Redox Geochemistry
J. Willard Gibbs
• Gibbs realized that for a reaction, a certain
amount of energy goes to an increase in
entropy of a system.
• G = H –TS or
DG0R = DH0R – TDS0R
• Gibbs Free Energy (G) is a state variable,
measured in KJ/mol or Cal/mol
DG   ni G ( products)   ni G (reactants )
0
R
0
i
i
0
i
i
• Tabulated values of DG0R available…
Equilibrium Constant
 aCc aDd 
RT ln  a b   RT ln Q
 a A aB 
•
for aA + bB  cC + dD:
•
Restate the equation as:
DGR = DG0R + RT ln Q
•
DGR= available metabolic energy (when
negative = exergonic process as opposed to
endergonic process for + energy) for a
particular reaction whose components exist in a
particular concentration
Activity
• Activity, a, is the term which relates Gibbs
Free Energy to chemical potential:
mi-G0i = RT ln ai
• Why is there now a correction term you might
ask…
– Has to do with how things mix together
– Relates an ideal solution to a non-ideal solution
Ions in solution
• Ions in solutions are obviously nonideal
states!
• Use activities (ai) to apply thermodynamics
and law of mass action
ai = gimi
• The activity coefficient, gi, is found via
some empirical foundations
Activity Coefficients
• Extended Debye-Huckel approximation
(valid for I up to 0.5 M):
 log g 
Az 2 I
1
2
I  aBI
1
2
 0.2 I
• Where A and B are constants (tabulated),
and a is a measure of the effective
diameter of the ion (tabulated)
Speciation
• Any element exists in a solution, solid, or
gas as 1 to n ions, molecules, or solids
• Example: Ca2+ can exist in solution as:
Ca++
Ca(H3SiO4)2
Ca(O-phth)
CaB(OH)4+
CaCH3COO+
CaCO30
CaCl+
CaF+
CaH2SiO4
CaH3SiO4+
CaHCO3+
CaNO3+
CaOH+
CaPO4CaSO4
CaHPO40
• Plus more species  gases and
minerals!!
Mass Action & Mass Balance
c
 n
[CL] [ H ]
i 
c
l
[C ] [ HL ]
mCa   mCa L
2
2 n
x
• mCa2+=mCa2++MCaCl+ + mCaCl20 + CaCL3- +
CaHCO3+ + CaCO30 + CaF+ + CaSO40 +
CaHSO4+ + CaOH+ +…
• Final equation to solve the problem sees the
mass action for each complex substituted into
the mass balance equation
Geochemical models
• Hundreds of equations solved iteratively
for speciation, solve for DGR
• All programs work on same concept for
speciation thermodynamics and
calculations of mineral equilibrium – lots of
variation in output, specific info…
Oxidation – Reduction Reactions
•
•
•
•
Oxidation - a process involving loss of electrons.
Reduction - a process involving gain of electrons.
Reductant - a species that loses electrons.
Oxidant - a species that gains electrons.
• Free electrons do not exist in solution. Any
electron lost from one species in solution must be
immediately gained by another.
Ox1 + Red2  Red1 + Ox2
Half Reactions
• Often split redox reactions in two:
– oxidation half rxn  e- leaves left, goes right
• Fe2+  Fe3+ + e-
– Reduction half rxn  e- leaves left, goes right
• O2 + 4 e-  2 H2O
• SUM of the half reactions yields the total
redox reaction
4 Fe2+  4 Fe3+ + 4 eO2 + 4 e-  2 H2O
4 Fe2+ + O2  4 Fe3+ + 2 H2O
Half-reaction vocabulary part II
• Anodic Reaction – an oxidation reaction
• Cathodic Reaction – a reduction reaction
• Relates the direction of the half reaction:
• A  A+ + e- == anodic
• B + e-  B- == cathodic
ELECTRON ACTIVITY
• Although no free electrons exist in solution, it is useful
to define a quantity called the electron activity:
pe   log ae
• The pe indicates the tendency of a solution to donate or
accept a electron.
• If pe is low, there is a strong tendency for the solution to
donate electron - the solution is reducing.
• If pe is high, there is a strong tendency for the solution to
accept electron - the solution is oxidizing.
THE pe OF A HALF REACTION - I
Consider the half reaction
MnO2(s) + 4H+ + 2e-  Mn2+ + 2H2O(l)
The equilibrium constant is
K
aMn2
4
H
a a
2
e
Solving for the electron activity
 aMn2
ae    4
 Ka 
 H




