Oxidation - Reduction and
Electron Activity in Water

Presentation Review Powerpoint #1

Presentation Review Powerpoint #3

Oxidation and Reduction are very important concepts related to water as they also determine species and set limits on the species.

They are a major method of solubilization of metal in the environment and are important concepts in pollution and pollution prevention and prediction of fate and transport.

Oxidation/Reduction defined (sometimes referred to as redox)

The reactions are frequently expressed as Half Reactions

Oxidation (losing e^- , increasing in oxidation number)

Reduction (gaining e^- , decreasing in oxidation number)

Reactions may have other side reactions that may not appear in the simplistic representation, i.e.

Some redox reactions have other driving forces such as -
living organisms - bacteria - plants

Not so easy to write a chemical equation - lots of reactions are missing.

Energy from the Sun and Aquatic plants (driving force for all life)

This reaction stores most of the energy for other reactions of living organisms. Driven by sun light and stored in the organic molecules.

Did you think of these reactions as Redox reactions before?

Biological reactions are chemistry.

Remember: All the electrons being transferred in biological cycles end up stored in molecules.

Gibbs Free Energy: Reviewed

Example:
The conversion of ammonia to a more biologically useful nitrogen form -nitrate:

Many species in water undergo exchange of H ⁺ and e^-. Both reactions occur for some species such as Fe.

Example:

Frequently H⁺ is also involved in electron transfers in aqueous systems and thus frequently pH plays an important role in redox reactions.

At neutral pH (7.0), 3H⁺ ions are released from water as Fe³⁺ hydrated ion (H₂O) goes to the hydroxide (OH^- ) and the water becomes very much lower in pH or higher in [H⁺].

Oxidation State Assignment - Review and Reminder

(Reference - General Chemistry, McQuarrie and Rock, Freeman pg. 102, 1991.)

Free or M°= 0
Ion Charge = net charge
Alkali +1 {group 1}
F^-
Alkaline Earths +2 & Zn and Cd {A.E. is group 2}
H⁺
O^2- {HO or ho ho ho}
Al³⁺ and Ga³⁺ are 3+

Solubility and Transformation Redox Reactions

Some redox reactions transform or solubilize other (and even toxic) metals or change the species to other forms with different environmental significance. i.e.

Example of transformation of Cr⁶⁺ to Cr³⁺

Conditions leading from Fe³⁺ to a large concentration of Fe²⁺ may lead to the conversion of chromium in this case from a toxic species to a biologically more supportive one. (What are these conditions?)
(Ref. for this reaction - McQuarrie and Rock, pg. 758-761)

{Review of the half-reactions in this example}

Solubilization in the environment due to redox reactions is very common and very important!

This is another primary reason why we must adjust the solubility in the environment and the real world.

Example of environmental solubilizing of a toxic species.

Practical application:(this occurs in older homes built before the 1970s)

Water with a high concentration of Cu²⁺ ions flowing through a pipe with a lead based solder.

The source did not have a high Pb content, but it came in contact with a Pb° and through a redox reaction transferred electrons from Pb° to Cu²⁺ and created soluble Pb²⁺ ions in the water.

Corrosion - an anthropogenic environmental interaction

What do we write in undergraduate chemistry as the reaction for the transformation for iron to rust?

It is a balanced redox reaction, but:

"Corrosion of metal involves redox reactions between different sections of the same piece of metal or between two dissimilar metals in electrical contact with each other."

Fe²⁺ oxidizes to Fe³⁺ (relatively rapidly) and spontaneously in the presence of oxygen

Spontaneously, Fe³⁺ goes to iron(III) oxide {rust}

Corrosion of iron.

Fe²⁺ is the more soluble form - why?

Fe(OH)₂(s) <----> Fe²⁺ + 2OH^-     K _sp = 8 x 10^-16

Fe(OH)₃(s) <----> Fe³⁺ + 3OH^-     K _sp = 4 x 10^-38

Effects of redox reaction

Fe³⁺ can be solubilized depending on other aqueous conditions
by conversion to Fe²⁺

How can you prevent corrosion?

