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OCN 623 – Chemical Oceanography

Reading: Libes, Chapter 7

Structure & properties of water •  Water accounts for 96.5

weight percent of seawater •  Innate characteristics affect

nearly all properties of seawater & processes that occur in it

•  Much greater affinity of oxygen versus hydrogen for shared electrons, resulting in a dipole

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Structure & properties of water •  Polarity of water makes it

an excellent solvent for salts and polar molecules

•  A word on solutes – The hydrated sodium ion

•  Chemical speciation – Dependence upon water

•  Is a geochemical system at chemical equilibrium?

•  If not, what reactions are most likely to occur?

•  Solubility -

•  Redox -

•  Complexation -

•  Carbonate system -

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•  Equilibrium calculations give the energy available from a reaction & the direction it will proceed - Usually simpler & require less info than those for

kinetics •  Often a good approximation for many systems

•  In some cases, equilibrium calculations can predict kinetic rate constants

•  HOWEVER, most natural water reactions are not at equilibrium and knowledge of kinetics is often required

- Steady state, states of dynamic equilibrium, reaction rates, are topics outside of the scope of this course, but will be covered in 643 in Fall.

Consider a reversible reaction taking place at constant temperature:

aA + bB cC + dD

The reactants A and B combine to form products C and D.

The concentrations of A and B decrease until they reach values that do not change with time:

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•  Note that at equilibrium, the forward and reverse reactions proceed at the same, stable rate.

•  The time-invariant concentrations of reactants and products are called equilibrium concentrations.

•  The ratio of these concentrations (or activities – active concentrations) is characteristic for each reaction, and is called the equilibrium constant, K:

ba

dc

BADCK}{}{}{}{

≡

•  A criterion for equilibrium is that the total free energy (Gibbs free energy, Gr) of the reaction is at a minimum:

•  If we add more reactant or more product, the reaction will proceed spontaneously (without external help) as long as the value for Gr decreases.

•  Thus, a reaction in the direction of decreasing Gr is spontaneous. A reaction in the direction of increasing Gr is not spontaneous, and will not occur in a closed system.

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As any reaction proceeds an incremental amount, the change in Gr can be calculated as:

where νi is the stoichiometric coefficient (a,b,c,d) and Gfi is the free energy of formation per mole.

1.  If ΔG < 0, (i.e., ΔG is negative and thus Gr decreases as the reaction proceeds), then the reaction proceeds spontaneously as written.

2.  If ΔG > 0, (i.e., ΔG is positive and thus Gr increases as the reaction proceeds), then the reaction proceeds spontaneously in the opposite direction as written.

3.  If ΔG= 0, (i.e., ΔG is at a minimum), then the reaction is at equilibirium and will not proceeds spontaneously in either direction.

reactantsifii

productsifiir GGG ⎟

⎠

⎞⎜⎝

⎛−⎟

⎠

⎞⎜⎝

⎛=Δ ∑∑ υυ

Values for ΔG for a reaction give us a powerful tool to predict if a reaction is possible. We calculate in-situ ΔGr using this equation:

where

(The the superscript zero (°) indicates standard state: 25°C (298°K),1 atm pressure, and activity = 1.)

Gfi° is the standard-state free energy of formation per mole of species i.

{ } = activity (active concentration)

R = the ideal gas constant = 1.987 cal °K-1 mol-1 = 8.31 J °K-1 mol-1

T = °K

ba

dc

BADCRT

}{}{}{}{lnG G rr +°Δ=Δ

In-situ Std. state

reactantsifii

productsifiir GGG ⎟

⎠

⎞⎜⎝

⎛°−⎟

⎠

⎞⎜⎝

⎛°=°Δ ∑∑ υυ

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Standard free energy of formation (ΔG°fi): •  G°fi = 0 at standard state for all pure elements (solid

reference).

•  G°fi = 0 for H+ at a concentration of 1 mole/liter at standard state (solution reference).

•  Allows the measure of the energy change involved in forming compounds at standard state from their component elements at standard state.

