1. REDOX CLASSIFICATION OF NATURAL WATERS
Oxic waters - waters that contain measurable dissolved oxygen.
Suboxic waters - waters that lack measurable oxygen or sulfide, but do contain significant dissolved iron (> ~0.1 mg L-1).
Anoxic waters - waters that contain both dissolved iron and sulfide.
Barcelona and Holm (1991) presented the classification above for natural waters with respect to Eh.

2. DEFINITION OF Eh Eh - the potential of a solution relative to the SHE.
Both pe and Eh measure essentially the same thing. They may be converted via the relationship:
Where  = kJ volt-1 eq-1 (Faraday’s constant).
At 25°C, this becomes or
As mentioned before, Eh is the potential of a solution relative to the SHE. This slide shows that there is a fairly simple relationship between pe and Eh. The symbol “Eh” comes from the fact that “E” is the normal symbol for a potential (or electromotive force), and the lower case “h” reminds us that the reference electrode is the SHE.
Eh and pe measure the same thing. High values of Eh or pe correspond to oxidizing conditions, and low values of Eh or pe correspond to reducing conditions.

3. Eh – Measurement and meaning
Eh is the driving force for a redox reaction
No exposed live wires in natural systems (usually…)  where does Eh come from?
From Nernst  redox couples exist at some Eh (Fe2+/Fe3+=1, Eh = +0.77V)
When two redox species (like Fe2+ and O2) come together, they should react towards equilibrium
Total Eh of a solution is measure of that equilibrium

4. FIELD APPARATUS FOR Eh MEASUREMENTS
To have any chance at getting reliable Eh measurements, certain protocols must be followed. The above slide shows a suggested procedure for the measurement of Eh in groundwater. The flow cell permits measurement of the Eh of the groundwater sample without exposure of the solution to atmospheric oxygen (which would probably increase Eh). The apparatus shown above also permits the reference solution (Zobell’s solution) to thermally equilibrate to the temperature of the groundwater. When measuring the Eh of a water already in contact with the atmosphere (e.g., stream or near-surface lake water), it is not necessary to shield the solution from the atmosphere, but it is necessary to equilibrate the Zobell’s solution to the temperature of the water sample. The above apparatus is also useful for accurate measurement of pH, which would also be affected by the introduction or loss of CO2.
Also, to get accurate Eh-pH measurements, it is necessary to purge thoroughly the well to remove any atmospheric oxygen and insure that virgin ground water reaches the flow cell. Eh (or pH) is monitored continually until a reasonably constant value is obtained.
Note that, in the field, use of the SHE as a reference electrode is not very convenient. One would have to lug around a cylinder of H2 gas and a bottle of acid to prepare the SHE. Thus, secondary reference electrodes such as Ag/AgCl or saturated calomel (SCE) electrodes are employed. The SCE consists of mercury in HgCl2 solution. The Eh readings vs. these reference electrodes must then be corrected to the SHE scale.

5. PROBLEMS WITH Eh MEASUREMENTS
Natural waters contain many redox couples NOT at equilibrium; it is not always clear to which couple (if any) the Eh electrode is responding.
Eh values calculated from redox couples often do not correlate with each other or directly measured Eh values.
Eh can change during sampling and measurement if caution is not exercised.
Electrode material (Pt usually used, others also used)
Many species are not electroactive (do NOT react at electrode)
Many species of O, N, C, As, Se, and S are not electroactive at Pt
electrode can become poisoned by sulfide, etc.
Examples of redox pairs to which the platinum Eh electrode does not respond are: O2-H2O, SO42--H2S0, CO2-CH4, NO3--N2, N2-NH4+, and nearly all reactions involving solid phases.
It is also quite common to have mixed potentials in natural waters. These are potentials that result from a combination of parts of two different redox systems. For example, in a solution containing both Fe2+ and O2(aq), the following reactions may take place:
Fe2+  Fe3+ + e-
¼O2 + e- + H+  ½H2O
These two reactions may not be in equilibrium, but they may nevertheless fix the potential measured by the platinum electrode at some value. The only problem is that this value may have no meaning for any individual redox pair.

6. Figure 5-6 from Kehew (2001). Plot of Eh values computed from the Nernst equation vs. field-measured Eh values.
This diagram comes from an article by Lindberg and Runnells (1984). In this paper, they presented a comparison of Eh measured using a platinum electrode and Eh calculated from various redox couples using the Nernst equation. The symbols correspond to the following redox couples: Fe3+/Fe2+ - diamonds; O2(aq)/H2O - open triangles down; HS-/SO42- - open circles; HS-/S(rhombic) - open squares; NO2-/NO3- - solid squares; NH4+/NO3- - solid triangles down; NH4+/NO2- - open triangles up; CH4(aq)/HCO3- - plus signs; NH4+/N2(aq) - crosses; Fe2+/Fe(OH)3(s) - solid circles.
The dashed line represents a perfect correlation between measured and calculated Eh. It is clear that there is little correlation between the values of Eh measured directly via the platinum electrode, and those calculated from the Nernst equation from redox pairs.
Lindberg and Runnells (1984) Science v. 225,