What can you eliminate?

Corrosion Prevention

Iron can be protected in pipelines and in automobiles by galvanizing or providing a sacrificial anode.

Iron can be protected in the environment by sacrificing other metal such as Zn in the presence of water and oxygen. Zn is preferentially oxidized and supplies electrons to Fe preventing the Fe from being oxidized.

Zn supplies the electrons (e^-) to the Fe and prevents Fe°
from going to Fe²⁺ in the presence of O₂ and H₂O.

The two half reactions are identical

Protection of an iron pipe from corrosion with sacrificial zinc metal.

Evaluation and Prediction of Oxidation and Reduction Reactions

Why is Zn preferentially oxidized over Fe?

We must investigate numeric methods of predicting these tendencies and spontaneous reactions. Only through a mathematical evaluation and ranking can we predict these spontaneous relationships.

pE - a gauge of a systems Oxidizing or Reducing potential

Just as the activity of H⁺ ion is used to express acidity of water (related to concentration),
the e^- activity is an indication of the degree of oxidizing or reducing condition in aqueous medium.

Note that within the same natural water system the top layer is relatively oxidizing (high pE) and the bottom is relatively reducing (low pE).

Different species of the same constituents depending on the pE.

Relationship to natural water systems:

A pE gradient in natural water.

Redox Reactions
Formal and Traditional Definitions and Explanation

The reference standard is the hydrogen electron transformation,
i.e., AHE (standard hydrogen electrode)

With a standard electrode potential of 0.0 volts. E° = +0.00 volts
By definition, all scales are relative. (T= °K, = 0°C, = 32°F)
{Standard hydrogen potential}

Two half reactions, an oxidation and a reduction are added together with the same number of electrons transferred in each half rxn. to give a complete redox reaction.

Electrode potential, E, is the voltage potential of one half reaction

Again using iron as the example:

The classical definition uses an experimental apparatus with a standard hydrogen electrode to produce the standard electrode potential.

Assuming activity equal to 1 then the iron electrode potential, E is the standard electrode potential (or as defined by IUPAC the standard reduction potential), E°.

For iron:

Voltage in the half reactions is a measure of the tendency of the equilibrium to occur and to drive to completion. As referenced to the hydrogen electrode.

Given:

Each half reaction connected with an electrical conduit Pt electrode and salt bridge then:

The resulting voltage (electrode potential) E is
the Standard Voltage E° = + 0.77 volts.

The + voltage means that this reaction will proceed as written and will occur.

What if the components are not at an activity of 1? Then what?

Then E is not = to E° and must be corrected for the shift inequilibrium as predicted by the equilibrium.

E the actual electrode potential for these conditions is corrected by using the Nernst Equation.

The Nernst Equation

Where:
E° is a constant called the standard electrode potential, which is characteristic of each half-reaction
R is the gas law constant, 8.314 JK^-1mol ^-1
T is the temperature in K (Kelvin) (usually given at 273K + °C)
n is the number of moles of electrons that appear in the half-reaction for the electrode process as it has been written
F is the faraday = 96,485 C (coulombs)
ln is the natural logarithm = 2.303 x Log (base 10)

And the equilibrium

Where:

E = electrical potential volts

and

E° = standard electrical potential in volts

pE° values of redox reactions important in natural waters (at 25 °C).

The reactions are written as reductions by IUPAC convention

Equilibrium Constant - K, (K_eq)

Nernst Equation:

The Nernst Equation can be simplified by substituting in numerical values and converting to base 10 log and specifying 25 °C.

E = ° - log = E° - log

Then specifically of the half-reaction of the reduction of Fe³⁺ toFe²⁺

E = E° - log or= , E = E° - log

This form will give the potential and the likelihood for the reaction to proceed as written based on the concentration (activity assumed to be the concentration in moles/L) of the reactants and products in a specific example.(Note: similar example pg. 336 Skoog 5th ed. 1992)

Note: important difference with text and convention.
Inversion in Manahan, pg 95 (non IUPAC convention). IUPAC Convention -reverse the fraction when you change signs. Manahan does not seem to be following the convention of writing the half-reaction from the reduction and thus has a sign inversion in the Nernst equation. To explain this concept using equilibrium, it is necessary to write it correctly.

