Electrochemical Phenomena

Eh and pE Approaches

Redox Reactions

pE-pH Diagrams

Flooded Soils

Eh and pE Approaches

aA + bB = cC + dD + ne

K = (C)c (D)d / (A)a (B)b

where (X) is the activity of X

ΔG = ΔGo + RT ln [(C)c (D)d / (A)a (B)b]

If this reaction is an oxidation – reduction reaction,

ΔG = nEhF and ΔGo = nEhoF

where n is the number of e-sE is the potential of the reactionF is the Faraday constant

Eh = Eho + (RT / nF) ln [(C)c (D)d / (A)a (B)b]

Alternatively, can write an equilibrium expression for the reduction half-reaction and take logs

cC + dD + ne = aA + bB

log K = log [(A)a (B)b / (C)c (D)d (e)n]

= log [(A)a (B)b / (C)c (D)d] + npE

where pE = - log (e)

Large values of pE favor electron-poor (oxidized) chemical species

Small values of pE favor electron-rich (reduced) chemical species

Note that these are generally of the form

mAox + nH+ + e = pAred + qH2O

From which can be written

K = (Ared)p (H2O)q / (Aox)m (H+)n (e) or

log K = log [(Ared)p / (Aox)m] + npH + pE

Eh = Eho + (RT / F) ln [(Aox)m (H+)n / (Ared)p (H2O)q]

Eh = Eho + 0.059 log [(Aox)m / (Ared)p] – 0.059n pH

Oxic ~ pE > 7 at pH = 7Suboxic ~ 2 < pE < 7 at pH = 7Anoxic ~ pE < 2 at pH = 7

Microbial limits and observed soil limits to pE – pH domain

Above pE = 5 to pE = 11, O2 is consumed by aerobic respiration

At ~ pE = 8, NO3- is reduced oxic to anoxic

At ~ pE = 7, Mn4+ is reduced oxic to anoxic

At ~ pE = 5, Fe3+ is reduced suboxic to anoxic

At ~ pE = 0, SO42- is reduced anoxic

Microbial activity forces depletion of O2, NO3- and so forth

in this sequence and enrichment in es. Easy to see reduced activity of O2 reducers, NO3

- reducers as concentration of the e acceptor decreases with decreasing pE. However, the activity of anaerobic organisms is also reduced by high values of pE.

Redox Reactions

Reduction half-reactions are coupled with oxidation half-reactions as with

1/24 C6H12O6 + 1/4 H2O = 1/4 CO2 + H+ + e

1/8 NO3- + 5/4 H+ + e = 1/8 NH4

+ + 3/8 H2O

Example use of Table 6.2

mAox + nH+ + e = pAred + qH2O

From which can be written

K = (Ared)p (H2O)q / (Aox)m (H+)n (e) or

log K = log [(Ared)p / (Aox)m] + npH + pE

Can calculate ratio of a redox pair, pH or pE, given any two of these variables

1/8 SO42- + 9/8 H+ + e- = 1/8 SH- +1/2 H2O

K = (SH-)1/8 (H2O)1/2 / (SO42-)1/8 (H+)9/8 (e-)

log K = 1/8 log [(SH-) / (SO42-)] + 9/8 pH + pE

pE = log K – 9/8 pH + 1/8 log [(SO42-) / (SH-)]

Given log K = 4.3, pH = 7 and (SO42-) = (SH-), what is pE?

pE = 4.8 – (9/8)7 = -3.6 anoxic

For pH = 7 and pE = 2, what is the activity of SH- if (SO42-) = 0.001?

log (SH-) = 8 (log K – 9/8 pH - pE) + log (SO42-) = -47.6

(SH-) = 10-47.6 What volume of water contains one SH- ion?

Note that although reduction or oxidation may be thermodynamically favorable, equilibrium may not exist. Often these redox reactions are slow. However, the activity of microoganisms accelerates (catalyzes) these reactions so that equilibrium is closely approached.

Given the following two reactions, show that Fe3+ (aq) and S2 - (aq) are unstable equilibrium species in soil solutions. Fe 3+ (aq) + e (aq) = Fe 2+ (aq) log K = 13.0

S2- (aq) + H+ (aq) = HS-(aq) log K = 13.9

This is problem 1.

K = (Fe2+) / (Fe3+)(e)

13.0 = log [(Fe2+) / (Fe3+)] + pE

pE = 13 + log [(Fe3+) / (Fe2+)]

which for (Fe3+) > (Fe2+) is not seen

K = (HS-) / (S2-)(H+)

13.92 = log [(HS-) / (S2-)] + pH

pH = 13.92 + log [(S2-) / (HS-)]

which for (S2-) > (HS-) is not seen

pE – pH Diagrams

Based on rearrangement of

log K = log [(Ared)p / (Aox)m] + npH + pE

pE = log K - pH - log [(Ared)p / (Aox)m]

For example, let’s determine under what conditions of pE and pH that Mn2+(aq) is favored respect to MnO2(s) or MnCO3 and under what conditions one or the other of these minerals is favored.