•  Measured values are listed in tables. Units are:

•  kJ/mol (SI units)

•  kcal/mol

•  Example: net reaction for aerobic oxidation of organic matter:

CH2O + O2 → CO2 + H2O

•  In this case, oxygen is the electron acceptor – the half-reaction is:

O2 + 4H+ + 4e- → 2H2O

•  Different organisms use different electron acceptors, depending on availability due to local redox potential

•  The more oxidizing the environment, the higher the energy yield of the OM oxidation (the more negative is ΔG, the Gibbs free energy)

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•  Redox potential expresses the tendency of an environment to receive or supply electrons

–  An oxic environment has high redox potential because O2 is available as an electron acceptor

For example, Fe oxidizes to rust in the presence of O2 because the iron shares its electrons with the O2:

4Fe + 3O2 → 2Fe2O3

–  In contrast, an anoxic environment has low redox potential because of the absence of O2

the more positive the potential, the greater the species' affinity for electrons and tendency to be reduced

•  FeCl2 at different Fe oxidation states in the two sides

•  Wire with inert Pt at ends -- voltmeter between electrodes

•  Electrons flow along wire, and Cl- diffuses through salt bridge to balance charge

•  Voltmeter measures electron flow

•  Charge remains neutral

e-

e-

Voltmeter

Pt

Agar, KCl

Pt

Fe2+ - e- = Fe3+ Fe3+ + e- = Fe2+

Fe2+

Cl-Cl-Cl-

Cl-Cl-

Fe3+

Salt bridge

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•  Container on right side is more oxidizing and draws electrons from left side

•  Electron flow and Cl- diffusion continue until an equilibrium is established – steady voltage measured on voltmeter

•  If container on right also contains O2, Fe3+ will precipitate and greater voltage is measured

4Fe3+ + 3O2 + 12e-

→ 2Fe2O3 (s)

•  The voltage is characteristic for any set of chemical conditions

e-

e-

Voltmeter

Pt

Agar, KCl

Pt

Fe2+ - e- = Fe3+ Fe3+ + e- = Fe2+

Fe2+

Cl-Cl-Cl-

Cl-Cl-

Fe3+

Salt bridge

Consider the following simple electrochemical cell operating at 25°C:

ions

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We arbitrarily assign a potential of 0 to the reaction in the left cell:

2H+(aq) + 2e- → H2(g) E°= 0.000 V

Then the potential for the reaction in the right cell is:

Cu2+(aq) + 2e- → Cu0(s) E°= 0.337 V (always write as a reduction)

The standard potentials for all redox reactions are similarly determined against the standard hydrogen electrode:

= E° = E°H

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An electrochemical cell is capable of doing work – by driving electrons across a potential difference.

This can be measured as a change in free energy:

ΔG° = -nFE°

where

n = number of moles of electrons (equivalents) involved in the reaction

F = Faraday constant = 23.1 kcal V-1 equiv-1

E° = the cell potential (V) at standard state

For the general case: ΔG = -nFE

We know from a previous class:

Sustituting ΔG = -nFE, we get the Nernst Equation:

Or:

At 298°K:

reduced species

oxidized species

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Important points:

•  Geochemists usually use the symbol EH instead of E (indicating the hydrogen scale is being used).

•  The Nernst Equation relates the EH of a cell to the standard EH and to the activities of reactants and products.

•  When at standard state (all activities = 1), EH = E°

•  We can use EH as an indicator of the state of natural waters:

What species of V dominates in seawater?

1.  Assume measured Eh = 0.729 V

2.  From Table 7.1: Ehº= -0.26

3.  Plug into equation:

∴ V3+ dominates

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•  A mixture of constituents, not really separate cells

•  We insert an inert Pt electrode into an environment and measure the voltage relative to a standard electrode [Std. electrode = H2 gas above solution of known pH (theoretical, not practical). More practical electrodes are calibrated using this H2 electrode.]