Using the example given

E = 0.77 - (0.0592/1) log{[7.85 x 10^-5 M]/[2.35 x 10^-3 M]} = 0.77 - (- 0.054) = 0.82 volts

Thus a greater tendency to go to completion with the large concentration of [Fe³⁺ ] that is pushing the equilibrium to the right.

Logic check - does this make sense? What do we compare to?

Standard Temperature and Pressure and Activity or E°
Standard

Example: 100 to 1
Remember: It is the ratio, not absolute concentration in the equation.

This makes sense from Le Chatelier's principle.

pE conversion from E

Just as pH is

Scale is 0 - 14 with 7.0 being equilibrium with no influence from activity,and activity = concentration.

so pE is

Where a is activity

When:

The generalized form of the equation is:

Converting E to pE

The Nernst Equation can be expressed in terms of pE and pE°.

Therefore:

so: pE = pE° - 1/n log

remember pE° = ,
n=1 , one electron
using [Fe²⁺ ] = 7.85 x 10^-5 M and [Fe³⁺ ] =2.35 x 10^-3 M

pE = [(0.77)/(0.0592 v)] - 1/1 log{[7.85 x 10 ^-5 M]/[2.35 x 10^-3 M]} = 13.0 - ( -1.476) = 14.5

(Note - Manahan rounds 0.0592 to 0.059 the unknown additional difference of 0.1 from text gets 14.7 v)

The pE increased as did the E. With this change in concentration both an E of 0.82 over 0.77 v and 14.5 over 13.0 are indications of greater tendency to go to completion as written since the equilibrium is products over reactants and both show increases over E° and pE°.

So E° and pE° corrected for these concentrations which shift the equilibrium and others that change the activity of the species and both show tendencies to proceed as written or to reverse.

Use pE to gage reaction tendencies.

Questions that we need to answer.

Examples of reductions and their relative potentials expressed as pE°

When you reverse the reaction you also reverse the pE° sign.

Example : Why does lead go into a solution in high copper ion systems?

Proof: pE is also directly related log K

at Equilibrium K = = =

0 = pE = pE° - 1/n log = 7.84 - 1/2 log = 7.84 - 1/2 logK

Solving for K, Thus K = 5 x 10^-15 and log K = 15.7

It is beneficial to examine the reactions for the transfer of 1 mole of electrons.

This makes for some fancy division such as in these previously examined reactions.

an 8e^- interaction thus divided by 8 to get a 1 e^- mole change

Likewise:

a 4 e^- transfer thus divide by 4f.

now written for 1e^- mole

Remember that Gibbs free energy is an indication of the spontaniety of the reaction. Formally it is defined as:

Note: D G is written for 1e^- mole for comparison in tables
Governed by the second law of thermodynamics - "to be spontaneous a reaction must lead to an increase of entropy in the universe."

Second Law - The entropy of the universe increases in a spontaneous process and remains unchanged in an equilibrium process.

So will these reactions proceed as written?

Thus a direct comparison of pE° and (delta) G ° can be made.

Recall:

an 8e^- interaction thus divide by 8 to get a 1 e^- mole change

These pE° and pE_(w) values are compiled in Table 4.1, pg. 100, Manahan and in other texts such as.

Table references:
Principles and Applications of Aquatic Chemistry, Francis Morel and Janet Hering, John Wiley & Sons, Inc., NY, pgs. 430-432, 1993. (table 7.1 pE° 1/2 reactions.)

Aquatic Chemistry, by Strumm and Morgan 2nd ed. pg. 448, 449, (1981).

Measurements using half cells and platinum electrodes are not accurate for environmental systems. Why?

pE° values of redox reactions important in natural waters (at 25 ° C).