1
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:

pe 
Eh
2.303RT
Where  = 96.42 kJ volt-1 eq-1 (Faraday’s constant).
At 25°C, this becomes
pe  16.9 Eh
or
Eh  0.059 pe
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 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 acidbase pair
Electropotentials
• E0 is standard electropotential, also standard
reduction potential (write rxn as a reduction ½ rxn)
– EH is relative to SHE (Std Hydrogen Electrode)
At non-standard conditions:
 RT
0
EH  EH  
 nF
At 25° C:
a b
  a AaB 
 ln  c d 
  aC aD 
a b

 0.0592V   a A aB 
0
EH  EH  
 log  c d 
n

  aC aD 
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E, 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
• Redox reactions with more negative reduction
potentials will donate electrons to redox reactions
with more positive potentials.
NADP+ + 2H+ + 2e-  NADPH + H+
O2 + 4H+ + 4e-  2H2O
-0.32
+0.81
NADPH + H+  NADP+ + 2H+ + 2eO2 + 4H+ + 4e-  2H2O
2 NADPH + O2 + 2H+  2 NADP+ + 2 H2O
+0.32
+0.81
+1.13
ELECTRON TOWER
more negative
more positive
oxidized/reduced forms
potential acceptor/donor
BOM – Figure 5.9
Microbes, e- flow
• Catabolism – breakdown of
any compound for energy
• Anabolism – consumption of
that energy for biosynthesis
• Transfer of e- facilitated by
e- carriers, some bound to
the membrane, some freely
diffusible
NAD+/NADH and NADP+/NADPH
• Oxidation-reduction reactions use NAD+ or
FADH (nicotinamide adenine dinucleotide,
flavin adenine dinucleotide).
• When a metabolite is oxidized, NAD+ accepts
two electrons plus a hydrogen ion (H+) and
NADH results.
NADH then carries
energy to cell for other uses
glucose
• transport of
electrons coupled
to pumping protons
CH2O  CO2 + 4 e- + H+
0.5 O2 + 4e- + 4H+  H2O
e-
Proton Motive Force (PMF)
• Enzymatic reactions pump H+ outside the
cell, there are a number of membranebound enzymes which transfer e-s and
pump H+ out of the cell
• Develop a strong gradient of H+ across the
membrane (remember this is 8 nm thick)
• This gradient is CRITICAL to cell function
because of how ATP is generated…
HOW IS THE PMF USED TO
SYNTHESIZE ATP?
• catalyzed by ATP
synthase
BOM – Figure 5.21
ATP generation II
• Alternative methods to form ATP:
• Phosphorylation  coupled to
fermentation, low yield of ATP
ATP
• Your book says ATP: “Drives
thermodynamically unfavorable reactions” 
BULLSHIT, this is impossible
• The de-phosphorylation of ATP into ADP
provides free energy to drive reactions!
Minimum Free Energy for growth
• Minimum free energy for growth = energy
to make ATP?
• What factors go into the energy budget of
an organism??
Growth Efficiency
• How much energy does it take to grow a
new microbe?
• How much energy does a microbe gain
from any metabolic reaction?
• How much energy is ‘wasted’, i.e., how
much energy does it ‘cost’ the microbe to
hang out in it’s environment that is not
directly attributed to the energy required
for growth and division…