1/2MnO2 + 2H+ + e = 1/2Mn2+ + H2O log K1 = 20.7

1/2MnO2 + 1/2CO2 + H+ + e = 1/2MnCO3 + 1/2H2O log K2 = 16.3

Combine the above to give MnCO3 – Mn2+ equation

1/2MnCO3 + H+ = 1/2Mn2+ + 1/2CO2 + 1/2H2O log K3 = 4.4

From which one writes, assuming unit activity for solid phases and H2O,

log K1 = 20.7 = 2pH + pE + 1/2log(Mn2+)

log K2 = 16.3 = pH + pE – 1/2log(PCO2)

log K3 = 4.4 = 1/2 log(Mn2+) + 1/2log(PCO2) + pH

Set (Mn2+) = 10-6 and PCO2 = 10-2

pE = 23.2 - 2pH

pE = 15.3 – pH

pH = 8.4

General procedure for constructing pE – pH diagrams

Choose sets of redox pairs (reactions along with log K values)

Assume unit activities for solid phases and water

Assume set values for solution activities (other than H+ and e, of course)

6.

½ SeO42- + H+ + e = ½ SeO3

2- + ½ H2O log K = 14.5

½ SeO32- + ½ H2O = ½ SeO4

2- + H+ + e½ MnO2 + 2H+ + e = ½ Mn2+ + H2O log K = 20.7

½ SeO32- + ½ MnO2 + H+ = ½ SeO4

2- + ½ Mn2+ + ½ H2O log K = 6.2

6.2 = ½ log[(SeO42-) / (SeO3

2-)] + ½ log [(Mn2+) / (H+)2]

20.7 = ½ log (Mn2+) – log (H+) + pH + pE

½ log[(Mn2+) / (H+)2] = 20.7 – pH – pE

6.2 = ½ log[(SeO42-) / (SeO3

2-)] + 20.7 – pH - pE

6.2 = ½ log[(SeO42-) / (SeO3

2-)] + 20.7 – pH – pE

½ log[(SeO42-) / (SeO3

2-)] = -14.5 + pH + pE

pH + pE = 14.5 for (SeO42-) = (SeO3

2-)

and

pH + pE > 14.5 for (SeO42-) > (SeO3

2-)

Flooded Soils

Eh = 0.059pE

Eh = Eo + (RT/nF)ln([oxidized]/[reduced])

2H2O O2 + 4H+ + 4e

9.

Fe(OH)3 + 3H+ + e = Fe2+ + 3H2O log K = 16.4

log K = log(Fe2+) + 3pH + pE

pE = log K – log(Fe2+) – 3pH

pE = 16.4 + 7.0 – 3pH = 23.4 – 3pH

Fe2+ + CO2 + H2O = FeCO3 + 2H+ log K = -7.5

log K = -2pH – log (PCO2) – log (Fe2+)

-7.5 = -2pH + 2.0 + 7.0

pH = 8.25

Fe(OH)3 + 3H+ + e = Fe2+ + 3H2O log K = 16.4

Fe2+ + CO2 + H2O = FeCO3 + 2H+ log K = -7.5

Fe(OH)3 + H+ + CO2 + e = FeCO3 + 2H2O log K = 8.9

log K = pH – log (PCO2) + pE

pE = 8.9 – 2.0 – pH = 6.9 - pH

pH

4 6 8 10

pE

-12

-6

0

6

12

Fe2+

Fe(OH)3

FeCO3

mAox + nH+ + e = pAred + qH2O

K = (Ared)p(H2O)q / (Aox)m(H+)n(e)

log K = log [(Ared)p(H2O)q / (Aox)m(H+)n] + pE = log K* + pE

Eh for half-reaction measured with respect to the standard H2 electrode

Pt, H2 / H+ // Ared / Aox, Pt

which gives the overall reaction

½ H2 = H+ + emAox + nH+ + e = pAred + qH2O

½ H2 + mAox + nH+ = H+ + pAred + qH2O

For which

K* = {(Ared)p(H2O)q / (Aox)m(H+)n} {(H+) / (H2)1/2}

And according to

E = Eo - (RT / nF) ln K*

E = Eoreduction + Eo

oxidation – (RT / nF) ln K*

And since Eooxidation = 0 and (H+) = (H2) = 1

Eh = Eoreduction – (RT / F) ln {(Ared)p(H2O)q / (Aox)m(H+)n}

Eh = Eoreduction – (RT / F) ln K*

Eh = Eoreduction – (2.303RT / F) log K*

Substituting, log K = log K* + pE

Eh = Eoreduction – (2.303RT / F) {log K - pE}

At equilibrium

Eoreduction = -(2.303 RT / F) log K

so,

Eh = (2.303RT / F) pE

which for standard conditions becomes

Eh = 0.0592 pE volts

Eh = 59.2 pE millivolts

Do problems 7 and 11.