The limits of pE in Water

Water may be either oxidized or reduced by the removal or addition of electrons at sufficiently high potential.

This is controlled by the thermodynamic stability of the water molecule. These are the boundary conditions for water.

Notice equation #1 in table 4.1.

The oxidizing limit of water (P_O2)^1/4

Thus at this point, O₂ from the air and H⁺ will combine to make water. This defines one side of the stability in water.

On the other side    (The reducing limit of water)

These are the theoretical limits, but temporary limits are greater when a catalyst is lacking.

Changing pE (also called EH) to pE°(w) table 4.1

To consider the pH of water.

In all these equations it is assumed that pH = 7
If this were not so then only pE° would change by substituting the concentration of [H⁺] at that pH (i.e. pH 6 (10^-6), pH 10 (10^-10)

Type (1) situation as already discussed:

The pE° column on in Manahan simply in table 4.1

pE = pE° + log [H⁺]

When in the half reaction H⁺ appears with the coefficient of 1 then the equation reduces to

pE = pE° - pH

Assuming pH of 7 or Log [1x10^-7]

Type (2) situation with a fractional integer as coefficient for H⁺

and when there is a coefficient such as in: (the second eq. in the table)

1/5NO₃^- + 6/5H⁺_(w) + e^- <----> 1/10N₂(g) + 3/5H₂O

pE = 21.05 + Log ([1x10^-7])^6/5 = 21.05 + (-8.4) = +12.65

as found on the pE°_(w) column of the table

another example:

1/8NO₃- + 5/4H+_(w) + e^- <----> 1/8NH₄(g) + 3/8H₂O

pE = 14.90 + Log ([1x10^-7])^5/4 = 14.90 + (-8.75) = +6.15

pE in Natural Waters

It is not reliable to measure the electrical potential (E) or the log function pE of natural water systems due to complex interactions from competing equilibrium.

The concentration of key oxidation components in water set some frequently referenced oxidizing potentials and general trends;

I. Air equilibrium of surface (oxygenated) waters and O₂ (Oxidizing ).

Natural water in equilibrium with air (more specifically O₂, 21% O₂).

II. Bottom (pure water) no O₂ and high levels of CO₂ and CH₄ ( Reducing) from bacterial degradation.

Oxidizing (Table 4.1 # 1) at pH 7.0

Reducing (Table 4.1 # 15) at pH 7.0

pE-pH Diagrams Species Boundaries.

To be complete pE, pH, solubilities, combining ion conc., ligand conc. should be present.

A simplified diagram for Fe species is constructed.

It is instructive to work through this example to determine how such a diagram is prepared and to understand its meaning.

We will consider:
K_sp of Fe(OH)₂(s), Fe²⁺ , Fe³⁺, pE, pH and the range of these species

The diagram is set up by establishing boundaries for the species.

For - Fe²⁺ -

For - Fe³⁺ -

To simplify the calculation, species of Fe such as FeCO₃, FeS, Fe(OH)₂ +*(H₂O)_x etc. have been omitted.

Species Diagrams (including pE-pH)

Note:
Phase Diagram of iron uses pE° (w) on left margin.

Because pH must be considered this must be the scale that is used.

Question
If that is true then why does it go to 20.75?

at pH 7 it is 13.8
pE = pE° + log (PO₂^1/4 [H+]) =
20.75 + log ((0.21)^1/4 x 1.0 x 10^-7)=13.6
((0.677) x 1.0 x 10^-7) log (6.77 x 10^-8) 20.75 + - 7.169 = 13.6
Point at middle above pH 7 on upper boundary

at pH 0 it is ?

pE = pE° + log (PO₂^1/4 [H+]) =

20.75 + log ((0.21)^1/4 x (1.0 x 10⁰, or 0)) = 20.75
log (0)
Point at upper left on upper boundary

Ok so when pH = 14 (with almost no disolved oxygen) what is it?

pE = pE° + log (PO₂^1/4  [H+]) =
20.75 + log ((0.21)^1/4 x 1.0 x 10^-14)=13.8

assume that O² (disolved oxygen becomes somewhat as scarce as Fe(OH)₂ to Fe(OH)₃ (at 10^-16 and 10^-38), say 10^-20,

