Free Energy and Electropotential

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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?E
• Where n is the of e-s in the rxn, ? is
  Faradays 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

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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 DG0r -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

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Nernst Equation

• Consider the half reaction
• NO3- 10H 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 25C is

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• Lets 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)
• -679.9 kJ mol-1

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• The Nernst equation now becomes
• substituting the known concentrations (neglecting
  activity coefficients)
• and

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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/Fe31, 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

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FIELD APPARATUS FOR Eh MEASUREMENTS
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CALIBRATION OF ELECTRODES

• The indicator electrode is usually platinum.
• In practice, the SHE is not a convenient field
  reference electrode.
• More convenient reference electrodes include
  saturated calomel (SCE - mercury in mercurous
  chloride solution) or silver-silver chloride
  electrodes.
• A standard solution is employed to calibrate the
  electrode.
• Zobells solution - solution of potassium
  ferric-ferro cyanide of known Eh.

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CONVERTING ELECTRODE READING TO Eh

• Once a stable potential has been obtained, the
  reading can be converted to Eh using the equation
• Ehsys Eobs EhZobell - EhZobell-observed
• Ehsys the Eh of the water sample.
• Eobs the measured potential of the water sample
  relative to the reference electrode.
• EhZobell the theoretical Eh of the Zobell
  solution
• EhZobell 0.428 - 0.0022 (t - 25)
• EhZobell-observed the measured potential of the
  Zobell solution relative to the reference
  electrode.

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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
  electrode)
• Many species of O, N, C, As, Se, and S are not
  electroactive at Pt
• electrode can become poisoned by sulfide, etc.

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Figure 5-6 from Kehew (2001). Plot of Eh values
computed from the Nernst equation vs.
field-measured Eh values.
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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.

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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 (gt 0.1 mg L-1).
• Reducing waters (anoxic) - waters that contain
  both dissolved iron and sulfide.

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The Redox ladder
O2
Oxic
H2O
NO3-
N2
MnO2
Post - oxic
Mn2
Fe(OH)3
Fe2
SO42-
Sulfidic
H2S
CO2
CH4
H2O
Methanic
H2
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. (Gibbs free
energy becomes more positive going down the
steps)
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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)

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Redox titration II

• Lets modify a bjerrum plot to reflect pe changes

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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!!

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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

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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.

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• As for the pe-pH diagram, we assume that pO2 1
  atm. This results in
• This yields a line with slope of -0.0592.

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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

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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)

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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

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Construction of these diagrams

• For selected reactions
• Fe2 2 H2O ? FeOOH e- 3 H
• How would we describe this reaction on a 2-D
  diagram? What would we need to define or assume?

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• How about
• Fe3 2 H2O ? FeOOH(ferrihydrite) 3 H
• KspH3/Fe3
• log K3 pH logFe3
• 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???)

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Brief respite from redox

• To determine whether or not a water is saturated
  with an aluminosilicate such as K-feldspar, we
  could write a dissolution reaction such as
• KAlSi3O8 4H 4H2O ? K Al3 3H4SiO40
• We could then determine the equilibrium constant
• from Gibbs free energies of formation. The IAP
  could then be determined from a water analysis,
  and the saturation index calculated.

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INCONGRUENT DISSOLUTION

• Aluminosilicate minerals usually dissolve
  incongruently, e.g.,
• 2KAlSi3O8 2H 9H2O
• ? Al2Si2O5(OH)4 2K 4H4SiO40
• As a result of these factors, relations among
  solutions and aluminosilicate minerals are often
  depicted graphically on a type of mineral
  stability diagram called an activity diagram.

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ACTIVITY DIAGRAMS THE K2O-Al2O3-SiO2-H2O SYSTEM

• We will now calculate an activity diagram for the
  following phases gibbsite Al(OH)3, kaolinite
  Al2Si2O5(OH)4, pyrophyllite Al2Si4O10(OH)2,
  muscovite KAl3Si3O10(OH)2, and K-feldspar
  KAlSi3O8.
• The axes will be a K/a H vs. a H4SiO40.
• The diagram is divided up into fields where only
  one of the above phases is stable, separated by
  straight line boundaries.

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Activity diagram showing the stability
relationships among some minerals in the system
K2O-Al2O3-SiO2-H2O at 25C. The dashed lines
represent saturation with respect to quartz and
amorphous silica.
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Seeing this, what are the reactions these lines
represent?