Aquatic Chemistry VII: Redox Reactions

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Aquatic Chemistry VIIRedox Reactions

• EVEN 6319
• Class 8 (Oct. 13)

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Misc issues

• Exam next week, Tuesday, October 19 1-3 pm open
  book, comprehensive

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Class objectives

• To understand how equilibrium constants K can be
  calculated from standard free energy changes ?Go
  from standard redox potentials Eo.
• To become familiar with the concepts of electron
  activity e- pE -loge- and to understand
  how these parameters affect redox reactions,
  especially in the environment.
• To be able to develop log C pE diagrams for
  redox half reactions.
• To understand how pE is related to electric
  potential E.
• To be able to interpret pE-pH predominance
  diagrams.

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Redox reactions

• Important redox reactions in environmental
  engineering
• Oxidation of organic matter in wastewater.
• Nitrification denitrification.
• Anaerobic fermentation methane production.
• Disinfection with chlorine or ozone.
• Oxidation or reduction of contaminants in
  groundwater.
• Chemical analyses.
• Unlike most acid-base reactions, redox reactions
  can take a long time to reach equilibrium.
• Redox reactions often mediated by bacteria.

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Free energy change for redox reactions

• Like all reactions, redox reactions attain
  equilibrium when the free energy G (or potential
  to do work) is zero.
• G is zero when electrons are in lowest energy
  orbitals (similar to G being zero for rock at
  bottom of cliff below).
• Thus, ?G is negative for all spontaneous redox
  reactions.

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Relationship between??Go, Eo, K

• Free energy change ?G for a reaction is given by

where ?G free energy change at existing concs.
(J) ?Go standard free energy change (J)
R universal gas constant (8.314
J/K-mol) T absolute temp (K).

• At equilibrium ?G 0, and thus

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Relationship between??Go, Eo, K (cont.)

• The free energy change ?G for a redox reaction is
  related to the redox potential E produced in an
  electrochemical cell
• ?G -zFE (3)
• where ?G free energy change (J/mol, or
  coulomb-volts/mol)
• z electron eqs/mol of chemical change in
  reaction
• F 96,485 coulombs/electron eq.
• E emf or voltage produced in
  electrochemical cell (volts)

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Relationship between??Go, Eo, K (cont.)

• Solving ?Go -zFEo ?Go -RTlnK for lnK gives

• Thus, if ?Go or Eo for a reaction is known is
  (e.g., by calculating from tabulated ?Gfo or
  half-reaction Eo values), K can be calculated.
• A redox reaction will be at equilibrium if
• ?G E 0.
• A redox reaction will occur spontaneously if
• ?G is negative (or equivalently, if E is
  positive).

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Electron activity redox equilibrium

• Consider following half-reaction where Fe3 is
  reduced
• Fe3 e- ? Fe2
• At equilibrium

• Solving for the apparent e- activity e- gives

• At high e-, Fe2 will be greater than Fe3
  at equilibrium.

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pE notation

• Just like acid-base reactions, redox reactions
  occur in a direction towards equilibrium.
• As pH measures apparent H activity in solution
  H , pE measures apparent e- activity in
  solution e-
• pH -logH (units for pH are dimensionless)
• pE -loge- (units for pE are dimensionless)
• pE is a measure of the availability of electrons
  in solution (even though no free electrons exist
  in solution).
• (In other texts pE is notated as pe or p?).

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Similarities between pH pE

• Apparent H activity H is high in solutions
  with low pH values
• Chemical species tend to be protonated at low pH.
• Conditions with low pH are acidic conditions.
• For example HAc at low pH, but Ac- at high pH.
• Apparent e- activity e- is high in solutions
  with low pE values
• Chemical species tend to be reduced at low pE.
• Conditions with low pE are reducing conditions.
• For example, NH4 at low pE, but NO3- at high pE.
• Reducing conditions are generally anaerobic.

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Similarities between pH pE (cont.)
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Relationship between pE E

• The relationship between e- the redox
  potential E is given by

• where E redox potential (V)
• pE -loge- (dimensionless)
• Note pE ? loge- pE ? -log(E)
• see following log C - pE diagram
• When pE or E is large, e- is low the system
  tends to be under oxidizing conditions.
• When pE or E is small, e- is high the system
  tends to be under reducing conditions.

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Logarithmic concentration diagram showing the
relationship between
as a function of pE for pH 7 and
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standard pE or pEo

• The standard pE or pEo for a given reduction
  half reaction is defined as
• pEo log K
• (where K equilibrium constant for the half
  reaction)
• The above is by definition it is not a derived
  equation.

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The standard hydrogen electrode

• The standard redox potential Eo for any redox
  half reaction is defined with respect to the
  standard hydrogen electrode (next picture).
• Eo for the following half-cell reaction is
  arbitrarily assigned a value of 0 V
• 2H3O(aq) 2e- ? H2(g) 2H2O(l) Eo 0 V
  (by def.)
• Thus, K 1 for above reaction (by def).
• (and thus pEo log K 0)
• All other half-cell potentials are then
  determined from this reference potential.
• See table of half-reaction standard potentials
  (after next slide).

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standard hydrogen electrode
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Text example on pp. 191-194

• Problem Draw a log C diagram showing
  relationship between NO3- NH4 as a
  function of pE, assuming
• pH 7.0
• NO3- NH4 10-3 M
• The reduction half reaction is

(Note that half reactions can be derived see
text p. 23).
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Text example on pp. 191-194 (cont.)