7. Other methods of determining the redox state of natural systems
For some, we can directly measure the redox couple (such as Fe2+ and Fe3+)
Techniques to directly measure redox SPECIES:
Amperometry (ion specific electrodes)
Voltammetry
Chromatography
Spectrophotometry/ colorimetry
EPR, NMR
Synchrotron based XANES, EXAFS, etc.
Ideally you would like to know what the distibution of all possible redox couples are

8. Free Energy and Electropotential
Talked about electropotential (aka emf, Eh)  driving force for e- transfer
How does this relate to driving force for any reaction defined by DGr ??
DGr = nDE or DG0r = nDE0
Where n is the # of e-’s in the rxn,  is Faraday’s constant (23.06 cal V-1), and E is electropotential (V)
pe for an electron transfer between a redox couple analagous to pK between conjugate acid-base pair

9. Electromotive Series
When we put two redox species together, they will react towards equilibrium, i.e., e- will move  which ones move electrons from others better is the electromotive series
Measurement of this is through the electropotential for half-reactions of any redox couple (like Fe2+ and Fe3+)
Because DGr = nDE, combining two half reactions in a certain way will yield either a + or – electropotential (additive, remember to switch sign when reversing a rxn)
-E  - DGr, therefore  spontaneous
In order of decreasing strength as a reducing agent  strong reducing agents are better e- donors

10. Reaction directions for 2 different redox couples brought together??
Biology’s view  upside down?
Reaction directions for 2 different redox couples brought together??
More negative potential  reductant // More positive potential  oxidant
Example – O2/H2O vs. Fe3+/Fe2+  O2 oxidizes Fe2+ is spontaneous!

11. Nernst Equation Consider the half reaction:
NO H+ + 8e-  NH4+ + 3H2O(l)
We can calculate the Eh if the activities of H+, NO3-, and NH4+ are known. The general Nernst equation is
The Nernst equation for this reaction at 25°C is
The Eh or pe of a natural water can be calculated if we know the activities of species involved in a half reaction. In the case illustrated, we will use the nitrate (NO3-)-ammonium(NH4+) redox couple to calculate Eh. First, we must write a correctly balanced half reaction involving these species. Next, we use an equation called the Nernst equation. This equation relates the ion activity product (IAP) for the half reaction and the standard electrode potential for the half-reaction (E0) to the Eh of the solution. The general form of the Nernst equation is given as the first equation above; this form can be applied to any half reaction. The second equation gives the Nernst equation specific to this reaction at 25°C. Note that, at 25°C, the collection of constants 2.303RT/ = In the Nernst equation, n refers to the number of electrons transferred.
WARNING: When using the Nernst equation, you need to be careful with regard to conventions. The forms of the Nernst equation and the equation relating E0 and Gr° used by Kehew (2001) and in my lecture notes are correct for reactions written as reductions (i.e., electrons on the left side of the half reaction). Different sign conventions apply if we write the reactions as oxidation reactions. Note that, the convention employed by Kehew (2001) is just the opposite of the convention employed by the textbooks used in my GEOL 423 and GEOL 478/578 classes. To avoid confusion and errors, when you are using the Nernst equation in this class, ALWAYS WRITE YOUR HALF-CELL REACTIONS AS REDUCTIONS WITH THE ELECTRONS ON THE LEFT SIDE OF THE HALF REACTION!!!!

12. First, we must make use of the relationship
Let’s assume that the concentrations of NO3- and NH4+ have been measured to be 10-5 M and 310-7 M, respectively, and pH = 5. What are the Eh and pe of this water?
First, we must make use of the relationship
For the reaction of interest
rG° = 3(-237.1) + (-79.4) - (-110.8)
= kJ mol-1
Let us now assume that we have measured the pH and the concentrations of NO3- and NH4+ in our natural water sample, and we obtained the values shown above. We can now plug these into the Nernst equation to get an estimate of the Eh of our water sample (assuming that the half reaction has attained equilibrium and is controlling the solution Eh). However, before we can do this, we must obtain the value of E0. For some simple half reaction, the standard electrode potential is available in reference tables in many chemical handbooks. However, in most cases we have to calculate E0 from Gr° using the first equation above, keeping in mind that Gf° = 0 for H+ and e-.

13. The Nernst equation now becomes
substituting the known concentrations (neglecting activity coefficients)
and
Now, with our calculated value of E0, and the given values of pH and concentrations of NH4+ and NO3-, we plug everything into the Nernst equation and obtain an estimate of Eh. Note that we have assumed activity coefficients are unity. The Eh estimate can readily be converted to a pe value using the equation previously introduced. As we will see, in natural waters, Eh values calculated from redox couples and the Nernst equation may be more accurate and more relevant than Eh values measured directly with a platinum electrode.

