100 Redox Equilibria

8/13/2019 100 Redox Equilibria

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I. Oxidation-Reduct ion Reactions

A. Defini tions

Oxidation is the removal of electrons from an atom of an element, often by oxygen;

this causes an increase in valence. Reduction is the addition of electrons, decreasing valence. All redox reactions involve the transfer of electrons.

Many elements occur in multiple valence states in the earth. Major elements include H,

O, C, S, N (all important volatile components of fluids), Fe and Mn. Minor elements

include U, Cr, As, Mo, Cu, Hg and others.

Can write redox reactions in terms of oxygen transfer:

Eq. I-1 Fe2O32 Fe3O4+ O2Or in terms of electron transfer:

Eq. I-2 3 Fe2O3+ 2H++ 2e

-2 Fe3O4+ H2O

The two methods are thermodynamically equivalent, but the latter is closer to reality for

aqueous solutions.

In Eq. I-2 H2O is the source of O2. Thus, oxidation generally releases protons, while

reduction consumes them. As a result, the pH of a fluid is intimately related to the

oxidation state as measured by Eh or pe.

B. Electromotive Series

Some elements are more readily oxidized than others. The oxidation potential is ameasure of how much energy is needed to remove an electron from an element in a given

valence state. The electromotive series ranks the elements and their ions in terms of their

strengths as reducing agents.

C. Redox Equilibria and Electrochemical Cells

Complete redox reactions represent the sum of two half-reactions, an oxidation reaction

and a reduction reaction. All electrons produced by an oxidation must be consumed by a

corresponding reduction - there are no free electrons in solution.

Oxidation: H2(g)H++ e- E= 0

Reduction: Fe3+

+ e-Fe2+ E= + 0.77V

Redox (sum) Fe3+

+ H2(g)H++ Fe

2+ E= + 0.77V

Eis the standard electromotive force (emf), the potential difference in volts betweenexpressed in volts relative to the SHE: the Standard Hydrogen Electrode, represented by

the oxidation reaction above, and is also referred to as Eh. Species with positive standard


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electrode potentials such as Fe3+

act as electron acceptors in the standard state

(concentration of 1mfor aqueous species, partial pressure of 1 atm. for gases).

D. Thermodynamics

A fundamental thermodynamic relationship discovered by Michael Faraday is:

Eq. I-3 G = -nFEwhere n: # of electrons transferred in the reaction

F: Faradays constant = 96,489 coulombs/mole = 96.5 kJ/Volt mole

E: electromotive force in voltsThis equation is equivalent to the statement: charge * potential = work. F represents the

quantity of electricity that will produce a chemical change involving one equivalent

(mole), i.e., the total charge of one mole of electrons.

Another fundamental thermodynamic relationship is:

Eq. I-4 Gr= Gr + RTlnKeqNotes: 1. At equilibrium, Gr= 0, and lnKeq= -Gr/RT2. If all species in their standard states, activities = 1, RTlnKeq= 0, and Gr=

Gr.

Substituting Eq. I-3 into Eq. I-4 and dividing by nF, we obtain the Nernst Equation:

Eq. I-5eq

eqKnF

RTEK

nF

RTEh

1lnlnE +== oo

For T=298K, this reduces to:

Eq. I-6 Eh = E + 0.059/n log KeqAnalogous to Eh (E) is pe, the activity of electrons, = -log ae-. The two have a linearrelationship according to:

Eq. I-7 pe = (F/2.303RT )Eh; at 25C Eh = 0.059pe

D. Balancing Half Reactions

1. Write reaction with oxidized form on left and reduced form on right.

2. Balance all elements but H and O.

3. Balance O by adding H2O.

4. Balance H by adding H+.

5. Balance charge by adding e-s to left side (i.e., write reaction as a reduction).

Half reactions include e-s; a full redox reaction is obtained by adding together

complementary oxidation and reduction reactions, which always occur together because

e-s dont usually float around in solution.


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Example half reactions:

Fe2O3- Fe2+

: Fe2O3+ 2e-+ 6H

+2Fe2++ 3 H2O

HS-

- SO42-

: SO42-

+ 8e-

+ 9H+

HS-

+ 4 H2OMn2O3- MnCO3: Mn2O3+ 2e

-+ 2H

++ 2CO22MnCO3+ H2O

E. Types of Redox Equilibria

1. Two aqueous species (speciation): Fe2+

- Fe3+

2. Solid - aqueous specie (solubility): Fe2O3 Fe2+

3. Solid-solid (solid buffers): Fe2O3- Fe3O4(Hematite-Magnetite)

F. Eh-pH and pe-pH Diagrams

Redox equilibria generally involve the transfer not only of electrons but also of

H+, and therefore are pH dependent. The stabilities of aqueous species and of minerals

containing multivalent elements are generally described by constructing Eh-pH or pe-pHdiagrams, which are special types of activity-activity diagrams.

1. Stability Limits of Water

Written in terms of half-reactions. Dont need to add SHE reaction to make complete

redox reaction because the Eh is generated entirely by the half-reactions describing the

decomposition of water.

a) Upper Stabili ty Limi t (oxidizing, high Eh)

H2O decomposes to form O2:

H2O(l) = 2 H++ O2+ 2 e-

[ ] [ ]( )[ ] pHOEh

HOKn

EEh eq

059.0log01479.023.1

log2

059.023.1log

059.0

2

22/1

2

0

+=

+=+= +

This equation relates Eh and pH of an environment to its fO2.

b) Lower Stabili ty Limi t (reducing, low Eh)

H2O decomposes to form H2, i.e., [H2] = PH2= 1 atm (and [O2= 10-83.1

atm.)

H2= 2 H++ 2 e

-, E

0= 0 volts


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[ ][ ]

[ ]

[ ] pHHEh

atmHifH

HEEh

059.0log22

059.00

.,1;log2

059.02

2

2

0

=+=

=+=

+

+

c) Solubili ty of hematite (Fe2O3)

Fe in natural waters is predominantly in the form of Fe2+

; Fe compounds are generally

more soluble at low Eh and pH. Write solubility as an oxidation half-reaction:

2 Fe2+

+ 3 H2O = Fe2O3+ 6 H++ 2 e

-

[ ][ ][ ]+

+

+

=

+=

+==

2

22

6

00

log059.0177.065.0

log2059.065.0

65.0,16.30

FepHEh

FeHEh

VEkcalGr

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100 Redox Equilibria