20.75 + log ((0.21)^1/4 x 1.0 x 10^-14)=13.8

Log((1 x 10^-20) x (1 x 1.0 x 10^-14))= log (1 x 10^-34) = - 34 20.75 + (- 34) = - 13.25
Point at lower right on lower boundary

Species Diagrams (including pE-pH)

Given: pE = 20.75 - pH, (at pH 7.0) the limit is 13.75; and Given: 1.0 x 10^-5 M is the definition of disolved.

Assuming the standard limits of water

pE = 20.75 - pH (at pH 7.0) the limit is 13.75

Taking pH to extremes

or from O₂ at pH 7.0
pE = pE° + log (PO₂ 1/4 [H⁺]) = 20.75 + log (0.21)^1/4 x 1.0 x 10 ^-7 = 13.8

Example 1 : solubility of Fe⁺³

(vertical limit of Fe3+ solubility line on the diagram)

Assumption: Choosing 1 x 10^-5 M as the definition of soluble.
At what pH does Fe³⁺ become soluble. (does this make sense?)

Example 2 : Solubility of Fe²⁺
(vertical limit of Fe²⁺ solubility line on diagram) for Fe²⁺
Given: dissolved is 1.0 x 10^-5 M

Fe(OH)₂(s) +2H<--->Fe²⁺ +2H₂O

Ksp = [Fe²⁺]/[H+]² = 8.0 x 10¹²

[H+]² = [Fe²⁺]/Ksp = (1.00 x 10^-5)/(8.0 x 10¹²) = (.251 x 10^-18)^1/2; pH=8.95

Examples 3 and 4 (the line between Fe₊₂ and Fe(OH)₃

To determine pE - pH range for Fe₂₊ substitute Ksp into pE expression (pE for Fe³⁺ to Fe²⁺ ref. pg 432 Morel)

pE = 13.0 + log = 13.0 + log{(Ksp' [H+]³) /([Fe²⁺])} =

pE = 13.0 + log 9.1 x 10³ - log 1.00 x 10^-5 + x log[H+] =

pE = 22 - 3 x pH     yields a relationship which establishes the line.

Thus the boundary between the two species Fe²⁺ and Fe(OH)₃ ^{depends on this pE and pH relationship and follows that line.}

Example: Low pH and low pE correspond to a high hydrogen ion activity and low electron activity.

Specific Cases:

In normal water, pH of 5-9 Fe(OH) ₃ and Fe²⁺ are stable and predominate. Which one predominates will depend on the pE.

Fe²⁺ is the dominant form of soluble iron in solution when low pE is present. This is why the bottom of natural water systems have high Fe²⁺ and why from the top to the bottom there may be different chemistry and water content.

In a reducing environment, (low O₂ ) and Fe³⁺ may be in solution and when mixed with oxygen from the air raise the pE and the Fe³⁺ is no longer stable and forms Fe(OH)₃(s) and precipitates.

pE-pH diagrams for the Fe, CO ₂, H₂O, and Mn-CO₂ systems (at 25° C).

Other references

Aquatic Chemistry (An Introduction Emphasizing Chemical Equilibria in Natural waters), 2nd ed., Warner Strumm and James Morgan, John Wiley & Sons, Inc., NY, 1981.

Principles and Applications of Aquatic Chemistry, Francois Morel and Janet Hering, John Wiley & Sons, Inc., NY, pgs. 3, 369, 377-379, 394,1993.

General Chemistry, Donald McQuarrie and Peter Rock, 3rd ed. Chapter, 20 (Solubility & Precipitation Reactions), In chapter I & J, W. H. Freeman and Company NY, 1987.

Fundamentals of Analytical Chemistry, Skoog, West, Holler, Saunders College Publishing, NY, pg. 288-289, 1992.

Notes Table of Contents

Environmental Chemistry Home Page

Duquesne University Home Page

Revised 4/23/99.