conditions
of Eh and pH is siderite, FeCO3 (s), stable? To
answer this question assume that PCO2 (g) is
10-3.47 bar, roughly the global average value for
the partial pressure of carbon dioxide.
21
The iron oxygen diagram that we have developed
is a strong function of the species considered
and would look differently, if other species were
taken into account, e.g. FeOH2 (aq), Fe(OH)2,
etc. For example, if hematite, Fe2O3 (s), had
been considered, it would occupy the entire
stability field now occupied by geothite, FeO(OH)
(s) and since hematite is thermodynamically more
stable, it would be the species represented on
the diagram. Geothite is a precursor to hematite
and kinetically it takes several months to
convert geothite to hematite and so the diagram
developed in these notes would apply to the short
time formation of iron precipitates. An Atlas
of Eh pH Diagrams, Intercomparison of
Thermodynamic Databases, Geological Survey of
Japan, Open File Report No. 419, National
Institute of Advanced Industrial Science and
Technology Research Center for Deep Geological
Environments Naoto TAKENO, May 2005 is available
on the web at http//www.gsj.jp/GDB/openfile/file
s/no0419/openfile419e.pdf Pages 101 to 103 of
this reference cover the iron oxygen
system. There are a number of commercial
software packages that will generate Eh pH
diagrams, notably STABCAL http//www.mtech.edu/hh
uang/predominance.htm developed by Hsin-Hsiung
Huang of the Metallurgical Engineering Department
at Montana Tech. These comments just point out
that these diagrams should be used with caution.
22
(No Transcript)