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 G0R = H0

R – TS0R

• Gibbs Free Energy (G) is a state variable, measured in KJ/mol or Cal/mol

• Tabulated values of G0R available…

)reactants()( 000i

iii

iiR GnproductsGnG

Equilibrium Constant

• for aA + bB cC + dD:

• Restate the equation as:

GR = G0R + RT ln Q

• GR= 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

QRTaa

aaRT

bB

aA

dD

cC lnln

Activity

• Activity, a, is the term which relates Gibbs Free Energy to chemical potential:

i-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 = imi

• The activity coefficient, i, is found via some empirical foundations

Activity Coefficients

• Extended Debye-Huckel approximation (valid for I up to 0.5 M):

• Where A and B are constants (tabulated), and a is a measure of the effective diameter of the ion (tabulated)

I

aBII

IAz2.0log

2

1

2

12

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++ CaCl+ CaNO3

+

Ca(H3SiO4)2 CaF+ CaOH+

Ca(O-phth) CaH2SiO4 CaPO4-

CaB(OH)4+ CaH3SiO4

+ CaSO4

CaCH3COO+ CaHCO3+ CaHPO4

0

CaCO30

• Plus more species gases and minerals!!

Mass Action & Mass Balance

• mCa2+=mCa2++MCaCl+ + mCaCl20 + CaCL3- +

CaHCO3+ + CaCO3

0 + CaF+ + CaSO40 +

CaHSO4+ + CaOH+ +…

• Final equation to solve the problem sees the mass action for each complex substituted into the mass balance equation

lc

nc

i HLC

HCL

][][

][][

nxLmCamCa 22

Geochemical models

• Hundreds of equations solved iteratively for speciation, solve for GR

• 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 + Ox2LEO says GER

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 e-

O2 + 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:

• 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.

e

ape log

THE pe OF A HALF REACTION - I

Consider the half reaction

MnO2(s) + 4H+ + 2e- Mn2+ + 2H2O(l)

The equilibrium constant is

Solving for the electron activity

24

2

eH

Mn

aa

aK

21

2

4

H

Mne Ka

aa

DEFINITION OF EhEh - 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:

Where = 96.42 kJ volt-1 eq-1 (Faraday’s constant).

At 25°C, this becomes

or

EhRT

pe303.2

Ehpe 9.16

peEh 059.0

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 Gr ??

Gr = - nE– 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 acid-base 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:

dD

cC

bB

aA

HH aa

aa

nF

RTEE ln0

dD

cC

bB

aA

HH aa

aa

n

VEE log

0592.00At 25° C:

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 Gr =-nE, combining two half reactions in a

certain way will yield either a + or – electropotential (additive, remember to switch sign when reversing a rxn)

+E - Gr, 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+ -0.32O2 + 4H+ + 4e- 2H2O +0.81

NADPH + H+ NADP+ + 2H+ + 2e- +0.32O2 + 4H+ + 4e- 2H2O +0.812 NADPH + O2 + 2H+ 2 NADP+ + 2 H2O +1.13

ELECTRON TOWERmore negative

more positiveBOM – Figure 5.9

oxidized/reduced formspotential acceptor/donor

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

• transport ofelectrons coupledto pumping protons

glucosee-

CH2O CO2 + 4 e- + H+0.5 O2 + 4e- + 4H+ H2O

Proton Motive Force (PMF)

• Enzymatic reactions pump H+ outside the cell, there are a number of membrane-bound 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…