Eh-pH Diagrams
What Are These Things Again?
Eh–pH diagram: aka Pourbaix diagram, potential-pH diagram, electrochemical phase diagram
Invented in 1930’s by Marcel Pourbaix (Belgian)
Used in lots of places: extractive metallurgy, corrosion (their original purpose),
environmental engineering, geochemistry
Closely tied to aqueous thermodynamics
The Basics
x-axis is pH; usually 0–14, but sometimes
as low as –3, and sometimes up to 16
pH = –log [H+]; change of 1.0 pH unit
changes [H+] by factor of 10
y-axis is electrode potential relative to
SHE (range varies); positive is oxidizing condition, negative is reducing
Assumes constant temperature, aH2O = 1
Diagram is divided into predominance regions, where one phase prevails
Requires definition of predominance in terms of chemical potential
For solids, activity = 1; for gases, set a partial pressure; for solutions, set an
activity
The Basics
Two lines shown here are present on
nearly all Eh-pH diagrams
Line (a) is for 2 H+ + 2 e– = H2 (g)
Usually presumes pH2 = 1 atm
Since ΔG° = 0, applying Nernst equation,
E = 0 – 0.05915 pH
Result: E = 0 at pH = 0 (SHE), slope of
straight line = –0.05915
When conditions are below line, reduction reaction generates H2 (g); when
conditions are above line, H2 (g) oxidizes to H+
Line (b) is for 4 H+ + O2 + 4 e– = 2 H2O; E = 1.23 – 0.05915 pH
Above line, oxidizing conditions generate O2; below line, reduction reaction
generates H2O
Most hydrometallurgical processes operate between the lines
Add A Metal
Eh-pH diagram shows Cu–H2O system
Dotted lines represent water stability
region; solid lines represent equilibria between copper species
Two aqueous species, Cu2+ and CuO22Oxidation state of Cu as Cu0 is 0
Oxidation state of Cu as Cu2O is +1
Oxidation state of Cu in Cu2+, CuO,
and CuO22- is +2
Lower oxidation states are stable at bottom, higher oxidation states at top
Activity of solid compounds = 1 when predominant; varies for aqueous species
(1 in this case, could be as low as 10–6)
Predominance activity determined by purpose, value of metal
More on Metal – H2O Diagrams
Type of stable ion depends on pH
For CuO + 2 H+ = Cu2+ + H2O, low pH
drives reaction to right
Simple ions like Cu2+ are stable at low
pH
For CuO + H2O = 2 H+ + CuO22–, high
pH drives reaction to right
Oxyions like CuO22– are stable at high
pH
Solid oxides, hydroxides most stable in center of diagram
More on Metal – H2O Diagrams
Three kinds of lines separate copper
species in this diagram
First is vertical: CuO + 2 H+ = Cu2+ +
H2O; CuO + H2O = CuO22– + 2 H+
Reactions involve exchange of H+, but
no electrons (no oxidation/reduction); independent of E
Second type of line is horizontal:
Cu2+ + 2 e– = Cu
Reaction involves oxidation/reduction, but no H+; independent of pH
Third type of line is diagonal: Cu2O + 2 H+ + 2 e– = 2 Cu + H2O
Reaction involves both oxidation/reduction and H+ exchange, so line is a
function of E and pH
(No curved lines in most diagrams.)
Why Does This Matter? (Part I)
Diagram at bottom left is Cu–H2O system
Presence of stability region between lines for Cu and ions shows that Cu can be
produced hydrometallurgically
Diagram at bottom right is Au–H2O system
No stability region for gold ions between lines; can’t dissolve Au in aqueous
solutions (for now)
The Effect of Ion Activity
Diagram shows Co–H2O system
Tiny 0, –2, –4, –6 represent base-10
log of ion activity (Co2+, HCoO2–)
As required activity of ions decreases,
predominance area for ions grows
(sideways and vertically)
Easier to “produce” ions if desired
concentration isn’t as high
Easier to reduce ions to metal is concentration of ions is higher
The Effect of Temperature
Partial Eh-pH diagrams below show Cu–H2O system at 25° (left) and 100°C
(Use log aCu(2+) = 0 lines for low–temperature diagram)
Notice slight change in slope of diagonal lines
Cu2+ region shrinks (unusual), Cu2O region is smaller, CuO and Cu regions ↑
Water stability region also moves
Can use changes in temperature to
our advantage
Eh-pH Diagrams for Anions
Diagram shows S–H2O system at 25°C
H2S is dissolved in solution, not gas
Can do this for other anions as well
Matters because pure oxide minerals are
uncommon, and anions are used for
leaching, precipitation; need the right
one!
Why This Matters (Part II)
Diagrams below show Au–H2O and Au–CN–H2O diagrams at 25°C
Diagram at left shows why we can’t dissolve gold; diagram at right shows how
we can
(This is why cyanide is used)
Notice vertical line at bottom for H+ + CN– = HCN (g); impacts other lines
Also notice curvature of lines; reflects changing activity coefficients
Add An Anion And Another Metal
(Hope you’re taking notes!)
Diagram shows Cu–Fe–S–H2O system at 25°C
Requires setting activity for aqueous
Cu, Fe, and S species
CuFeS2 is chalcopyrite, main copper
mineral
Cu5FeS4 is bornite
FeS2 is pyrite; FeS is pyrrhotite
Notice separate predominance regions
for several species; impact of
changing predominant S species
Why This Matters (Part III)
Chalcopyrite contains copper ($3/lb)
and iron ($0.08/lb). How to
separate?
Could smelt, oxidize iron to slag; requires energy, flux, slag disposal
Why not leach?
Where on this diagram can I put Cu
into solution and leave Fe behind?
Limitations of Eh-pH Diagrams
• Doesn’t include impact of kinetics
• Presumes only one predominant species (sometimes activities of ions are
nearly equal)
• Depends on accurate thermodynamic data (not always available for complex
compounds)
For More Information…
• University of Montana Geology Department
http://www.umt.edu/geosciences/faculty/moore/G431/lectur7.htm
• University of Idaho Geology Department
http://www.sci.uidaho.edu/geol464_564/Powerpoint/Lecture_9a_468_568nc.pp
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