1. Oxidation and Reduction
Lecture 9

2. Redox in Aqueous Solutions
Redox reactions occur over a wide range of conditions: from groundwaters to magma. They are approached differently. We begin with aqueous solutions.

3. Electrochemical Cells
A simple redox reaction would be:
We want to know ∆G of the reaction. Measuring energy of it in electrochemical cell might be good approach.
However, such a cell can only measure exchange of electrons (e.g., between Zn and Cu)
We really want to know are energies for individual redox reactions such as:

4. Hydrogen Scale Potential
We assign a potential of 0 for the reaction:
½H2(g) = Haq+ + e-
in practice one side has Pt electrode in H2 gas, the other acid with aH+ = 1.
Then for the reaction
The potential is assigned to
Potentials measured in this way are called hydrogen scale potentials, written EH and have units of volts.

5. Table 3.3 EH˚ and pe˚ for half-cell reactions

6. EH and ∆G
Electrochemical energy is a form of free energy. EH is related to ∆Gr by:
∆Gr = -zFEH
where F is the Faraday constant (96,485 coulombs) and converts volts to joules.
and ∆G˚ = -zFE˚
Values of E˚ available in compilations (e.g., Table 3.3)
Since
then
This is known as the Nernst Equation.

7. pe Consider again the reaction:
The equilibrium constant expression for this reaction is ?
In log form:
We define pe as: So

8. Standard State pe and Relation to EH
Continuing with the reaction
In an aqueous solution, the standard state activities are?
Therefore pe˚ = log K
More generally,
So for this reaction:
pe is related to EH as:

9. What pe is really telling us
We have defined pe as the negative log of the activity of the electron. So a high pe means a low activity and concentration of electrons in our system. A low concentration of electrons implies an oxidized system; a high concentration (and low pe) implies a reduced system.
Same is true of EH.
So these are parameters that tell us about the redox state of our system (just as pH tells us about acidity).

10. Speaking of pe and pH…
A commonly used diagram to illustrate chemical variation in aqueous solutions is the pe-pH diagram (or EH-pH)
Water only stable over limited range, so we start by setting boundaries.
½O2(g) + 2e- + 2H+ = H2O
In the standard state:
pe = pH
The is a line with intercept of and slope of -1.
Similarly:
H+ + e- = ½H2(g)
and pe = -pH

11. pe-pH Diagrams To construct the diagrams
Write a reaction relating species of interest.
Redox reactions should contain e-
pH dependent reactions should contain H+
Write the equilibrium constant expression.
Get in log form, solve for pe with equation of the form
pe = a + bpH
Find or calculate value of log K.

12. Drawing stability boundaries
Now consider:
For equal activities of the two species,
pe = log K
(horizontal line with intercept = K)
Next Fe3+–Fe(OH)2+:
Fe3+ + H2O = Fe(OH)2+ + H+
Use H+ rather than OH-!

13. Fe2+–Fe(OH)2+ Our reaction is: Equilibrium constant expression is:
In the form we want:
We can write it as as the sum of two reactions,
we sum
to yield
The log equilibrium constant of the net reaction is the sum of the equilibrium constants of the two.

14. Line 5 has a slope of -1 and an intercept of log K.
We can also use pe-pH diagrams to illustrate stability of solid phases in presence of solution. In this case, we must choose concentration.

15. More about pe-pH diagrams
pe-pH diagrams are a kind of stability or predominance diagram.
They differ from phase diagrams because lines indicate not phase boundaries, but equal concentrations.
There is only 1 phase in this this diagram – an aqueous solution.
Regions are regions of predominance.
The aqueous species continue to exist beyond their fields, but their concentrations drop off exponentially.

16. Environmental Interpretation of pe-pH

17. Redox in Magmas

18. Oxygen Fugacity
Igneous geochemists use oxygen fugacity ƒO2 to represent the redox state of the system. Hence, the oxidation of ferrous to ferric iron would be written as:
2FeO + O2(g) = Fe2O3
For example, oxidation of magnetite to hematite:
2Fe3O4+ ½O2(g) = 3Fe2O3
(Actually, there isn’t much O2 gas in magmas. Reaction more likely mediated by water and hydrogen).

19. Redox in Magmatic Systems
For magnetite-hematite
2Fe3O4+ ½O2(g) = 3Fe2O3
assuming the two are pure solids
At a temperature such as 1000K

20. Oxygen Fugacity Buffers
The log ƒO2 – T diagram is a phase diagram illustrating boundaries of phase stability. The two phases coexist only at the line.
Reactions such as magnetite-hematite (or iron-wüstite or fayalite-magnetite-quartz) are buffers.
For example, if we bleed O2 into a magma containing magnetite, the ƒO2 cannot rise above the line until all magnetite is converted to hematite (assuming equilibrium!)