• The first step is to determine the equilibrium
  constant K. Note that pEo ( log K) is listed as
  14.88 in Table 2.4.
• Alternatively, we can derive K from free energy
  of formation (?Gfo) values (see Appendix in
  text)
• reactants (KJ/mol) products (KJ/mol)
• ?Gfo(NO3-) -111.34 ?Gfo(NH4) -79.37
• ?Gfo(H) 0 ?Gfo(H2O(l)) -237.18
• ?Gfo(e-) 0
• Thus, ?Go for the reaction is

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Text example on pp. 191-194 (cont.)

• K can now be calculated from ?Go for the
  reaction
• ?Go -RTlnK (2)
• where R 8.314 J/mol-K
• T 298 K
• Solving this equation for K gives
• K 1014.88
• or
• log K pEo 14.88

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Text example on pp. 191-194 (cont.)

• The next step is to develop equations for NO3-
  NH4 as a function of pE -loge-.
• At equilibrium, the reaction conforms to

• Taking log of both sides rearranging gives

• Substituting pH -logH pE -loge-

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Text example on pp. 191-194 (cont.)

• Substituting logK 14.88 pH 7 rearranging

• Now, since NO3- NH4 10-3 M, we can
  substitute
• NH4 10-3 - NO3-
• giving

or
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Text example on pp. 191-194 (cont.)

• NH4 can then be determined as a function of pE
  using the mass balance
• NH4 10-3 M NO3-
• The last two equation for NO3- NH4 can be
  used to develop the log C pE diagram (next
  slide)
• spreadsheet

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Text example on pp. 191-194 (cont.)

• At very low pE values H in water is reduced to
  H2
• H e- ? ½ H2(g)
• The equilibrium constant for the above half
  reaction is

• Taking the log of both sides gives

• Substituting pEo logK, pE -loge-, pH -
  logH, rearranging gives

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Text example on pp. 191-194 (cont.)

• Now substituting pEo 0 for the H reduction
  half reaction pH 7 solving for logH2
  gives

• Similarly, at very high pE values H2O in water is
  oxidized to O2
• ¼ O2 H e- ? ½ H2O
• The equilibrium constant for the above half
  reaction is

• Substituting H2O 1 taking log of both sides
  gives

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Text example on pp. 191-194 (cont.)

• Substituting pEo logK, pE -loge-, pH -
  logH, rearranging gives

• Now, substituting pEo 20.77 pH 7
  rearranging gives

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Text example on pp. 191-194 (cont.)

• Eqs. 4 5 can be added to our log C pE
  diagram
• log C - pE diagram
• See spreadsheet file
• If pE for aqueous system is to left of H2 line,
  system is highly reducing.
• If pE for aqueous system is to right of O2
  line, system is highly oxidizing.
• Natural waters have pE values between these two
  extremes.

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pEpH predominance diagrams

• The preceding log C pE diagram assumed a pH of
  7.
• pE is a function of pH for any redox reaction.
• Predominance or pE-pH diagrams are used to show
  relationship between pH, pE, most stable
  species in a give oxidation-reduction system.
• A nitrogen system pE-pH diagram appears on next
  slide.
• The lines in the pE-pH diagram represent points
  of transition from predominance by one nitrogen
  form to predominance by another.

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pE?pH diagram illustrating predominant nitrogen
forms at equilibrium in an aqueous system.
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pEpH predominance diagrams (cont.)

• To construct pE-pH diagram, equilibrium equations
  were needed for following redox couples
  NH4/NO3-, NH4/NO3-, NO2-/NO3-, NH3/NO3-,
  NH3/NO2-, NH4/NO2-.
• The general form of the equilibrium equation for
  each couple is

where pE -loge-, pEo logK, (reduced)
represents species on reduced side of half
reaction, (oxidized) represents species on
oxidized side of half reaction.
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pEpH predominance diagrams (cont.)

• From preceding pE-pH diagram
• reduced species (NH4 NH3) are predominant at
  low pE (or equivalently high e-).
• oxidized species (NO3- NO2-) are predominant at
  high pE (or equivalently lowe-).
• Thus, low pE corresponds to reducing conditions,
  high pE corresponds to oxidizing conditions.
• In general, reducing conditions are anaerobic,
  oxidizing conditions are aerobic.
• Characterizing the pE pH of a system can
  provide information about what chemical reactions
  can occur.

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pEpH predominance diagrams (cont.)

• Following diagram shows which species predominate
  at each pE-pH zone in natural systems (diagram)
• The aerobic zone occurs at high pE is
  characteristic of most natural streams, lakes,
  and ocean waters with dissolved oxygen.
• The anaerobic zone occurs at low pE is
  characteristic of sediments other anaerobic
  environments where SO42- is reduced sulfide and
  organic matter is reduced to CH4.
• The anoxic zone is a transition zone that occurs
  at intermediate pE is characteristic of
  environments where NO3- is reduced to N2 gas.
• Note that the pE at which anaerobic conditions
  are attained is higher when pH is low than when
  pH is high (why?).

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pE-pH diagram illustrating major
oxidation-reduction zones in aqueous systems.
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Solving equilibrium problems with computers

• Equilibrium problems are solved using equations
  for
• Equilibrium
• Mass balance
• Charge balance
• Proton balance (sometimes).
• In complex problems, many species can be
  involved, requiring computer solutions using
  numerical methods.
• Most available programs (e.g., MINEQL MINTEQ)
  come with databases for equilibrium constants
  thermodynamic values.

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Next week

• Mid-term exam
• Work on MINTEQ Project for following week

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Assignment for next week

• Review Ch. 4.4.10-11 and Ch. 19.
• Explore following website
• http//www.lwr.kth.se/english/OurSoftware/vminteq/
  index.htm
• Do problems 6 and 7 from Chapter 3.
• Do problems 97, 98 and 99 from Chapter 4.
• Prepare for mid-term exam (comprehensive).