Individual Projects

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Individual Projects

• Now that you have seen the mine
• Friday Lab ? Individual meeting times to
  discuss/decide on your own project, what has to
  get done for it
• Project ? Incorporate field, lab, modeling
  components, any project may emphasize some
  combination

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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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Phase rule

• Remember the phase rule? This governs how many
  components and phases must be determined for a
  particular degree of freedom
• fc-p2
• On these stability diagrams, 1 degree is a point,
  2 degrees is a line ? to construct these, we
  generally are describing a line, therefore cp
  WHEN T and P are defined!

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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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Mineral dissolution/ precipitation
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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?
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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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Bjerrum plot showing the activities of inorganic
carbon species as a function of pH for a value of
total inorganic carbon of 10-3 mol L-1.
In most natural waters, bicarbonate is the
dominant carbonate species!
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Lets think about these stability diagrams in 3-D
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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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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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Environmental Electrochemistry

• Different kinds of electrochemical cells
• Electrodes 3 electrode systems and how they
  work
• ISE and pH electrodes

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Electrochemistry - electron transfer reactions

• 1) Chemical Reactions
• Fe2 MnO2 ? Mn2 FeOOH
• 2) Electrochemical cells - composed of oxidation
  and reduction half reactions
• a) Galvanic (Voltaic) cell - thermodynamically
  favorable or spontaneous (?G lt 0)
• e.g., batteries, pH and ion selective electrode
  (ISE) measurements
• b) Electrolytic cell - non-spontaneous or
  thermodynamically unfavorable reactions (?G gt 0)
  are made to occur with batteries (EAPPL E
  applied)
• e.g., electrolysis, electroplating, voltammetry

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Electrolytic Cell

• Forcing a redox reaction to go in a particular
  direction by APPLYING the energy required to go
  forward

APPLIED Potential!
Reaction would not normally go in water
Fe2 2e- ? Fe0
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Electrodes

• The parts of a cell that are the sites of anodic
  and cathodic reactions
• Working and counter electrodes - conductive
  materials where the redox reactions occur
• Most cells also use a reference electrode ?
  recall that all Energy is relative to a
  predetermined value, the reference electrode
  provides an anchor for the system
• The electrical measuring device measures a
  property of the electrodes in a solution

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Current - voltage curves for ideal electrodes
POLARIZATION
dashed lines show departure from ideal behavior
by real electrodes
A
B
C
current
Electrode potential
D
Ideal Polarized electrode (IPE electrode of
fixed I) i 0 over a wide range of V (A to B)
Ideal nonpolarized electrode (electrode of fixed
V reference electrodes). V 0 over a wide range
of I (C to D)
?i/ ?V 0
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• Direct current (EIR) in an electrochemical cell
• Current, I, is maintained by mass transport
• There is always some resistance of ions to
  movement at the boundary between two half cells
  so the cell has a resistance (R) liquid junction
  potentials arise from salt bridges!!
• at the electrode charge balance is the same BUT a
  charge imbalance in solution occurs due to the
  differing rates of movement of ions (ionic
  mobility) to each electrode e.g., H gt Na gt K
  H 7 X Na and 5 x Cl-
• USE a supporting electrolyte (e.g., KCl, Na2SO4,
  KNO3) to carry migration current in solution, use
  100 fold excess of this electrolyte!!
• Rate of ionic mobility of K Cl- (within 4
  only 1 mV junction potential)
• Thus, ECELL Eeq ECAT - EAN - IR
• IR is termed an overvoltage (electrolytic cell)
  or ohmic drop (galvanic cell)

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Overvoltage

• Excess applied potential required to drive a
  reaction forward
• ? E Eeq ? i.e. the extra push
• ECELL ECATHODE EANODE IR ?CATHODE
  ?ANODE

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Pathway of a general electrode reaction
Interface - electrode surface region
bulk
electrode
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Electroanalytical methods
bulk methods
Interfacial methods
dynamic methods i gt 0
Conductometry G1/R
Static methods i0
Conductometric titrations
Potentiometric titrations volume
potentiometry E
Coulometric titrations Qit
Electrogravimetry (wt)
Amperometric titrations volume
Electrogravimetry (wt)
Voltammetry If(E)
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Voltammetry (electrolytic cell)

• Apply voltage (EAPPL) and measure current (i).
  Because current is passed, POLARIZATION occurs.
• NEED
• Working electrode small, inert, polarizable
  (Hg, Pt, C, Au)
• Reference electrode - nonpolarizable (SCE,
  Ag/AgCl)
• Counter electrode - Pt wire
• a device to apply Voltage and measure i
  simultaneously
• Polarography specifically refers to the dropping
  mercury electrode (DME) as the working electrode.
  Developed by Heyrovsky in the 1920s - won 1959
  Nobel prize!