–  Example: when O2 is present, electrons migrate to the Pt electrode:

O2 + 4e- + 4H+ → 2H2O

–  The electrons are generated at the H2 electrode:

2H2 → 4H+ + 4e-

•  Voltage between electrodes measures the redox potential

•  General reaction:

Oxidized species + e- + H+ ↔ reduced species

•  Redox is expressed in units of “pe,” analogous to pH:

pe = - log [e-] (or Eh = 2.3 RT pE/F)

where [e-] is the electron concentration or activity

•  “pe” is derived from the equilibrium constant (K) for an oxidation-reduction reaction at equilibrium:

]][][[][

+−=Hespeciesoxidized

speciesreducedK

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If we assume [oxidized] = [reduced] = 1 (i.e., at standard state), then:

logK pe pH= +

pHpeppKHeoxredK

K

oxred

Hespeciesoxidizedspeciesreduced

+++−=

−−−=

=

+−

+−

log][log][log][log][loglog

]][][[][

Oxidized species + e- + H+ ↔ reduced species

The Nernst Equation can be used to relate this equation to measured Pt-electrode voltage (Eh, Eh , EH):

where: Eh = measured redox potential as voltage

R = the Universal Gas Constant (= 8.31 J K-1 mol-1)

T = temperature in degrees Kelvin

F = Faraday Constant (= 23.1 kcal V-1 equiv-1)

2.3 = conversion from natural to base-10 logarithms

logK pe pH= +

Eh2.3RTFpEpe =≡ or Eh = 2.3 RT pE/F

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Assume:

•  pE in a given environment is controlled by this reaction:

Fe3+ + e- → Fe2+

(∴n = 1)

•  {Fe3+} = 10-5

•  {Fe2+} = 10-3 Table 7.1

Assume: Natural water at pH 7.5 in equilibrium with atmosphere

Conclusion: This environment has lower electron activity than Example #2, and is thus more oxidizing

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Garrels & Christ (1965)

¼ O2 + H+ + e- ← ½ H2O

H2O + e- → ½ H2 + OH-

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pE-pH stability field diagrams show in a comprehensive way how protons (pH) and electrons (pE) simultaneously shift equilibria of reactions under various conditions.

These diagrams also indicate which species predominate under any given condition of pE and pH.

Two equations are used to produce the diagrams:

Oxidizing limit of diagrams: ¼ O2 + H+ + e- → ½ H2O

Reducing limit of diagrams: H2O + e- → ½ H2 + OH-

OH- + H+ → H2O

H+ + e- → ½ H2

pE° = +20.75 (Table 7.3)

n = 1

pH = -log{H+}

Set limit: {O2} = 1

pE° = 0.0 (Table 7.3)

n = 1

pH = -log{H+}

Set limit: {H2} = 1

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Oxidizing limit of diagrams:

O2 + H+ + e- → ½ H2O

Reducing limit of diagrams:

H+ + e- → ½ H2

•  Phase-boundary lines on a pE-pH diagram indicate stability field boundaries – defined as lines where activities of both adjacent dominant species are equal.

•  Lines are defined by reactions between adjacent dominant species

•  Reactions must have known log K or pE° values.

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Acid-base reactions with no pE dependency

=1

Redox reactions of dissolved species

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Redox reactions of dissolved and solid species

=1

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 ΔGr ??

ΔGr = - nℑE –  Where n is the # of e-’s in the rxn, ℑ is Faraday’s

constant (23.06 cal V-1), and E is electropotential (V) •  pe for an electron transfer between a redox

couple analogous to pK between conjugate acid-base pair

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•  The higher the energy yield, the greater the benefit to organisms that harvest the energy

•  In general:

–  There is a temporal and spatial sequence of energy harvest during organic matter oxidation

–  Sequence is from the use of high-yield electron acceptors to the use of low-yield electron acceptors

•  Light used directly by phototrophs

•  Hydrothermal energy utilized via heat-catalyzed production of inorganics

Nealson and Rye 2004

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•  Redox reactions control organic-matter oxidation and element cycling in aquatic ecosystems

•  Eh – pH diagrams can be used to describe the thermo-dynamic stability of chemical species under different biogeochemical conditions

•  Biogeochemical reactions are mediated by the activity of microbes, and follow a sequence of high-to-low energy yield that is thermodynamically controlled

–  Example – organic matter oxidation:

•  O2 reduction (closely followed by NO3- reduction) is the

highest- yield redox reaction

•  CO2 reduction to CH4 is the lowest-yield redox reaction

Equations are written as

REDUCTIONS

Note: These equations will be provided on

exams, if necessary, but MGG students will be

expected to know them during PQE, Comps,

etc.

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…a word on convention…

SI

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