14. Stability Limits of Water
H2O  2 H+ + ½ O2(g) + 2e-
Using the Nernst Equation:
Must assign 1 value to plot in x-y space (PO2)
Then define a line in pH – Eh space

15. UPPER STABILITY LIMIT OF WATER (Eh-pH)
To determine the upper limit on an Eh-pH diagram, we start with the same reaction
1/2O2(g) + 2e- + 2H+  H2O
but now we employ the Nernst eq.
In the next three slides, we repeat the calculation of the stability limits for water, but this time in Eh-pH coordinates. There are two reasons for repeating the calculation in this way. The first is to show how pe-pH diagrams and Eh-pH diagrams relate to each other, and to show the slight differences in how they are calculated. The second reason is so that we can use a published Eh-pH diagram to show where different geological environments sit with respect to pH.
The reaction governing the upper stability limit for water on an Eh-pH diagram is exactly the same reaction that we used for the pe-pH diagram. The difference is that, instead of using the mass-action (equilibrium constant) expression, we use the Nernst equation. To employ the Nernst equation given the convention Kehew (2001) has adopted, we must right the reaction as a reduction reaction.
Once the appropriate Nernst equation is written, we can proceed to the next step. Note that, in employing the Nernst equation, the convention employed is that ae- = 1. This is a major difference compared to the pe-pH diagram, where ae- is not necessarily equal to 1. The pe = -log ae-, so if we set ae- = 1 we could not plot a pe-pH diagram, because all pe values would be zero. However, such a situation would make many students happy!

16. As for the pe-pH diagram, we assume that pO2 = 1 atm. This results in
This yields a line with slope of
We need to calculate E0 from the value of Gr° as shown above, and then rearrange the Nernst equation so that we have an equation of a straight line with Eh on the Y-axis and pH on the X-axis. We find that we still have to fix the value of the partial pressure of oxygen to plot the boundary, and so we choose 1 atm as for the pe-pH diagram.

17. LOWER STABILITY LIMIT OF WATER (Eh-pH)
Starting with
H+ + e-  1/2H2(g)
we write the Nernst equation
We set pH2 = 1 atm. Also, Gr° = 0, so E0 = 0. Thus, we have
Again, the lower limit of water solubility in Eh-pH space is governed by the same reaction as in pe-pH space. We repeat the same steps as before, except that for this reaction, E0 = 0, because all the reactants and products have free energies of formation that are zero by convention.

19. O2/H2O
C2HO

20. Redox titrations
Imagine an oxic water being reduced to become an anoxic water
We can change the Eh of a solution by adding reductant or oxidant just like we can change pH by adding an acid or base
Just as pK determined which conjugate acid-base pair would buffer pH, pe determines what redox pair will buffer Eh (and thus be reduced/oxidized themselves)

21. Making stability diagrams
For any reaction we wish to consider, we can write a mass action equation for that reaction
We make 2-axis diagrams to represent how several reactions change with respect to 2 variables (the axes)
Common examples: Eh-pH, PO2-pH, T-[x], [x]-[y], [x]/[y]-[z], etc

22. Construction of these diagrams
For selected reactions:
Fe H2O  FeOOH + e- + 3 H+
How would we describe this reaction on a 2-D diagram? What would we need to define or assume?

23. How about:
Fe H2O  FeOOH(ferrihydrite) + 3 H+
Ksp=[H+]3/[Fe3+]
log K=3 pH – log[Fe3+]
How would one put this on an Eh-pH diagram, could it go into any other type of diagram (what other factors affect this equilibrium description???)

24. Redox titrations
Imagine an oxic water being reduced to become an anoxic water
We can change the Eh of a solution by adding reductant or oxidant just like we can change pH by adding an acid or base
Just as pK determined which conjugate acid-base pair would buffer pH, pe determines what redox pair will buffer Eh (and thus be reduced/oxidized themselves)

25. Redox titration II
Let’s modify a bjerrum plot to reflect pe changes

26. Redox titrations in complex solutions
For redox couples not directly related, there is a ladder of changing activity
Couple with highest + potential reduced first, oxidized last
Thermodynamics drives this!!

27. The Redox ladder
H2O H2 O2
NO3- N2
MnO2
Mn2+
Fe(OH)3
Fe2+
SO42-
H2S
CO2
CH4
Oxic
Post - oxic
Sulfidic
Methanic
Aerobes
Dinitrofiers
Maganese reducers
Sulfate reducers
Methanogens
Iron reducers
The redox-couples are shown on each stair-step, where the
most energy is gained at the top step and the least at the bottom step. (Gibb’s free energy becomes more positive going down the steps)