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e- movement current, I

potentiostat
EI/R
Counter electrode
Working electrode
Reference electrode
e-
e-
HS- Hg ? HgS e-
2 H2O 2 e- ? H2 2 OH-
H2 2 OH- ? 2 H2O 2 e-
HgS e- ? HS- Hg
Salt bridge or common solution
HS-
HS-
Junction potential resistance to diffusion due
to ionic mobility constraints creates a
resistance (Ohmic drop) Dependent on salt bridge
(diffusion rates of KCl- ?1mV resistance) In
liquid diffusion rates of electrolytes which
are different should create more resistance with
greater spatial separation, but how much?
HS-
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Environmental Voltammetry
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Current - voltage curves for ideal electrodes
POLARIZATION
dashed lines show departure from ideal behavior
by real electrodes
A
B
C
current
Electrode potential
D
Ideal Polarized electrode (IPE electrode of
fixed I) i 0 over a wide range of V (A to B)
Ideal nonpolarized electrode (electrode of fixed
V reference electrodes). V 0 over a wide range
of I (C to D)
?i/ ?V ?
?i/ ?V 0
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Variables affecting the rate of an electrode
reaction
EXTERNAL VARIABLES temperature, pressure, time
ELECTRODE VARIABLES Material surface area (A)
geometry surface condition
ELECTRICAL VARIABLES potential, current, quantity
of electricity
MASS TRANSFER VARIABLES mode ( diffusion,
convection), surface concentrations, adsorption
SOLUTION VARIABLES bulk concentration of analyte,
concentrations of other species (electrolytes,
pH, ), solvent
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2 vs 3 electrode cell
-

-

2 electrode cell - current passes through
reference ( can cause IR drop and degradation of
the reference) R in aqueous solutions is 100
ohms so when i lt 10 ?A, iR lt 1 mV
3 electrode cell - current is passed through the
counter (auxiliary) electrode useful for high
resistance (non-aqueous) solutions
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Variation of applied potential from a power supply
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Mercury electrodes -liquid Hg
Static dropping Hg electrode can be used as a DME
and a HMDE (hanging Hg drop electrode) mechanical
drop knocker to dislodge Hg drop
Free fall dropping Hg electrode (DME)
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Voltammetry compared to UV-VIS spectroscopy

• Readout is a plot of current vs applied potential
• Peak or wave height (I) depends on concentration
• Half-wave potential (E1/2) is a f (structure,
  medium)
• Shape of I-E curve depends on the nature of the
  electrode process

• Readout is a plot of absorbance vs wavelength
• Absorbance depends on concentration
• Maximum A at a wavelength is a f(structure,
  medium)
• Shape of A-? depends on the nature of electronic
  transition

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Reduction of A to P

• A ne- ? P
• Eappl EoA - (0.0592/n) log (coP / coA) - Eref
• co is the molar concentration at the electrode
  surface
• SCE//Mn (xM)/ Hg(DME)

il limiting current
id diffusion current ? A
ir residual current
E1/2 half wave potential
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id (faradaic current) vs time curve for a planar
electrode (constant E)

Current decays as t-1/2
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Diffusion control A vs distance plots
E 0 V
E Z V
I ? ?C / ?x
Concentration profiles at the electrode/solution
interface
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Controlled potential methods - 1
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Controlled potential methods - 2
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Potentiometry

• Measurement of potential in absence of applied
  currents
• Depends on galvanic cells no forced reactions
  by applying external potential
• Reference electrodes are a potentiometric
  application that stays at a defined (Nernst),
  constant, and steady potential
• Calomel ? Hg/Hg2Cl2(satd),KCl(x M)
• Ag/AgCl ? Ag/AgCl(satd), KCl (x M)

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Metallic Indicator electrodes

• Several electrodes which can be used to detect
  different metals, halides, cations
• Metallic redox indicators, such as the Pt Eh
  electrode, depend on Nernstian behavior (requires
  reversibility) where
• Eindicator E0 0.0592 log(Fe2/Fe3)
• However ? many reactions are not reversible and
  thus do not behave predictably at this surface!
  why Eh readings with these elctrodes are often
  erroneous

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Ion Specific Electrodes (ISEs)

• Most utilize a membrane which selects for
  specific ion(s) H, Ca2, K, S2-, F-, etc.
• This is done through either ion exchange,
  crystallization, or complexation of the analyte
  with the electrode surface
• Instead of measuring the potential of the
  galvanic cell, this relates more to a type of
  junction potential due to separation of an ion

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pH

• pH electrodes are another kind of ion specific
  electrode

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pH - log H glass membrane electrode
H gradient across the glass Na is the charge
carrier at the internal dry part of the
membrane soln glass soln glass
H NaGl- ? Na HGl-
pH electrode has different H activity than the
solution
E1
E2
SCE // H a1 / glass membrane/ H a2, Cl-
0.1 M, AgCl (satd) / Ag ref1 // external
analyte solution / EbE1-E2 / ref2